#### Study sets matching "calculus b"

#### Study sets matching "calculus b"

Piecewise Function

Volume of a sphere

Horizontal Line Test

Vertical Line Test

Ex. y ={-3x - .5, -1 < x < 1 ; 2x + 1, 1 <= x <= 3

4/3

**r^3**PIA test to see if a horizontal line passes through the graph m…

A test use to determine if a relation is a function. A relati…

Piecewise Function

Ex. y ={-3x - .5, -1 < x < 1 ; 2x + 1, 1 <= x <= 3

Volume of a sphere

4/3

**r^3**PIIVT (Intermediate Value Theorem)

MVT (Mean Value Theorem)

EVT (Extreme Value Theorem)

AVT (Average Value Theorem)

On a continuous function you will hit every y-value between 2…

If conditions are met, there is at least one point where the…

Every continuous function on a closed interval has a highest…

If f(x) is integratable on [a,b] its average (mean) value on…

IVT (Intermediate Value Theorem)

On a continuous function you will hit every y-value between 2…

MVT (Mean Value Theorem)

If conditions are met, there is at least one point where the…

Definition of Continuity

Intermediate Value Theorem

Definition of Derivative

Alt. Form of Derivative

lim f(x) x->c f(x) = f(c)

1. If f is continuous [a,b] 2. and f(a) < k < f(b) or f(b) <…

f'(x) = lim h-> 0 f(x+h) - f(x) / h

f'(x) = lim x-> c f(x) - f(c) / x-c

Definition of Continuity

lim f(x) x->c f(x) = f(c)

Intermediate Value Theorem

1. If f is continuous [a,b] 2. and f(a) < k < f(b) or f(b) <…

Corner

Vertical tangents

Cusp

Discontinuity

Piece wise and absolute value functions

_... 1/odd or odd\| Infinity on both sides

Even/odd power<1 one side +infinity one side -infinity

0 in denominator

Corner

Piece wise and absolute value functions

Vertical tangents

_... 1/odd or odd\| Infinity on both sides

Telescoping series

Harmonic series

Geometric series

Integral test

1/(n * (n+1))... -converges at 1

1 + 1/2 + 1/3 + 1/4 +...... -diverges

a + ar + ar^2 + ar^3 +...... -converges with sum S = a/(1 - r) I…

series E(an) where f(n) = an and f(x) is when x replaces n. I…

Telescoping series

1/(n * (n+1))... -converges at 1

Harmonic series

1 + 1/2 + 1/3 + 1/4 +...... -diverges

Infinite Series

Infinite Series (sequence of partial s…

Convergence of an Infinite Series

Geometric Series

Sn =a1+a2+a3....+an

S1 =a1 ... S2= a1+ a2... Sn = a1+a2+....+an

In inifinite series converges to S if lin Sn as N approaches…

a + ar + ar^2 = ar^3 +....> + ar^n-1 + ....

Infinite Series

Sn =a1+a2+a3....+an

Infinite Series (sequence of partial s…

S1 =a1 ... S2= a1+ a2... Sn = a1+a2+....+an

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

Function

Relation

Domain

Range

A relationship from one set (called the domain) to another se…

An association between two or more variables. If one of the v…

All of the input or x values in a function

All of the output or y values in a function

Function

A relationship from one set (called the domain) to another se…

Relation

An association between two or more variables. If one of the v…

10

5

6

3/2

Evaluate the limit in Part A given the following information:

Evaluate the limit in Part B given the following information:

Evaluate the limit in Part C given the following information:

Evaluate the limit in Part D given the following information:

10

Evaluate the limit in Part A given the following information:

5

Evaluate the limit in Part B given the following information:

Complex Fraction

Compound Inequality

Cube root

Distance Formula

A fraction that contains one or more fractions in its numerat…

Two or more inequalities joined together by "and" or "or"

a number that when multiplied three times equals a given number

d = √[( x₂ - x₁)² + (y₂ - y₁)²]

Complex Fraction

A fraction that contains one or more fractions in its numerat…

Compound Inequality

Two or more inequalities joined together by "and" or "or"

10

5

6

3/2

Evaluate the limit in Part A given the following information:

Evaluate the limit in Part B given the following information:

Evaluate the limit in Part C given the following information:

Evaluate the limit in Part D given the following information:

10

Evaluate the limit in Part A given the following information:

5

Evaluate the limit in Part B given the following information:

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

Fundamental Theorem of Algebra

Complex Zeros Occur in Conjugate Pairs

Logarithmic Functions

Natural Logarithmic Functions

1.A polynomial of degree n, where n>o, has exactly n roots in…

1.If a + bi, where b does not equal 0, is a zero of the funct…

1.For x>0, a>0, and a can't equal 1, y=log of x with base a i…

1.For X>0, y=lnx if and only if X=e to the y power.... 2.The fun…

Fundamental Theorem of Algebra

1.A polynomial of degree n, where n>o, has exactly n roots in…

Complex Zeros Occur in Conjugate Pairs

1.If a + bi, where b does not equal 0, is a zero of the funct…

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)

Intermediate Value Theorem

If f is continuous on [a,b] and k is b…

Rolle's Theorem

If f is continuous on [a,b] and f is d…

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

there is a number c in [a,b] such that f(c)=k.... (Intermediate…

If f is continuous on [a,b] and f is differentiable on (a,b)…

there is at least one number c in (a,b) such that f'(c)=0.... (…

Intermediate Value Theorem

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

If f is continuous on [a,b] and k is b…

there is a number c in [a,b] such that f(c)=k.... (Intermediate…