Quiz about Unit 1 - Limits and Derivatives Vocab

Question 1

Shall we stand and fight?

Accepted Answer

Yes, we shall stand and fight.

Answer

No, we should retreat instead.

Answer

Let's negotiate for peace.

Answer

We should run away and hide.

Question 2

What is the slope formula?

Accepted Answer

m = (y2 - y1) / (x2 - x1)

Answer

m = (y1 + y2) / (x1 + x2)

Answer

m = (x1 - x2) / (y1 - y2)

Answer

m = (y2 + y1) / (x2 - x1)

Question 3

What a tangent line?

Accepted Answer

A tangent line is a line that touches a curve at one point.

Answer

A tangent line is a line that runs parallel to a curve at all points.

Answer

A tangent line is a line that curves along with the shape of the curve.

Answer

A tangent line is a line that intersects a curve at two points.

Question 4

What is a secant line in terms of tangent lines in calculus?

Accepted Answer

A secant line is the limit of a series of tangent lines as the points of intersection converge to a single point.

Answer

A secant line is a line that touches a curve at exactly one point.

Answer

A secant line is always parallel to the tangent line at a given point.

Answer

A secant line is the derivative of a function at a specific point.

Question 5

True or False: When trying to find the slope of a point on a graph, we can't choose the point twice to find its slope because than it would become undefined.

Accepted Answer

True

Answer

False

Question 6

The fancy limit notation really is just saying a point is approaching another point by a slope

Accepted Answer

Limit notation describes the behavior of a function as it approaches a point.

Answer

Limit notation is used to find the area under a curve.

Answer

Limit notation indicates the maximum value of a function.

Answer

Limit notation only applies to linear functions.

Question 7

After approximating a slope through the limit, we can use this equation. What is it called and where does it come from?

$$y-y_1=m\left(x-x_1\right)$$

Accepted Answer

Point-slope form of a linear equation.

Answer

Standard form of a linear equation.

Answer

Quadratic equation form.

Answer

Slope-intercept form of a linear equation.

Question 8

Change in Position/Time

Accepted Answer

Average Velocity

Answer

Instantaneous Velocity

Question 9

Velocity at a given point instant of time, represented by a slope

Accepted Answer

Instantaneous Velocity

Answer

Average Velocity

Question 10

Change in Position/Time

Accepted Answer

Average Velocity

Answer

Instantaneous Velocity

Question 11

When trying to find the slope of two points, its best to try looking on both sides to find a good estimate

Accepted Answer

Estimate the slope by considering points on both sides.

Answer

Only consider points on one side.

Answer

Ignore the points and use a formula.

Answer

Estimate the slope using only the y-coordinates.

Question 12

Galileo's Law: What is that?

Accepted Answer

Galileo's Law states that all objects fall at the same rate in a vacuum.

Answer

Galileo's Law states that heavier objects fall faster than lighter ones.

Answer

Galileo's Law applies only to objects on Earth.

Answer

Galileo's Law states that objects in a vacuum do not fall at all.

Question 13

$$\lim_{x\rightarrow y}f\left(x\right)=L$$

What does f(x) represent here?

Accepted Answer

f(x) is a function.

Answer

f(x) is a constant.

Answer

f(x) is a limit.

Answer

f(x) is a variable.

Question 14

$$\lim_{x\rightarrow y}f\left(x\right)=L$$

What does L represent here?

Accepted Answer

L is the limit of the function f(x) as x approaches y.

Answer

L represents the derivative of f(x) at x = y.

Answer

L is the value of f(y) when x equals y.

Answer

L is the maximum value of f(x) in the neighborhood of y.

Question 15

$$\lim_{x\rightarrow y}f\left(x\right)=L$$

What does x to y represent here?

Accepted Answer

The variable 'x' is approaching the value 'y'.

Answer

The variable 'x' is a constant value.

Answer

The variable 'x' is moving away from 'y'.

Answer

The variable 'x' is equal to 'y'.

Question 16

When finding the limit of the function, is best to try to make sure you aren't making estimates but can make sure its the limit

Accepted Answer

True

Answer

False

Question 17

When there is multiple limits to one function, we can say the limit doesn't exist.

Accepted Answer

The limit does not exist.

Answer

The limit is infinite.

Answer

The limit is equal to zero.

Answer

The limit is undefined.

Question 18

$$\lim_{x\rightarrow a^-}f\left(x\right)=L$$

What does the a^- represent?

Accepted Answer

It represents approaching 'a' from the left.

