BC

Limits

100

Limits are only concerned with the _____ of the function as x approaches some value

Behavior

200

Solve the limit as x->0 of |x|/x

the limit does not exist

300

Solve the limit as x->+∞ (e^(-8x)-4e^(4x))

-∞

400

Solve the limit as x->0 (√(x+4)+5x-2)/x

21/4

500

True of False:x^(3) grow faster than 6x^(2)+e^(x) as x->∞

false

Derivatives

100

A function can be _____(without lifting the pencil) but could also be not _____ at a certain point.

continous, diffenentiable

200

The ___________ tells about the ____________ what the first derivative what the ____________ tells about the ____________. -Bates

second derivative,first derivative,first derivative,original

300

If f(x)=5x^(4)+2e^(7x)sin(3x), then f'(x)=

What is 20x^(3)+14e^(7x)sin(3x)+6e^(7x)cos(3x)

400

Find the derivative of ln(y)-3x^(2)+7y=-13

dy/dy=6x/(y^(-1)+7)

500

If the v(t) of the particle is >0 but the a(t)<0, the the particle is _______(its motion).

slowing down

Integrals

100

The Integral is the _________ of the ____ under the curve of the function.

accumulation, area

200

∫(-sin(x)/cos(x)dx

lncos(x)+C

300

∫5x^(2)cos(2X)dx

((5x^2)/2)sin(2x)+(5x/2)cos(2x)-(5/4)sin(2x)+C

400

∫((1/2)x+4)/(x^2+x-6)dx

(-1/2)ln(x+3)+ln(x-2)+C

500

The area between the two curves with respect to the y-axis can generally be written as A=

∫[f(y)-g(y)]dy

Volume and Area

100

The volume of rotating circular cross sectional disk for a single function about the x-axis can be written as V=

V=∫π[f(x)]^2dx

200

The set up for the washer method is written as with respect to the y-axis is V=

V=∫π[f(y)]^2dy-∫π[g(y)]^2dy

300

The Volume of a function is the __________ of all the cross sectional areas under the curve.

accumlation

400

The general set up for the area of a polar function is A=

(1/2)∫[r(θ)]^(2)dθ

500

The general set up up for the area between two polar function is A=

(1/2)∫[f(θ)^2-g(θ)^2]dθ

Series

100

The general term for the Maclaurin series of f(x)=e^x is

(x^n)/n!

200

The first three terms of the series for sin(x^3) is

x^3-(x^(6)/3!)+(x^(8)/5!)

300

The first three term for the for the Taylor Series e^(x+3)

1+(x+3)+((x+3)^2/2!)

400

Does the limit as x->∞ of 1/x^(0.5) converge of diverge.

diverge

500

does the series converge or diverge for Σ(2/3)^n

converge