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

Estimate the slope by considering points on both sides.

Only consider points on one side.

Ignore the points and use a formula.

Estimate the slope using only the y-coordinates.

Galileo's Law: What is that?

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

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

Galileo's Law applies only to objects on Earth.

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

$$\lim_{x\rightarrow y}f\left(x\right)=L$$ What does L represent here?

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

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

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

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

$$\lim_{x\rightarrow y}f\left(x\right)=L$$ What does x to y represent here?

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

The variable 'x' is a constant value.

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

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

$$\lim_{x\rightarrow a^-}f\left(x\right)=L$$ What does the a^- represent?

It represents approaching 'a' from the left.

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

It indicates the value of 'a' itself.

It represents approaching 'a' from the right.

$$\lim_{x\rightarrow a^-}f\left(x\right)=L$$ What does the a^+ represent?

It represents approaching 'a' from the right.

It indicates the value of 'a' itself.

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

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

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

Limits cannot be defined for any function.

Limits can only be split into two parts.

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

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

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

Limits can only be calculated for linear functions.

The limit is always equal to the function value.

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?

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

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

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

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

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?

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

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

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

f(x) remains constant as x approaches a.

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

Limits can describe behavior approaching infinity or negative infinity.

Limits can describe fixed values only.

Limits cannot describe any behavior.

What is vertical asymptote?

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

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

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

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

The vertical line x=0 is called a vertical asymptote of the curve y=f(x) if at least one of the following statements is true

The vertical line x=0 is a vertical asymptote if f(x) approaches ±∞ as x approaches 0.

The vertical line x=0 is where f(x) is always equal to zero.

The vertical line x=0 is a point of inflection for the curve y=f(x).

The vertical line x=0 is a horizontal asymptote of the curve y=f(x).

$$\lim_{x\rightarrow a}\sqrt[n]{x}=\sqrt[n]{a}$$ What is this equation called?

Limit of the n-th root function

Derivative of the n-th root function

Integral of the n-th root function

Continuity of the n-th root function

What is the greatest integer in terms of calculus?

The greatest integer function is denoted as ⌊x⌋.

The greatest integer function is represented by x.

The greatest integer is the same as the ceiling function.

The greatest integer function is denoted as ⌈x⌉.

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?

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

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

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

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

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.

Evaluate limits from both directions.

Only evaluate limits from one direction.

Ignore the limits and use a graph instead.

Assume the limit exists without checking.

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

The limit does not exist and is infinite.

The limit exists and is finite.

The limit oscillates between two values.

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.

The limit does not exist, but can be infinite.

The limit can only be negative.

The limit exists and is finite.

What are undefined values in calculus?

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

Points where a function has a maximum value.

Values that are always zero in calculus.

Points where a function is continuous.

What are bounded values in calculus?

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

Values that can increase indefinitely

Values that are always negative

Values that are not defined in any range

What are bounded values in calculus?

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

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

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

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

What are unbounded values in calculus?

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

Unbounded values are values that oscillate between two limits.

Unbounded values are fixed values that do not change.

Unbounded values are always negative numbers.

What are continious values in calculus?

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

Continuous values cannot be represented on a graph.

Continuous values are limited to specific points.

Continuous values can only be whole numbers.

What is the theorme of limits for composite functions?

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) $.

The theorem applies only to linear functions.

The limit of a composite function is always zero.

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

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

No, holes do not count for the continuous rule.

Yes, holes count as discontinuities.

Holes affect the continuity of the function.

Holes are considered in the limit calculation.

Limits can exist also for trig functions!

Yes, limits can exist for trig functions.

Trig functions cannot have limits.

Limits do not apply to trig functions.

All trig functions are undefined at certain points.

When than finding the limit through factoring and still inputting results in an undefined value, what does this mean?

It means there is a removable discontinuity or the limit does not exist.

The limit can be calculated using L'Hôpital's rule.

The function is continuous at that point.

It indicates a vertical asymptote exists.

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

Use algebraic manipulation and trigonometric identities.

Apply only numerical methods without algebra.

Ignore the undefined values completely.

Use calculus to find derivatives only.

What is clearly not a strategy in finding limits?

Guessing the limit without justification.

Using the epsilon-delta definition.

Applying L'Hôpital's rule correctly.

Evaluating the limit at a specific point.

Unit 1 - Limits and Derivatives Vocab

Authored by Leonel Roman Avalos

Mathematics

12th Grade

Used 28+ times

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83 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Shall we stand and fight?

No, we should retreat instead.

Let's negotiate for peace.

We should run away and hide.

Yes, we shall stand and fight.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the slope formula?

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

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

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

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What a tangent line?

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

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

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

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

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

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

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

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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.

False

True

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

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

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

Limit notation indicates the maximum value of a function.

Limit notation only applies to linear functions.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Standard form of a linear equation.

Quadratic equation form.

Point-slope form of a linear equation.

Slope-intercept form of a linear equation.

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Unit 1 - Limits and Derivatives Vocab

Shall we stand and fight?

What is the slope formula?

What a tangent line?

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

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.

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

Change in Position/Time

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

Change in Position/Time

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