Math Madness

Limits and Continuity

1

Limit as x approaches 5 of x squared minus 25 over x squared plus x minus 30

What is 10/11?

2

Limit as x goes to 1- of (x^2+2x-3)/(|x-1|)=

What is -4

3

Limit as x goes to 0 of (sinx-x)/tanx=

What is 0

4

The limit as x goes to infinity of lnx/x=

What is 0

5

If f(x)=(3x^2+x)/(2x) for x is not = 0 and f(0)=k, and if f is continuous @ x=0, then k=

What is 3/2

Derivatives

1

d/dx tanx=

What is sec^2xdx

2

d/dx (sin^-1x) =

What is dx/(1-x^2)^(1/2)

3

Find dy/dx for y^3 + xy - 2y - x^2 = -2

What is (2x-y)/(3y^2+x-2)

4

Find dy/dx for y= [(x^2+1)/(x^2-1)]^(1/3)

What is (1/3) [1/(x^2+1) - 1/(x^2-1)]

5

d/dx (1+x^3)^7 = 

What is 7(1+x^3)^6 * 3x^2

Integrals

1

Integral of (x-5)^-4dx

What is (-1/3)(x-5)^-3 + k

2

Integral of x*(2x^2+5)^4dx

What is 1/20*(2x^2+5)^5+k

3

Integral of (1-2x)/(x^2+2x+1) *hint use partial fraction

What is -2ln|x+1| + (-3/x-5)^-3+k

4

Integral of 1/(1+x^2)dx

What is arctan(x)+c

5

Integral of e^(3x-2)dx

What is (1/3)e^(3x-2) + k

Sequence and Series (4 terms)

1

Write out the Maclaurin series for e^x

What is 1+x+x^2/2!+x^3/3!+...

2

What is the formula for the sum of an infinite geometric series?

What is a/(1-r)?

3

The first term of an arithmetic sequence is equal to 6 and the common difference is equal to 3. Find a formula for the n th term

What is 3n+3

4

The first term of an arithmetic sequence is equal to 6 and the common difference is equal to 3. Find the value of the 50 th term

What is 153

5

Write out the Maclaurin series for sinx

What is x-x^3/3!+x^5/5!-x^7/7!+...

Random!

1

If f(x)=3x^2, then f(x)=

What is y= (x-2)/3

2

A boy 5ft tall walks at a rate of 3ft/sec towards a streetlamp that is 12 ft above ground, what rate is the rate of change of length of shadow

What is 15/7 ft/sec

3

True or False. The two functions f and g defined by f(x) = 3x + 3 for x real and g(t) = 3t + 3 for t real and positive are equal?

What is False

4

A conical tank 20 ft in diameter and 30 ft tall (w/ a vertex down) leaks water @ a rate of 5 ft^3/hr. At what rate is the water level dropping when the water is 15 ft deep?

What is 1/5(pi) ft/hr

5

The slope of the tangent line to the curve y=cos(x)sin(x) + tan(x) - arctan(x) at (1,3) is

What is 2.509...