Answer

It denotes a fixed point at 'a' without direction.

Answer

It indicates the value of 'a' itself.

Answer

It represents approaching 'a' from the right.

Question 19

$$\lim_{x\rightarrow a^-}f\left(x\right)=L$$

What does the a^+ represent?

Accepted Answer

It represents approaching 'a' from the right.

Answer

It indicates the value of 'a' itself.

Question 20

Although some function don't have a limit, we can split the limits based on left or right

Accepted Answer

Limits can be split into left-hand and right-hand limits.

Answer

Left-hand limits are always equal to right-hand limits.

Answer

Limits cannot be defined for any function.

Answer

Limits can only be split into two parts.

Question 21

Sometimes the limit will equal to its function and sometimes not, why is this the case?

Accepted Answer

The limit equals the function value if the function is continuous at that point; otherwise, it does not.

Answer

The limit is determined by the highest degree term in the function.

Answer

Limits can only be calculated for linear functions.

Answer

The limit is always equal to the function value.

Question 22

Definition Let f be a function defined on both sides of a, except possibility at a itself. Than

$$\lim_{x\rightarrow a}f\left(x\right)=\infty$$

What does this represent?

Accepted Answer

The function f(x) approaches infinity as x approaches a.

Answer

The function f(x) approaches zero as x approaches a.

Answer

The function f(x) oscillates between values as x approaches a.

Answer

The function f(x) is undefined at x = a.

Question 23

Means that the values of f(x) can be made arbitrarily large by taking x sufficiently close to a, but not equal to. Similarly

$$\lim_{x\rightarrow a}f\left(x\right)=-\infty$$

What does this mean?

Accepted Answer

As x approaches a, f(x) tends to negative infinity.

Answer

As x approaches a, f(x) tends to positive infinity.

Answer

The function f(x) is undefined at x = a.

Answer

f(x) remains constant as x approaches a.

Question 24

Although limits cannot exist, but we can describe if its getting super large or super low.

Accepted Answer

Limits can describe behavior approaching infinity or negative infinity.

Answer

Limits can only approach zero.

Answer

Limits can describe fixed values only.

Answer

Limits cannot describe any behavior.

Question 25

What is vertical asymptote?

Accepted Answer

A vertical asymptote occurs where a function approaches infinity as the input approaches a specific value.

Answer

A vertical asymptote is where a function has a maximum value.

Answer

A vertical asymptote occurs at the x-intercepts of a function.

Answer

A vertical asymptote is a point where the function is defined.

Question 26

$$\lim_{x\rightarrow y}\left[f\left(x\right)+g\left(x\right)\right]=\lim_{x\rightarrow y}f\left(x\right)+\lim_{x\rightarrow y}g\left(x\right)$$

Accepted Answer

Sum Law

Answer

Quotient Rule

Answer

Product Law

Answer

Difference Law

Answer

Constant Multiple Law

Question 27

$$\lim_{x\rightarrow y}\left[f\left(x\right)-g\left(x\right)\right]=\lim_{x\rightarrow y}f\left(x\right)-\lim_{x\rightarrow y}g\left(x\right)$$

Accepted Answer

Difference Law

Answer

Quotient Rule

Answer

Product Law

Answer

Sum Law

Answer

Constant Multiple Law

Question 28

$$\lim_{x\rightarrow y}\left[f\left(x\right)g\left(x\right)\right]=\lim_{x\rightarrow y}f\left(x\right)\lim_{x\rightarrow y}g\left(x\right)$$

Accepted Answer

Product Law

Answer

Quotient Rule

Answer

Sum Law

Answer

Difference Law

Answer

Constant Multiple Law

Question 29

$$\lim_{x\rightarrow y}\left[\frac{\left(f\left(x\right)\right)}{g\left(x\right)}\right]=\left(\frac{\left(\lim_{x\rightarrow y}f\left(x\right)\right)}{\left(\lim_{x\rightarrow y}g\left(x\right)\right)}\right)$$

Accepted Answer

Quotient Rule

Answer

Product Law

Answer

Sum Law

Answer

Difference Law

Answer

Constant Multiple Law

Question 30

$$\lim_{x\rightarrow y}\left[df\left(x\right)\right]=d\lim f\left(x\right)$$

Accepted Answer

Constant Multiple Law

Answer

Quotient Rule

Answer

Product Law

Answer

Sum Law

Answer

Difference Law

Question 31

$$\lim_{x\rightarrow a}\left[f\left(x\right)\right]^n=\left[\lim_{x\rightarrow y}\left(f\left(x\right)\right)\right]^n$$

