Calculus I
Calculus II
Calculus III
Differential Equations
Bonus
100

Find the derivative of f(x)=x10

10x9

100

Write a formula for the nth term of the given sequence. 

1,2,4,8,16,32

an= 2n-1

100

Let f(x,y)= x2+xy3

compute f(-3,-2)

33

100

What is the name of this differential equation?

x2y"+xy'+4y=0

Cauchy- Euler Equation

100

Determine whether the sequence converges or diverges 

an= 4/(n4)

The series converges 

200

Evaluate the limit as x approaches 2 for the function 

8-3x+12x2

50

200

Find the derivative of each function:

f(x)=6csch35x

6[3csch25x *(-csch5xcoth5x)5]

200

What is the magnitude of the gradient at (0,2)

f(x,y)=3x+y2

5

200

Find the Wronskian of the functions y1=e2x and y2=e-4x

-6e-2x

200

What are the two forms for Green's Theorem?

Circulation Curl & Flux Divergence

300

Integrate 

(1/x2)dx

(-1/x)+C

300

Evaluate the integral involving inverse trigonometric functions

"S" means integral

S {(4x)/ sqrt[81-x4]} dx

2sin-1(x2/9) +C

300

fxxyzz for f(x,y,z)= z3y2ln|x|

(-12zy)/x2

300

Consider the Differential Equation:

(x3-y3)dx+xy2dy=0

Find the solution to the above DE using the substitutions y=ux and dy=udx+xdu

ln|x|= (-1/3)(y/x)3+C

300

Write out the 7th line of Pascals Triangle

(a+b)6=a6+6a5b+15a4b2+20a3b3+15a2b4+6ab5+b6

400

What rule is this:
dxd[f(g(x))]=f′(g(x))g′(x)

The chain Rule

400

Integrate= "S" 

S (sin7x/ cos4x)dx

(1/3cos3x)-(3/cosx)-3cosx+(1/3)cos3x+C

400

Find the angle between vectors

u= <-2,3>        and v= <-4,-1>

70 (1/4)

400

Solve the initial value problem:

y"-6y'+9y=0,             y(0)=1,             y'(0)=8

y=e3x+5xe3x

400

Assume that y1=e2x and y2=e-4x are two solutions to an ordinary DE, and the Wronskian values of the ODE are W=-6e-2x, W1=e-5x-2e-6x, and W2=2-ex. Use variation of parameters to find the solution of this DE.

y= C1e2x+C2e-4x+(1/9)e-x-(1/4)e-2x

500

(d/dx) arcsin(x)= ?

(d/dx) arccos(x)= ?

(d/dx) arctan(x)= ?

{1/ sqrt(1-x2)}

-{1/ sqrt(1-x2)}

1/ (1+x2)

500

What is the volume of the solid made by rotating y= cubed root x and y= (x/4) in the first quadrant about the y- axis?

V= (512pi/21)

500

"S" means integral

ss2xy dA in a quart circle centered at the origin and with r= 5

625

500

Using an integration factor, find the explicit solution to the linear differential equation:

x(dy/dx)+5y= 2


Find the Singular points and any transient terms

y= (2/5)+(C/x5)

Singular points: x=0

Transient terms: (C/x5)

500

Give the equation for the Elliptic Paraboloid.

z=

z= (x2/a2) + (y2/b2)

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