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

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

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

Change in Position/Time

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

Change in Position/Time

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

Galileo's Law: What is that?

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

What does f(x) represent here?

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

What does L represent here?

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

What does x to y represent here?

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

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

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

What does the a^- represent?

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

What does the a^+ represent?

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

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

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?

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?

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

What is vertical asymptote?

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

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

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

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

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

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

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

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

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

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

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

What is this equation called?

What is the greatest integer in terms of calculus?

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?

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?

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.

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

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.

What are undefined values in calculus?

What are bounded values in calculus?

What are bounded values in calculus?

What are unbounded values in calculus?

What are continious values in calculus?

What is the theorme of limits for composite functions?

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

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

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

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!

Limits can exist also for trig functions!

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

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

What is this called?

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

What is this called?

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

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

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

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

What is clearly not a strategy in finding limits?

When trying to find a limit, what is the number one thing you must do to note waste your time through intedetermine form?

When all other ways of solving for limit of a function fails, what remains? It's the 1st way tought to solve a limit!

What is the squeeze therome in basic terms?

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?

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

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

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

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

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

What is an infinite limit?

True or False: One-sided limits of infinity don't exist.

What is a limit of infinity of quotients

When finding the limit of infinity of quotients, you basically are following the rational rules

If the degree of the numerator is less than the degree of the denominator, than the limit is ---

If the degree of the numerator is equal to the degree of the denominator, then the limit is the ratio ---

If the degree of the numerator is greater than the degree of the denominator, then the limits is ----

when finding the limits at infinity of quotients with square roots, you want to divide each side by the the highest degree of the numerator, and ignoring the other terms besides the highest terms of each numerator and denominator

When dealing infinity of quotients with square roots, can't you assume than to ignore other terms that aren't the highest terms of the numerator and denominator?

What is a intermediate Value Theorem?

In the Intermediate Theorem what isn't a rule for it?

$$\lim_{x\rightarrow2^-}=-\infty$$

What asymptote is it?

What asymptote is it?

$$\lim_{x\rightarrow\infty}f\left(x\right)=4$$

There is three types of discontinuities in AP calc BC, what are they?