Accepted Answer

Product Law

Answer

Root Law

Question 32

$$\lim_{x\rightarrow y}\sqrt[n]{f\left(x\right)}=\sqrt[n]{\lim_{x\rightarrow y}f\left(x\right)}$$

Accepted Answer

Root Law

Answer

Product Law

Question 33

$$\lim_{x\rightarrow y}b=$$

Accepted Answer

b

Answer

x

Answer

y

Question 34

$$\lim_{x\rightarrow y}x=$$

Accepted Answer

x

Answer

y

Answer

b

Question 35

$$\lim_{x\rightarrow a}\sqrt[n]{x}=\sqrt[n]{a}$$

What is this equation called?

Accepted Answer

Limit of the n-th root function

Answer

Derivative of the n-th root function

Answer

Integral of the n-th root function

Answer

Continuity of the n-th root function

Question 36

If $$\lim_{x\rightarrow y}f\left(x\right)\le\lim_{x\rightarrow y}g\left(x\right),$$

What does this tell us about their limits comparably?

Accepted Answer

The limit of f(x) is less than or equal to the limit of g(x) as x approaches y.

Answer

The limits of f(x) and g(x) are equal as x approaches y.

Answer

The limit of f(x) is greater than the limit of g(x) as x approaches y.

Answer

The limit of g(x) is less than the limit of f(x) as x approaches y.

Question 37

When you have three functions that smugging each other, and in the one in-between. All of them have same limit at that area. Hmmm. What theorem states this is true?

Accepted Answer

Squeeze Theorem

Answer

Limit Theorem

Answer

Continuity Theorem

Answer

Intermediate Value Theorem

Question 38

If you're unsure that a function has a limit, you can divide it up based on directions to see if they both with the same limit.

Accepted Answer

Evaluate limits from both directions.

Answer

Only evaluate limits from one direction.

Answer

Ignore the limits and use a graph instead.

Answer

Assume the limit exists without checking.

Question 39

As a number ever reaches a greater number both negative or positive, we can say the limit is not existence, but also is infinite!

Accepted Answer

The limit does not exist and is infinite.

Answer

The limit exists and is finite.

Answer

The limit is always zero.

Answer

The limit oscillates between two values.

Question 40

When looking at a function limit from left and right, and don't align together, their limit doesn't exist. However, we must than consider if their two parts are infinite, which we can state.

Accepted Answer

The limit does not exist, but can be infinite.

Answer

The limit can only be negative.

Answer

The limit is always zero.

Answer

The limit exists and is finite.

Question 41

What are undefined values in calculus?

Accepted Answer

Undefined values in calculus are points where a function does not produce a valid output.

Answer

Points where a function has a maximum value.

Answer

Values that are always zero in calculus.

Answer

Points where a function is continuous.

Question 42

What are bounded values in calculus?

Accepted Answer

Bounded values in calculus are values that are confined within a specific range and do not approach infinity.

Answer

Values that can increase indefinitely

Answer

Values that are always negative

Answer

Values that are not defined in any range

Question 43

What are bounded values in calculus?

Accepted Answer

Bounded values in calculus are values that do not exceed certain limits within a given domain.

Answer

Bounded values refer to the average of all values in a dataset.

Answer

Bounded values are values that can vary infinitely within a domain.

Answer

Bounded values are the maximum values in a function's range.

Question 44

What are unbounded values in calculus?

Accepted Answer

Unbounded values are values that can grow indefinitely without approaching a finite limit.

Answer

Unbounded values are values that oscillate between two limits.

Answer

Unbounded values are fixed values that do not change.

Answer

Unbounded values are always negative numbers.

Question 45

What are continious values in calculus?

Accepted Answer

Continuous values are those that can take any value within a specified interval.

Answer

Continuous values cannot be represented on a graph.

Answer

Continuous values are limited to specific points.

Answer

Continuous values can only be whole numbers.

Question 46

What is the theorme of limits for composite functions?

Accepted Answer

The theorem of limits for composite functions states that $ \lim_{x \to c} f(g(x)) = f(\lim_{x \to c} g(x)) $ if f is continuous at $ \lim_{x \to c} g(x) $.

Answer

The theorem applies only to linear functions.

Answer

The limit of a composite function is always zero.

Answer

The limit of a composite function is the product of the limits of the individual functions.

