# Study sets matching "ap calculus"

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On the unit circle, the x value is ____…

On the unit circle, the y value is ____…

When determining the sign of sin, cos,…

Sin🚫=

Cosine

Sine

"All in the 1st, Sin in the 2nd, Tan in 3rd, Cos in 4th" (refe…

1/csc🚫

On the unit circle, the x value is ____…

Cosine

On the unit circle, the y value is ____…

Sine

A function f(x) is continuous at a poin…

f is continuous at c if and only if...

Continuity of an interval

Continuity on an open interval

the limit as x approaches c from the left equals f(c) equals t…

1. f(c) is defined... 2. the limits as x approaches c of f(x) exi…

A function f(x) is continuous on an interval I, if and only if…

A function f(x) is continuous on an open interval (a,b) if and…

A function f(x) is continuous at a poin…

the limit as x approaches c from the left equals f(c) equals t…

f is continuous at c if and only if...

1. f(c) is defined... 2. the limits as x approaches c of f(x) exi…

Definition of a Limit

When testing values for a limit, one sh…

Does every function have a limit at any…

Limits at holes...

In general, lim x->a (f(x)) = L... If we an move the values of f(…

...the outputs don't surpass the expected Limit

For some functions, they do not exist at a given point

...still exist. Limit is behavior approaching a point, not arr…

Definition of a Limit

In general, lim x->a (f(x)) = L... If we an move the values of f(…

When testing values for a limit, one sh…

...the outputs don't surpass the expected Limit

-6x^2 / (|2x^3| sqrt(4x^6 - 1))

-5x^4 / (|x^5| sqrt(x^10 - 1))

-10x / sqrt(1 - 25x^4)

4x / (4x^4 + 1)

derivative of arccsc(2x^3)

derivative of arccsc(x^5)

derivative of arccos(5x^2)

derivative of arctan(2x^2)

-6x^2 / (|2x^3| sqrt(4x^6 - 1))

derivative of arccsc(2x^3)

-5x^4 / (|x^5| sqrt(x^10 - 1))

derivative of arccsc(x^5)

complicity

deploy

explicate

implicate

(noun) ... Involvement as an accomplice in a crime or wrongdoing.…

(trans.verb) ... a. to station(person or forces) systematically o…

(trans.verb) ... To explain; make meaning clear. ... Latin: ex=meani…

(trans.verb) ... a. to involve or connect incriminatingly... b. to i…

complicity

(noun) ... Involvement as an accomplice in a crime or wrongdoing.…

deploy

(trans.verb) ... a. to station(person or forces) systematically o…

Limit definition of the derivative

Where a function is not differentiable

Limit definition of the derivative at a…

d/dx [sin x]

f'(x) = limit as h→0 of [f(x+h) - f(x)]/h

1. discontinuous... 2. vertical tangent (slope undefined)... 3. cusp

f'(a) = limit as h→0 of [f(a+h) - f(a)]/h

cos x

Limit definition of the derivative

f'(x) = limit as h→0 of [f(x+h) - f(x)]/h

Where a function is not differentiable

1. discontinuous... 2. vertical tangent (slope undefined)... 3. cusp

An asymptote is a ____ that the graph o…

As the graph of the function approaches…

Finding any zeros of the _____ will giv…

You can find the equation for the line…

Line; remember, an asymptote does not need to be straight

Infinity or negative infinity ... intersecting/touching

Denominator

Polynomial long division

An asymptote is a ____ that the graph o…

Line; remember, an asymptote does not need to be straight

As the graph of the function approaches…

Infinity or negative infinity ... intersecting/touching

Vertical

Horizontal

Horizontal

Horizontal

set the denominator of the function equal to zero and solve fo…

subtract the amount of x's in the numerator from the number of…

if the answer is negative, then y=0

if the answer is 0, then y= a/b (ax/bx)

Vertical

set the denominator of the function equal to zero and solve fo…

Horizontal

subtract the amount of x's in the numerator from the number of…

d: (-infinity, infinity)... r: (-infinity,…

d: (-infinity, infinity)... r: [0, infinit…

d: (-infinity, infinity)... r: (-infinity,…

d: (-infinity, infinity)... r: [0, infinit…

linear

absolute value

cubic

quadratic

d: (-infinity, infinity)... r: (-infinity,…

linear

d: (-infinity, infinity)... r: [0, infinit…

absolute value

Limit from the left of f(x) as x -> a

Limit from the right of f(x) as x -> a

Lim x -> a (f(x)+g(x))

Lim x -> a (f(x)-g(x))

lim x -> a- f(x)

lim x -> a+ f(x)

F+G; Sum Limit

F-G; Difference Limit

Limit from the left of f(x) as x -> a

lim x -> a- f(x)

Limit from the right of f(x) as x -> a

lim x -> a+ f(x)