Derivatives
Derivative of sin(x²)
What is 2xcos(x²)?
∫cos(x) dx
What is sin(x) + C ?
Does Σ1/n converge or diverge?
What is diverges?
Find the critical points of f(x) = x² − 4x
What is x = 2 (minimum)?
P(rolling a 3 on a fair die)?
What is 1/6?
Use the quotient rule on (x²+1)/(x−1)
What is (x²−2x−1)/(x−1)²?
∫x·sin(x) dx
What is −x·cos(x) + sin(x) + C ?
Find the sum: 1 + 1/2 + 1/4 + ...
What is 2?
Find the equation of the tangent line to y=eˣ at x=0
What is y = x + 1 ?
P(A)=0.4, P(B)=0.3, independent. Find P(A∩B)
What is 0.12?
Differentiate y = ln(x³·sin(x))
What is y' = 3/x + cos(x)/sin(x) = 3/x + cot(x)?
∫₀¹ x·eˣ dx
What is 1?
Use the ratio test on Σ(n!/nⁿ). Does it converge or diverge?
What is converges?
A particle's position is p(t)=t³−6t. When is it at rest?
What is t = √2?
In a normal distribution, what % of data falls within 2σ?
What is 95%?
Find y' using implicit differentiation: x²+y²=25
What is y' = −x/y?
Find the area between y=x² and y=x+2
What is 9/2?
First 3 terms of Taylor series for sin(x) at x=0
What is x − x³/6 + x⁵/120 ?
Find the dimensions of a rectangle with perimeter 40 that maximizes area.
What is a square with sides 10 × 10, area = 100
State the Central Limit Theorem in plain terms
Regardless of the population's distribution, the sampling distribution of the sample mean approaches a normal distribution as sample size n increases (generally n ≥ 30)
Find y' for y = (x²+1)^(tan(x))
What is y' = (x²+1)^(tan(x)) · [sec²(x)·ln(x²+1) + 2x·tan(x)/(x²+1)] ?
Evaluate ∫ x²/√(1−x²) dx using trig substitution
What is θ/2 − sin(2θ)/4 + C ?
Acceptable as well:
(arcsin(x)/2 − x√(1−x²)/2 + C)
Determine the interval of convergence for Σ(xⁿ/n)
What is [−1, 1)?
Set up and evaluate the volume of revolution of y=√x around the x-axis from 0 to 4
What is 8π? (8pi)
A bag has 4 red and 6 blue marbles. You draw 3 without replacement. What is the probability all 3 are red?
What is 1/30?