Test 3 - Calc II

Solve:

x-ln|x-2| + C

Compute the following

ln|x-1| - ln|x| + C

Compute the following

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

Compute the following:

1/12[ln|sin(x)-2| - ln√(sin²(x)+2sin(x)+4) - √3 arctan((sin(x)+1)/√3)] + C

Compute the following:

9ln|x-5| - 7ln|x+2| + C

Compute the following

13/2 ln|x+6| + 3/2ln|x-2| + C

Compute the following

2ln|x+3| + 3/2ln|x²+4| - 5/2 arctan(x/2) + C

Compute the following

2ln|x+1| - ln|x+4| - 3/(x+4) + C

Compute the following

½ ln|x²+2| - √2/2 arctan((x√2)/2) + 1/(2(x²+2)) + C or ½ ln|x²+2| - 1/√2 arctan((x/√2) + 1/(2(x²+2)) + C

Compute the following

9ln|x-5| - 7ln|x+2| + C

Compute the following

13/2 ln|x+6| + 3/2 ln|x-2| + C

Compute the following

2ln|x+3| + 3/2 ln|x²+4| - 5/2 arctan(x/2) + C

Compute the following

2ln|x+1| - ln|x+4| - 3/(x+4) + C

Compute the following

½ ln|x²+2| - √2/2 arctan (x√2/2) + 1/(2(x²+2)) + C or

½ ln|x²+2| - 1/√2 arc tan(x/√2) + 1/(2(x²+2)) + C

Compute the following:

∞ (infinity), diverges

Compute the following, evaluate if it converges or diverges

1/8, converges

Compute the following, evaluate if it converges or diverges

1/2, converges

Compute the following, evaluate if it converges or diverges

π, converges

Compute the following, evaluate whether it converges or diverges

∞ infinity, diverges

Compute the following, evaluate whether it converges or diverges

4 (converges)

Compute the following

infinity (∞)

Compute the following

2√2

Find the particular solution to the differential equation dy/dx= 4x passing through point (1,4)

y= 2x² + 2

Assume that y= 2e^3x-2x-2 is a solution to y’+3y= 6x+4. Verify that a function is a solution to a general equation.

6x+4

Verify that the function y= 3e^2t+4sin(t) is a solution to the initial-value problem dy/dt-2y= 4 cos(t) - 8sin(t); y(0)=3

4 cos(t) - 8sin(t)

Solve the initial-value problem y’ = x² - 4x+ 3 - 6e^-x; y(0)=8

x³/3 - 2x² + 3x + 6e^-x+2

Find the general solution of xy’+3y = 4x² - 3x

y=4/5 (x²) - 3/4x + Cx^-3

Find the general solution to the differential equation: (x-2)y’+y=3x²+2x. (Assume x>2)

y= (x³+x²+C) / (x-2)

Solve the initial-value problem: y’-2y=4x+3; y(0)=-2.

y=-2x-5/2+(e^2x)/2