# Study sets matching "calculus ab"

Derivative of a Constant Function

Power Rule for Positive Integers

The Constant Multiple Rule (POTC)

The Sum + Difference Rule

If f is the function with a constant value c, then df/dx = d'/…

If n is an integer and x cannot equal 0,

Pull out the multiplicative constant

Derivative of a Constant Function

If f is the function with a constant value c, then df/dx = d'/…

Power Rule for Positive Integers

If n is an integer and x cannot equal 0,

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)]

Definition of Derivative

Alternate Form of Derivative

Types of Discontinuity

Conditions for Differentiablity

-corner... -cusp... -vertical tangent... -discontinuity

1) the function must be continuous... 2) the right hand derivativ…

Definition of Derivative

Alternate Form of Derivative

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

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

Intermediate Value Theorem

Mean Value Theorem

Rolle's Theorem

Trig Identity: sin2x =

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

If the function f(x) is continuous on [a,b], AND the first der…

If the function f(x) is continuous on [a,b], AND the first der…

2sin(x)cos(x)

Intermediate Value Theorem

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

Mean Value Theorem

If the function f(x) is continuous on [a,b], AND the first der…