# calculus Flashcards

Browse 500 sets of calculus flashcards

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

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'(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…

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…

Changing direction (left/right/up/down)

Displacement from t1 to t2

Velocity

Average velocity

Velocity=0 AND changed sign

Change in position... s(t2) - s(t1)

rate of change of position

Slope of position s(t2)-s(t1)/t2-t1

Changing direction (left/right/up/down)

Velocity=0 AND changed sign

Displacement from t1 to t2

Change in position... s(t2) - s(t1)

Derivative of a Constant Function

Power Rule

Derivative Constant Multiple Rule

Derivative of a Sum or Different

df/dx (c)= 0... If f has the constant value f(x)= c, then it equa…

d/dx x^n = nx^n-1... If n is any real number, then the above hold…

d/dx (cu)= c du/dx... If u is a differentiable function of x, and…

d/dx (u+v)= du/dx + dv/dx... If u and v are differentiable functi…

Derivative of a Constant Function

df/dx (c)= 0... If f has the constant value f(x)= c, then it equa…

Power Rule

d/dx x^n = nx^n-1... If n is any real number, then the above hold…

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…

Fundamental Theorem of Calculus (part 2…

Integral of dx/(sqrt(1-(x^2))) =

Integral from a to b of (rate of change…

Fundamental Theorem of Calculus (part 1…

F(b) - F(a), where F is an antiderivative of f.

arcsin(x) + C

The amount which that quantity has changed from t = a to t = b.

f(x)

Fundamental Theorem of Calculus (part 2…

F(b) - F(a), where F is an antiderivative of f.

Integral of dx/(sqrt(1-(x^2))) =

arcsin(x) + C

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

Definition of a limit

Riemann Sum

Linear Approximation

Reflect across x-axis

f(x+h)-f(x)/h

lim n -> ∞ Σ i = 1 to n f(xi*) • Δx... Δx = (b-a)/n ... xi* = a + Δxi

L(x) = f(a) + f'(a)(x-a)

-f(x)

Definition of a limit

f(x+h)-f(x)/h

Riemann Sum

lim n -> ∞ Σ i = 1 to n f(xi*) • Δx... Δx = (b-a)/n ... xi* = a + Δxi