Objective Questions

Find the first derivative of sec⁻¹(2x) with respect to x

d/dx[(log_e(2x-1))⁴] equals

Evaluate y' of y=5x²·tan(2x)

d/dx[3x²sin⁻¹x] equals

Evaluate d/dx[(1+x²)(4-3x⁴)³] at x=1

Given f(x)=3x²-4x+1, find f(f(2))

Obtain Δy/Δx of the derivative of y=sec(x) using first principle

Evaluate lim(x→2) (x³-64)/(x-4)... [as x approaches 4] i.e. lim(x→4) (x³-64)/(x…

Find $\int \ln \frac{x}{2} dx$.

Obtain ∫sin²x dx

The maximum value of f(x) = x³ - 27x + 15 occurs at x = ?

Find \( dy/dx \) for \( x = \sin t, y = \cos 2t \).

What is the limit of \( \frac{x^3 - 6x + 2}{x^2 + x + 9} \) as \( x \) approach…

Evaluate the limit of \( \frac{(x-2)^3 + 8}{x} \) as \( x \) approaches 0.

Evaluate the limit of \( \frac{x^2 + a^2}{x^3 + a^3} \) as \( x \) tends to inf…

Evaluate the limit of \( \frac{\sqrt{x+1} - 1}{x} \) as \( x \) tends to infini…

Given f(x,y) = 2cosx·sin²y + y³/x², compute f_x(x,y)

Given f(x,y) = 2cosx·sin²y + y³/x², compute f_y(x,y)

Given f(x,y) = 2cosx·sin²y + y³/x², compute f_xy(x,y)

Find the minimum value of y if y = x³-3x²+3

Evaluate lim(x→0) x³/(1-cos2x)

Evaluate lim(x→-3) (x³+x²-9x-9)/(x+3)

Find the derivative of y = 7^(4x+2) with respect to x

Find the derivative of cot⁻¹(x) with respect to x

Evaluate lim(x→1/3) (6x²-1)/(3x-1)

d/dx(√(4-x²)) equals

Obtain the derivative of y = ∛(5-7x²) with respect to x

Differentiate log_e(x²/(x³+5)) with respect to x

Find y' of y = tan(2x) at x = π/2

Evaluate lim(x→∞) (3x-5x³)/(3x³-8)

Evaluate ∫_(π/4)^(3π/4) cos(π-2x) dx

Given a is a positive constant and ∫ₐ^(3a) (2x+1)/x dx = ln12, find the exact v…

By Wallis' formula, evaluate ∫₀^(π/2) cos²x·sin⁶x dx

By Wallis' formula, evaluate ∫₀^(π/2) sin³x·cos⁴x dx

If y=x^(5x), find dy/dx

The hyperbolic cotangent of x (coth x) is given by

The Maclaurin series expansion of cosh(x) is

Find dy/dx of y=cosh³(2x)

∫dx/[(sin⁻¹x)√(1-x²)]

∫x/(1+8x²)² dx

∫dx/√(1-x²)

∫x dx/√(2-5x²)

By Wallis' formula, evaluate ∫₀^(π/2) sin⁵x dx

By Wallis' formula, evaluate ∫₀^(π/2) cos⁵x·sin²x dx

By Wallis' formula, evaluate ∫₀^(π/2) cos⁴x dx

By Wallis' formula, evaluate ∫₀^(π/2) sin⁶x dx

By Wallis' formula, evaluate ∫₀^(π/2) cos⁹x dx

Evaluate the integral ∫ln(x) dx

∫eˣ/(1-eˣ) dx

∫cot(√3x) dx

∫tan(x)/cos(x) dx

∫tan²x dx

∫dx/(cosx·sinx)

∫dx/(1-cosx)

If ∫sin³x dx = Acos³x+Bcosx+c, then A-B = ?

∫(cosx+sinx)/(cosx-sinx) dx

∫sin²x dx

∫eˣ/(eˣ+2+e⁻ˣ) dx

∫tanx/cosx dx

∫₋₁⁰ x·√(x+1) dx

What expression represents d/dx[ln(tanx)]?

Find dy/dx of y=cosec(3x/2+1/2)

Find dy/dx of y=sec(x)/tan(x)

Find the gradient of (3x+2)/(5x-3) at x=0

Which best describes the derivative of a function?

Given f(x-1)=3x²-4x+1, find f(x)

Using first principle, evaluate Δx/Δy of the derivative of ln(3x+1)

Using first principle, evaluate Δy/Δx of the derivative of cos(3x)

Evaluate Δy/Δx of the derivative of e^(3x+1) using first principle

Using first principle, evaluate Δx (i.e. x in terms of y and Δy) for the deriva…

Differentiate the implicit function 3x²y + xy² = 2y.

The 8th term of the Maclaurin series of e^x is:

The 3rd term of the Maclaurin series of ln(x+1) is:

What is the coefficient of x⁴ in the Maclaurin expansion of e^x / x?

Obtain dy/dx, if y = a^cosx

The function y = 9x³ – 45x² + 48x + 11 has a maximum value at y = ?

The function y = 9x³ – 45x² + 48x + 11 has a minimum value at y = ?

If y = 3x², the increment Δy is:

If y = sinx, what is d³y/dx³?

Evaluate ∫(x-1)/(x²-x-2) dx.

Obtain the integral ∫log xdx.

Obtain ∫sin²xdx.

Evaluate ∫₀² (4x/√x) dx.

Evaluate ∫ sinxcosx e^cos2x dx.

Obtain dy/dx, if y = a^{cos x}

If y = sin x, what is d³y/dx³?

Obtain the integral ∫log x dx

Solve ∫1/(x ln x) dx

Which of the following is true about I_n = ∫tanⁿ x dx, I

If y = log(sec x + tan x), find dy/dx

Find ∫2x/(x+1) dx

Evaluate ∫₀^π x sin x dx

Integrate ∫e^x / √(1-e^x) dx

Evaluate ∫sin(4x)cos(2x) dx

Obtain ∫(-x-1)/(x²-6x+8) dx

What is the limit of \( \frac{3 \sin 5x}{x} \) as \( x \) approaches 0?

What is the value of \( \cos(180^\circ) \) used in trigonometric limit calculat…

What is the value of \( \sin(360^\circ) \) used in trigonometric limit calculat…

Find ∫e^x cos x dx

Differentiate the function y = x² + 1/x²