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Derivative

Implicit differentiation

tangent

Secant

A function which gives the slope of a curve; that is, the slo…

The process of finding the derivative of a dependent variable…

A straight line or plane that touches a curve or curved surfa…

A secant is a line that intersects a circle at two points.

Derivative

A function which gives the slope of a curve; that is, the slo…

Implicit differentiation

The process of finding the derivative of a dependent variable…

Trig Derivatives

Solids of Revolution

Solids of Known Cross Section

Integrals as Net Change

V=∫(from a to b) A(x)dx... A(x)=πr²... 1. Sketch the region... 2. Dete…

v=∫(from a to b) A(x)dx... 1. Sketch the region and a cross sect…

∫(from a to b) v(t)dt = Displacement, give the net change in…

Trig Derivatives

Solids of Revolution

V=∫(from a to b) A(x)dx... A(x)=πr²... 1. Sketch the region... 2. Dete…

related rates

taylor polynomials

sinx

cosx

define your variables and draw a picture... describe your info w…

take the equation they give you and derive and solve with the…

cosx

-sinx

related rates

define your variables and draw a picture... describe your info w…

taylor polynomials

take the equation they give you and derive and solve with the…

End behavior

Exponential Decay

Exponential Growth

Limit

The appearance of a graph as it is followed farther and farth…

A model for decay of a quantity for which the rate of decay i…

This model is used for such phenomena as inflation or populat…

The value that a function or expression approaches as the dom…

End behavior

The appearance of a graph as it is followed farther and farth…

Exponential Decay

A model for decay of a quantity for which the rate of decay i…

Natural Numbers

Integers

Whole Numbers

Rational Numbers

The set of numbers 1, 2, 3, 4, ... Also called counting numbe…

The set of whole numbers and their opposites

Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...

The set of any numbers that can be expressed as a fraction

Natural Numbers

The set of numbers 1, 2, 3, 4, ... Also called counting numbe…

Integers

The set of whole numbers and their opposites

We use a Riemann Sum to approximate th…

= 0... Note the limits on the integral.

Note the limits on the integral. Use a…

f(x) must be continuous on [a, b]. The…

Riemann Sums

The "Zero" Integral

Order of Integration

Mean Value Theorem for Definite Integrals

We use a Riemann Sum to approximate th…

Riemann Sums

= 0... Note the limits on the integral.

The "Zero" Integral

Derivative

Discontinuity

Increasing Function

Infinity

A function which gives the slope of a curve; that is, the slo…

A point at which the graph of a relation or function is not c…

A function with a graph that goes up as it is followed from l…

A "number" which indicates a quantity, size, or magnitude tha…

Derivative

A function which gives the slope of a curve; that is, the slo…

Discontinuity

A point at which the graph of a relation or function is not c…

IVT

EVT

MVT

Rolles Theorum

If a function is continuous on [a,b], then it passes through…

If f is continuous over a closed interval, then f has a max a…

if f is continuous on [a,b] and differentiable, the instant r…

If f is continuous on [a,b] and diff, there must be a max and…

IVT

If a function is continuous on [a,b], then it passes through…

EVT

If f is continuous over a closed interval, then f has a max a…

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:

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:

Intermediate Value Theorem

Average Rate of Change

Instantenous Rate of Change

Formal definition of derivative

If f(1)=-4 and f(6)=9, then there must be a x-value between 1…

Slope of secant line between two points, use to estimate inst…

Slope of tangent line at a point, value of derivative at a po…

limit as h approaches 0 of [f(a+h)-f(a)]/h

Intermediate Value Theorem

If f(1)=-4 and f(6)=9, then there must be a x-value between 1…

Average Rate of Change

Slope of secant line between two points, use to estimate inst…

Definition of a Limit

IVT (Intermediate Value Theorem)

Definition of continuity

definition of Vertical Asymptote

lim f(x) = lim f(x)... x->a- .... x->a+

if f(x) is continuous on [a,b], there exists a point "c" betw…

f(x) is continuous if and only if :... f(a) exists... lim f(x) exis…

x=a is a VA if and only if ... lim f(x) = ∞ or -∞... x->a

Definition of a Limit

lim f(x) = lim f(x)... x->a- .... x->a+

IVT (Intermediate Value Theorem)

if f(x) is continuous on [a,b], there exists a point "c" betw…

Intermediate Value Theorem

Average Rate of Change

Instantenous Rate of Change

Formal definition of derivative

If f(1)=-4 and f(6)=9, then there must be a x-value between 1…

Slope of secant line between two points, use to estimate inst…

Slope of tangent line at a point, value of derivative at a po…

limit as h approaches 0 of [f(a+h)-f(a)]/h

Intermediate Value Theorem

If f(1)=-4 and f(6)=9, then there must be a x-value between 1…

Average Rate of Change

Slope of secant line between two points, use to estimate inst…

set function=0... factor(quadratic formul…

Point and Slope... (a, f(a)) , f'(a)... Use…

Point and Slope... (a,f(a)) , m=-1/f'(a)…

f(-x)=f(x)... y-axis symmetry

Find the Zeros

Find the equation of the line tangent to f(x) at (a,b)

Find the equation of the line normal to f(x) at (a,b)

Show that f(x) is even

set function=0... factor(quadratic formul…

Find the Zeros

Point and Slope... (a, f(a)) , f'(a)... Use…

Find the equation of the line tangent to f(x) at (a,b)

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…