Calculus

Limits, derivatives, integrals.

CalculusDerivatives★★★☆☆Hard+40 XP

What is the derivative of f(x) = 3x⁴ − 5x² + 7 evaluated at x = 1?

CalculusLimits★★★☆☆Hard+40 XP

Evaluate lim(x→0) sin(3x)/x.

CalculusIntegrals★★★☆☆Hard+40 XP

What is the area under y = x² from x = 0 to x = 3?

CalculusDerivatives★★☆☆☆Medium+30 XP

What is the derivative of f(x) = x³ at x = 2?

CalculusLimits★★☆☆☆Medium+30 XP

Evaluate lim(x→3) (x² − 9)/(x − 3).

CalculusDerivatives★★☆☆☆Medium+30 XP

What is the derivative of sin x at x = 0?

CalculusDerivatives★★★☆☆Hard+40 XP

What is the derivative of e^(2x) at x = 0?

CalculusIntegrals★★★☆☆Hard+40 XP

Evaluate ∫₀¹ (3x² + 2x) dx.

CalculusDerivatives★★★☆☆Hard+40 XP

If f(x) = x² sin x, what is f′(0)?

CalculusDerivatives★★★☆☆Hard+40 XP

What is the derivative of (2x + 1)⁵ at x = 0?

CalculusApplications of derivatives★★☆☆☆Medium+30 XP

At what x does f(x) = x² − 8x + 3 have its minimum?

CalculusIntegrals★★★☆☆Hard+40 XP

Evaluate ∫₁^e (1/x) dx.

Premium problem

Evaluate lim(n→∞) (1 + 1/n)ⁿ. (Answer with a single letter constant.)

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Evaluate ∫₀^π sin x dx.

CalculusApplications of integrals★★★★☆Expert+55 XP

What is the area between y = x and y = x² from x = 0 to x = 1? (Fraction.)

Premium problem

What is the derivative of ln(x² + 1) at x = 1?

CalculusDerivatives★★☆☆☆Medium+30 XP

What is the second derivative of x⁴ evaluated at x = 1?

Premium problem

Evaluate lim(x→0) (e^x − 1)/x.