Calculus (Calculator Non-Active (Unless I say otherwise))

Derivatives

101

The derivative of x³+3x²+x+10480293850289781249812749832049283509701975059703 is

3x²+6x+1

202

What is the derivative of cos(x)sin(x)

cos²(x)-sin²(x)

303

What is the derivative of cos²(x)/(x²+1)

(-2cos(x)sin(x)(x²+1)-2xcos²(x))/(x²+1)²

404

What is the derivative of arctan(cot(x²+1)) 

(Simplify fully)

-2x

505

What is the derivative of ln(x²+1)/(xsin(x))

(2x²sin(x))/((x²+1)(x²sin²(x))) - (ln(x²+1)(sin(x)+xcos(x)))/(x²sin²(x))

Integrals

101

The integral of ∫4x⁶−2x³+7x−4 dx is

4/7 x⁷ − 1/2 x⁴ + 7/2 x² − 4x + C

202

The integral of ∫tan(x) dx

-ln|cos(x)| + C or ln|sec(x)| + C

303

What is the area under the curve sqrt(4-x²)

2pi

404

The integral of ∫cos(x)e^x dx is 

(1/2)(e^x)(cos(x)+sin(x)) + C

505

The integral of ∫¹₀ (x²)/(sqrt(1-x²) is

pi/4

Series and Sequences

101

Does Σ^∞_n=1(1/n⁵) converge or diverge.

Converges

202

What does Σ^∞_n=2(4/5)ⁿ converge to

16/5

303

Does Σ^∞_n=1(-1)ⁿ(4/x) converge or diverge

Diverges

404

Does Σ^∞_n=2 1/(n(ln n)²) converge or diverge

Converges

505

Does Σ^∞_n=1(3n²+7)/(2n³-5) converge or diverge

Diverges

FUN QUESTIONS

101

Isn't this section going to be fun and enjoyable?

Yes

202

What does this power series converge to

1-(x²/2!)+(x⁴/4!)-(x⁶/6!)+(x⁸/8!)-...

e^x

303

What is the interval of convergence of Σ^∞_n=1(x+3)ⁿ/(4x²)ⁿ

x< -3/4 or x >1

404

What is the maximum possible error of the fourteenth-degree polynomial at x = 1 of the power series of sin(2x²) centered around x = 0

0.000353

505

Find the slope of the line tangent to the polar curve at θ = pi/4 for the rose curve r = 3sin(θ)cos(θ)

(btw aren't you having fun?)

-1

Misc.

101

1+1=

2

202

lim_x->∞(x²+3x+2)/(4x²+5)

1/4

303

Calculate the left Riemann sum with 5 equal subintervals from 0 to 10 for the graph x²

240

404

lim_x->∞(x⁵⁰+5x+3)/(e^x+3x¹⁰+2)

0

505

Whose fault is it that the jeopardy was hard, if you thought it was?

Jason