# calculus Flashcards

Browse 500 sets of calculus flashcards

f'(x) + g'(x)

cf'(x)

f(x)g'(x) + g(x)f'(x)

f'(x) - g'(x)

derivative of the summation of two functions

derivative of a constant times a function

derivative of the multiplaction of two functions

derivative of the difference between two functions

f'(x) + g'(x)

derivative of the summation of two functions

cf'(x)

derivative of a constant times a function

1.) F(c) exists... 2.) limit F(x) as x app…

Yes lim+=lim-=f(c)... No, f'(c) doesn't ex…

This is a graph of f'(x). Since f'(C) e…

1

f is continuous at x=c if...

Given f(x):... Is f continuous @ C... Is f' continuous @ C

Given f'(x):... Is f continuous @ c?... Is there an inflection point…

1.) F(c) exists... 2.) limit F(x) as x app…

f is continuous at x=c if...

Yes lim+=lim-=f(c)... No, f'(c) doesn't ex…

Given f(x):... Is f continuous @ C... Is f' continuous @ C

f is continuous at x=c if...

Intermediate Value Theorem

Global Definition of a Derivative

Alternative Definition of a Derivative

If f is continuous on [a,b] and k is a number between f(a) and…

f '(x) is the limit of the following difference quotient as x…

f is continuous at x=c if...

Intermediate Value Theorem

If f is continuous on [a,b] and k is a number between f(a) and…

1.) F(c) exists... 2.) limit F(x) as x app…

Yes lim+=lim-=f(c)... No, f'(c) doesn't ex…

This is a graph of f'(x). Since f'(C) e…

1

f is continuous at x=c if...

Given f(x):... Is f continuous @ C... Is f' continuous @ C

Given f'(x):... Is f continuous @ c?... Is there an inflection point…

1.) F(c) exists... 2.) limit F(x) as x app…

f is continuous at x=c if...

Yes lim+=lim-=f(c)... No, f'(c) doesn't ex…

Given f(x):... Is f continuous @ C... Is f' continuous @ C

f is continuous at x=c if...

Intermediate Value Theorem

Global Definition of a Derivative

Alternative Definition of a Derivative

If f is continuous on [a,b] and k is a number between f(a) and…

f '(x) is the limit of the following difference quotient as x…

f is continuous at x=c if...

Intermediate Value Theorem

If f is continuous on [a,b] and k is a number between f(a) and…

f is continuous at x=c if...

Intermediate Value Theorem

Global Definition of a Derivative

Alternative Definition of a Derivative

If f is continuous on [a,b] and k is a number between f(a) and…

f '(x) is the limit of the following difference quotient as x…

f is continuous at x=c if...

Intermediate Value Theorem

If f is continuous on [a,b] and k is a number between f(a) and…

Calculus

Differential Calculus

Intergral Calculus

Differential

The branch of mathematics that deals with the finding and prop…

Calculus that deals with differentials.

Calculus that deals with integrals.

Pertaining to a differential.

Calculus

The branch of mathematics that deals with the finding and prop…

Differential Calculus

Calculus that deals with differentials.

1.) F(c) exists... 2.) limit F(x) as x app…

Yes lim+=lim-=f(c)... No, f'(c) doesn't ex…

This is a graph of f'(x). Since f'(C) e…

1

f is continuous at x=c if...

Given f(x):... Is f continuous @ C... Is f' continuous @ C

Given f'(x):... Is f continuous @ c?... Is there an inflection point…

1.) F(c) exists... 2.) limit F(x) as x app…

f is continuous at x=c if...

Yes lim+=lim-=f(c)... No, f'(c) doesn't ex…

Given f(x):... Is f continuous @ C... Is f' continuous @ C

Rate

Derivative

Infinitesimal

Speed

The amount that one quantity changes with respect to another.

Infinitesimal change in the y value due to an infinitesimal ch…

Extremely small

The change in position over time

Rate

The amount that one quantity changes with respect to another.

Derivative

Infinitesimal change in the y value due to an infinitesimal ch…

f is continuous at x=c if...

Intermediate Value Theorem

Global Definition of a Derivative

Alternative Definition of a Derivative

If f is continuous on [a,b] and k is a number between f(a) and…

f '(x) is the limit of the following difference quotient as x…

f is continuous at x=c if...

Intermediate Value Theorem

If f is continuous on [a,b] and k is a number between f(a) and…

f'(x) + g'(x)

cf'(x)

f(x)g'(x) + g(x)f'(x)

f'(x) - g'(x)

derivative of the summation of two functions

derivative of a constant times a function

derivative of the multiplaction of two functions

derivative of the difference between two functions

f'(x) + g'(x)

derivative of the summation of two functions

cf'(x)

derivative of a constant times a function

Extreme Value Theorem

Intermediate Value Theorem

Mean Value Theorem

Rolle's Theorem

If f is continuous on [a,b] then f has an absolute maximum and…

If f is continuous on [a,b] and k is a number between f(a) and…

f'(c)=(f(b)-f(a))/(b-a)

if f(x) is a continuous and differentiable function, and f(a)=…

Extreme Value Theorem

If f is continuous on [a,b] then f has an absolute maximum and…

Intermediate Value Theorem

If f is continuous on [a,b] and k is a number between f(a) and…

f is continuous at x=c if...

Intermediate Value Theorem

Global Definition of a Derivative

Alternative Definition of a Derivative

If f is continuous on [a,b] and k is a number between f(a) and…

f '(x) is the limit of the following difference quotient as x…

f is continuous at x=c if...

Intermediate Value Theorem

If f is continuous on [a,b] and k is a number between f(a) and…