# Study sets matching "calculus ab"

Study sets

Diagrams

Classes

Users

What conditions must be to satisfied fo…

If the appropriate conditions are satis…

Limit

Quotient rule?

f(x) is continuous in the interval [a, b] and differentiable i…

There is at least one point c in the interval (a, b) at which…

A limit is the value that a function or sequence "approaches"…

(vu'-uv')/v^2

What conditions must be to satisfied fo…

f(x) is continuous in the interval [a, b] and differentiable i…

If the appropriate conditions are satis…

There is at least one point c in the interval (a, b) at which…

Area of a trapezoid

Trapezoidal rule

Simpson's rule

Natural log derivative

(1/2) [(y2+y1)/(x2-x1)]

[(b-a)/(2n)][f(x0)+2f(x1)+2f(x2)...+f(xn)]

(n must be even and f continuous on [a,b]): [(b-a)/(3n)][f(x0)…

U'/U

Area of a trapezoid

(1/2) [(y2+y1)/(x2-x1)]

Trapezoidal rule

[(b-a)/(2n)][f(x0)+2f(x1)+2f(x2)...+f(xn)]

When asked to INTERPRET

Numerical derivative on calculator port…

Rounding

Justification

state when, what, how, and how much

does not require work to be shown

Round to 3 decimals at the end, 5 during work

use what has been given to you

When asked to INTERPRET

state when, what, how, and how much

Numerical derivative on calculator port…

does not require work to be shown

exponential function

indefinite integral

Absolute minimum

Differentiable

A function of the form f (x) = a x where a is any positive con…

this represents the family of antiderivatives of the function f

The least single value that a function attains on a given inte…

A function f is said to be differentiable at a point x = a if…

exponential function

A function of the form f (x) = a x where a is any positive con…

indefinite integral

this represents the family of antiderivatives of the function f

Limit Definition of Derivative

Alternate Definition of Derivative

limit as x approaches 0: sinx/x

limit as x approaches 0: ... 1-cosx/x

limit (as h approaches 0)= F(x+h)-F(x)/h

limit (as x approaches a number c)=... f(x)-f(c)/x-c x≠c

1

0

Limit Definition of Derivative

limit (as h approaches 0)= F(x+h)-F(x)/h

Alternate Definition of Derivative

limit (as x approaches a number c)=... f(x)-f(c)/x-c x≠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

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 insta…

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

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 insta…

Limit definition

alternate form

continuity at a point

continuity over an open interval

f'(x) = lim f(x+∆x)-f(x)... ∆x→0 ∆x

f'(x) = lim f(x)-f(c)... ∆x→c x-c

function f is continuous at c if the following conditions are…

a function is continuous on an open interval (a,b) if it is co…

Limit definition

f'(x) = lim f(x+∆x)-f(x)... ∆x→0 ∆x

alternate form

f'(x) = lim f(x)-f(c)... ∆x→c x-c

Intermediate Value Theorem

Mean Value Theorem

Fundamental Theorem of Calculus #1

FTC #2

What Theorem covers this?... If f is continuous on [a,b] and k i…

Name this Theorem

What is Theorem called?... The definite integral of a rate of ch…

What is this called?

Intermediate Value Theorem

What Theorem covers this?... If f is continuous on [a,b] and k i…

Mean Value Theorem

Name this Theorem