Functions
f(x) = 2x + 3 and g(x) = x², find (f ∘ g)(2).
11
Find the 10th term of the arithmetic sequence 5, 8, 11, ...
32
Convert 210° to radians.
7π/6
Differentiate f(x) = 3x⁴ − 5x.
f′(x) = 12x³ − 5
Find ∫(6x² + 4) dx
2x³ + 4x + C
Find the inverse of f(x) = (x + 1)/(x − 2)
f⁻¹(x) = (2x + 1)/(x − 1)
Find the sum to infinity of the geometric series 12 + 4 + 4/3 + ...
18
Find the exact value of sin(π/3)·cos(π/6).
3/4
Differentiate y = e^(2x) sin x.
dy/dx = e^(2x)(2sin x + cos x)
Evaluate ∫₀² 3x² dx.
8
The graph of y = f(x) is transformed to
y = 2f(x − 3) + 1.
Where does the point (1, 4) on f end up?
(4, 9)
Find the coefficient of x³ in the expansion of (2 + x)⁵
40
If sin θ = 3/5 and θ is acute, find sin 2θ.
24/25
Differentiate y = ln(x² + 1).
dy/dx = 2x/(x² + 1)
Find ∫2x·e^(x²) dx using substitution.
e^(x²) + C
Find the values of k for which x² + kx + 9 = 0 has two distinct real roots.
k < −6 or k > 6
Solve ln x + ln(x − 3) = ln 4
x = 4
Solve sin 2x = cos x for 0 ≤ x ≤ 2π.
x = π/6, π/2, 5π/6, 3π/2
Use implicit differentiation to find dy/dx at (3, 4) on the curve x² + y² = 25.
-3/4
Find the area enclosed between y = x² and y = 2x.
4/3
Solve |x − 1| > |2x + 3|
−4 < x < −2/3
Solve 2^(2x) − 5(2^x) + 4 = 0
x = 0 or x = 2
Solve 2sin²x = 1 + cos x for 0 ≤ x ≤ 2π.
x = π/3, π, 5π/3
Find the x-coordinate of the minimum point of f(x) = x² − 6x + 5.
x=3
The region under y = √x from x = 0 to x = 4 is rotated 360° about the x-axis. Find the volume.
8π