Question 47

True or False: In a composite function, the inside function must have a limit and the outside function must be continuous

Accepted Answer

True

Answer

False

Question 48

When finding the limit of composite function, do holes count for the continuous rule?

Accepted Answer

No, holes do not count for the continuous rule.

Answer

Yes, holes count as discontinuities.

Answer

Holes affect the continuity of the function.

Answer

Holes are considered in the limit calculation.

Question 49

Like all limits, limits that seem to not exist together may still exist in either direction if we spit the limit into which direction?

Accepted Answer

two-sided limits

Accepted Answer

one-sided limits

Answer

undefined limits

Answer

infinite limits

Question 50

True or False: When dealing with limits of composite function, you also have to understand if the limit approaching under or below the limit when then looking at its continiousity!

Accepted Answer

True

Answer

False

Question 51

Limits can exist also for trig functions!

Accepted Answer

Yes, limits can exist for trig functions.

Answer

Trig functions cannot have limits.

Answer

Limits do not apply to trig functions.

Answer

All trig functions are undefined at certain points.

Question 52

Sometimes when solving for values or finding limits through substitution you get 0/0. Don't worry. It doesn't necessarily mean the limit doesn't exist. This is called

Accepted Answer

indeterminate form

Answer

zero limit

Answer

finite limit

Answer

undefined form

Question 53

What is this called?

$$\left(a+b\right)\left(a-b\right)=a^2-b^2$$

Accepted Answer

Difference of squares

Answer

Product of sums

Answer

Quadratic formula

Answer

Sum of squares

Question 54

What is this called?

$$\left(\sqrt[]{a}+b\right)\left(\sqrt[]{a}-b\right)=a-b^2$$

Accepted Answer

Difference of squares

Answer

Difference of cubes

Answer

Product of roots

Answer

Sum of squares

Question 55

$$\frac{\left(1+x\right)}{-\sqrt[]{x+3}-3}$$

You are going to rationalize the denominator here. What changed must you multiply the bottom with to cancel it out?

Accepted Answer

-\sqrt{x+3}+3

Answer

$\sqrt{x+3}-3$

Answer

$-\sqrt{x+3}-3$

Answer

$\frac{1+x}{\sqrt{x+3}+3}$

Question 56

When getting undefined values when using trig functions and finding limits, what can you manipulate to see if there is an answer?

Accepted Answer

Use algebraic manipulation and trigonometric identities.

Answer

Apply only numerical methods without algebra.

Answer

Ignore the undefined values completely.

Answer

Use calculus to find derivatives only.

Question 57

What is the squeeze therome in basic terms?

Accepted Answer

The squeeze theorem helps find the limit of a function that is 'squeezed' between two other functions with known limits.

Answer

The squeeze theorem is a method for solving differential equations.

Answer

The squeeze theorem states that all functions converge to zero.

Answer

The squeeze theorem is used to find the area under a curve.

Question 58

When finding the limit of a function that clearly tells you that you won't be able to plug in values, what statement must you state?

Accepted Answer

The limit cannot be evaluated by direct substitution.

Answer

You can always plug in values to find the limit.

Answer

The limit can be evaluated by direct substitution.

Answer

The limit is always equal to zero.

Question 59

A function is ---- when you plug in a value, for example, piece wise and from all ends get the samee result

Accepted Answer

continuous

Answer

bounded

Answer

linear

Answer

discrete

Question 60

F is continuous over (a,b) only if it continuous over...

Accepted Answer

[a,b]

Answer

[a,c]

Answer

(c,d)

Answer

(a,b)

Question 61

True or False For a function to be a continuous, the a and b are not included in (a,b)

Accepted Answer

True

Answer

False

Question 62

True or False: Two sided limit is required for a function to be continuous

Accepted Answer

True

Answer

False

Question 63

If a function isn't allowing you to make a it continuous, you can force it, but what must be written beside it?

Accepted Answer

Define the value at the discontinuity.

Answer

Change the function's formula completely.

Answer

Ignore the discontinuity entirely.

Answer

Add a random value beside it.

Question 64

What is an infinite limit?

Accepted Answer

An infinite limit is when a function's value approaches infinity or negative infinity as the input approaches a certain point.

Answer

An infinite limit occurs when a function's value is always zero.

Answer

An infinite limit refers to a function that has a maximum value at a certain point.

Answer

An infinite limit is when a function's value oscillates between two numbers.

Unit 1 - Limits and Derivatives Vocab

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics