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Two Special Trigonometric Limits

Definition of the Derivative of a Func…

Average Velocity or Average rate of Ch…

Properties of the Natural Logarithmic…

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…

Two Special Trigonometric Limits

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

Definition of the Derivative of a Func…

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) an…

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) an…

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

limit of a function

vertical asymptote

average velocity

instantaneous rate of change

suppose f(x) is defined when x is near A (in an open interval…

limx-->af(x)=+-infinity then A is this

displacement over change in time

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

instantaneous rate of change

limit of a function

suppose f(x) is defined when x is near A (in an open interval…

Calculus

Mathematics

Geometry

Algebra

the mathematical study of change, in the same way that geomet…

the study of topics such as quantity (numbers), structure, sp…

a branch of mathematics concerned with questions of shape, si…

one of the broad parts of mathematics, together with number t…

Calculus

the mathematical study of change, in the same way that geomet…

Mathematics

the study of topics such as quantity (numbers), structure, sp…

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

limit of a function

vertical asymptote

average velocity

instantaneous rate of change

suppose f(x) is defined when x is near A (in an open interval…

limx-->af(x)=+-infinity then A is this

displacement over change in time

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

instantaneous rate of change

limit of a function

suppose f(x) is defined when x is near A (in an open interval…

odd function

When is the origin the midpoint of any…

even function

parametric equation

symmetric in respect to origin; ... f (-x) = - f (x)... sin (x)

When the function is odd

symmetric over y axis;... f (-x) = f (x)... cos (x)

has a third variable (parameter, often shown as t) to find va…

odd function

symmetric in respect to origin; ... f (-x) = - f (x)... sin (x)

When is the origin the midpoint of any…

When the function is odd

Two Special Trigonometric Limits

Definition of the Derivative of a Func…

Average Velocity or Average rate of Ch…

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 Func…

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

State the Intermediate Value Theorem

State the Chain Rule for Differentiation

What is the integral of ln(x)?

What is the Product Rule?

If the function f(x) is continuous on [a,b], and y is a numbe…

n(f(x))^n-1 * f'(x)

...

[f(x) ** g'(x)] + [f('x) ** g(x)]

State the Intermediate Value Theorem

If the function f(x) is continuous on [a,b], and y is a numbe…

State the Chain Rule for Differentiation

n(f(x))^n-1 * f'(x)

State the Intermediate Value Theorem

State the Chain Rule for Differentiation

What is the integral of ln(x)?

What is the Product Rule?

If the function f(x) is continuous on [a,b], and y is a numbe…

n(f(x))^n-1 * f'(x)

...

[f(x) ** g'(x)] + [f('x) ** g(x)]

State the Intermediate Value Theorem

If the function f(x) is continuous on [a,b], and y is a numbe…

State the Chain Rule for Differentiation

n(f(x))^n-1 * f'(x)

limit definition (words)

limit DNE

vertical asymptote

horizontal asymptote

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

unbounded, infinite, oscillating behavior or jump in graph

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

as x → ∞, f(x) approaches some number

limit definition (words)

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

limit DNE

unbounded, infinite, oscillating behavior or jump in graph

Amorphous

Calculus

Ectopic

Ectopic oral calcification

Without definite shape or visible differentiation in structure

Abnormal concretion composed of mineral salts, usually occurr…

Out of place; arising or produces at an abnormal site or in a…

Examples are pulp stones, denticles, and salivary calculi

Amorphous

Without definite shape or visible differentiation in structure

Calculus

Abnormal concretion composed of mineral salts, usually occurr…

Limit

Continuity

Intermediate Value Theorem

Squeeze Theorem

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

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

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

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

Limit

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

Continuity

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