#### Study sets matching "calculus"

#### Study sets matching "calculus"

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…

limit definition (in words)

limit DNE

vertical asymptote

horizontal asymptote

the y-value a function approaches from both sides as x approac…

if there is unbounded, infinite, oscillating behavior or jump…

at some point x = a, f(x) → ∞... or there's 0 in the denominator

as x → ∞, f(x) approaches some number

limit definition (in words)

the y-value a function approaches from both sides as x approac…

limit DNE

if there is unbounded, infinite, oscillating behavior or jump…

Two Special Trigonometric Limits

Definition of the Derivative of a Funct…

Average Velocity or Average rate of Cha…

Properties of the Natural Logarithmic F…

limx-->0 (sinx) / x = 1... lim x-->0 (1-cosx) / x = 0

f ' (x) = lim Δx-->0 [f(x+Δ x) - f(x)] / Δx

[f(b) - f(a)] / (b - a)

a. The domain is (0, ∝) and the range is (-∝,∝)... b. ln(1) = 0... c…

Two Special Trigonometric Limits

limx-->0 (sinx) / x = 1... lim x-->0 (1-cosx) / x = 0

Definition of the Derivative of a Funct…

f ' (x) = lim Δx-->0 [f(x+Δ x) - f(x)] / Δx

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…

Limit

Continuity

Intermediate Value Theorem

Squeeze Theorem

As function, f, approaches a value, x approaches a certain val…

The limit has to exist. The limit of f(x) has to equal the lim…

In a continuous function with the x values [a, b], it has y va…

If f(x) < g(x) < h(x). When x is near a (g(a) can be undefined…

Limit

As function, f, approaches a value, x approaches a certain val…

Continuity

The limit has to exist. The limit of f(x) has to equal the lim…

Two Special Trigonometric Limits

Definition of the Derivative of a Funct…

Average Velocity or Average rate of Cha…

Guidelines for Implicit Differentiation

limx-->0 (sinx) / x = 1... lim x-->0 (1-cosx) / x = 0

f ' (x) = lim Δx-->0 [f(x+Δ x) - f(x)] / Δx

[f(b) - f(a)] / (b - a)

a. Differentiate both sides of the equation with respect to x.…

Two Special Trigonometric Limits

limx-->0 (sinx) / x = 1... lim x-->0 (1-cosx) / x = 0

Definition of the Derivative of a Funct…

f ' (x) = lim Δx-->0 [f(x+Δ x) - f(x)] / Δx