Objective Questions

Evaluate the limit of \( \frac{\sin x}{\tan x} \) as \( x \) approaches 0.

Solve ∫ sin x cos x · e^(cos²x) dx.

Solve ∫ 1/(x ln x) dx.

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

Evaluate ∫ x e^(-4x) dx.

Evaluate ∫₀^(π/2) cos² x dx.

Evaluate ∫₀^(π/2) sin⁶ x dx.

Integrate ∫ (eˣ - 1)/√(1-eˣ) dx.

Evaluate ∫ sin 4x cos 2x dx.

Find ∫ sin³ x cos³ x dx.

Obtain ∫ (x-1)/(x²-6x+8) dx.

What is the limit of \( x^3 \) as \( x \) tends to negative infinity?

Integrate ∫ x²/(x+1) dx.

Obtain ∫ xe^(x²) dx.

Integrate ∫ 2x³e^(-x⁴) dx.

Find ∫ eˣ cos x dx.

If ∫ x(ln x)ⁿ dx (evaluated from 1 to e) follows the reduction formula I_n = e²…

The 8th term of the Maclaurin series of eˣ.

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

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

Obtain dy/dx, if y = a^(cos x).

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

Obtain ∫ (x-1)/(x²-x-2) dx yields

Obtain the integral ∫ log x dx

Obtain ∫ sin²x dx

Evaluate ∫ from √2 to 4 of 4x / √(x²-1) dx

Solve ∫ (ln x / x) dx

Solve ∫ (1 / (x ln x)) dx

Find ∫(4x³+3x-1)dx

Integrate ∫(ln x)/x dx

Integrate ∫(e³x+8x)dx

Evaluate d/dx [kf(x)] where k is a constant.

Which of the following option best is correct regarding differentiation rules?

Which of the following option best is correct regarding calculus theorems?

Given the function y = cot(5x²+3), find dy/dx.

Which of the following option best represents the reduction formula for ∫se…

The first derivative of √(7-2x³) with respect to x is...

Obtain the first derivative of y = 7x³ tan 3x with respect to x.

The Quotient rule of differentiation formula for the function V = p(x)/q(x) is.…

Obtain ∫(1/(4+9x²)) dx.

Integrate ∫sec² x tan x dx.

Using the reduction formula, evaluate ∫ cos⁴x dx.

Using the Wallis formula, the integral of ∫₀^(π/2) sin⁶x dx is...

The nth term of the Maclaurin series expansion of cos x is...

What is the value of K for which the function f(x) = Ksinx + sin3x/3 has an ext…

Given the function y = (u/v)ⁿ, one of the following is correct.

For ∫√(3-x²)dx, the best substitution is

The derivative of a function y = f(u) of another function u = g(x) is given as.…

Which of the following best suits the Taylors series expansion of a given funct…

Find ∫(5x)/(x²+6x-7) dx

Obtain ∫x²cosx dx

Find the values of a and b that make f(x) continuous, f(x) = { x+1 for x<1 ; ax…

If y = √x, from first principle find Δy/Δx

Evaluate lim (x→0) (tan4x)/(3x)

Evaluate ∫(2x)/(x-1) dx

Evaluate the limit of \( \frac{x^2 + 1}{x^2 - 1} \) as \( x \) tends to infinit…

Find dy/dx if y = cos(5x-3y)

What is the limit of \( \ln(1+x) \) as \( x \) tends to 0?

Evaluate the limit of \( \frac{e^x - e^{-x}}{2} \) as \( x \) tends to 0.

Using the reduction formula, evaluate ∫ cos⁴x dx,

What is the value of K for which the function f(x) = p sin 3x + K/(3x) has an e…

∫√(3-x²) dx, the best substitution is

Which of the following best suits the Taylor series expansion of a given functi…

The nth term of the Maclaurin series expansion of the function e^-3x …

What is the limit of \( \frac{5x}{\sin 2x} \) as \( x \) tends to 0?

Evaluate the minimum value of y if y = x³-3x² +1.

Given that ∫₀^b (2x-6)² dx = 36, Find the value…

Integrate ∫ x² ln x dx

Find the values of a and b that make f(x) continuous, where f(x) is defined as:…

Given that dy/dx = cos(3√x)/√x, then y is...

Evaluate ∫ cosec²(5x)√cot(5x) dx

If y = √x, from first principle find Δy/Δx.

Find dy/dx if y = cos(5x-3y).

Find the minimum value of the function y = 2x³ - 21x² + 36x - 20.

The maximum value of the function f(x) = x³ + 2x² - 4x + 6 occurs …

Evaluate ∫₀^π (cosx - 2x) dx.

By using Partial fraction technique, ∫ dx/(x²-x) is

Obtain ∫ xe^(-x²) dx

Given the functions f(x) = 3x² – 2x + 1 and g(x) = 2x + 5

The d/dx(7^(5x-1) + log_7|5x²-x|) equals

Given y = log_7(4x²), find y'' - 3y'.

Evaluate the minimum value of y = x³ - 3x² + 1.

Find the values of a and b that make the function

Given that y = (3sinθ)/(2sinθ+2cosθ) and dy/dθ = K / (1+sin(…

Given the function f(u) = 5u² - 7u + 2, find f(f(3)).

Given the function f(u – 2) = 3u² – u + 1, find f(5).

Obtain d/dx {ln(x^2 / (x^2+1))}

Simplify ∫ (4x-5) / (x^2-x-2) dx

Find dy/dx if y = x^(tan x)

Differentiate y = log(x^3 - x) + 7^(2/3 * x)

Find dy/dx, if y = log_e cos x

Differentiate the implicit functions x^2 sin y - e^(2y) cos x = 3x^2 + 2x - 5 w…

If y = e^(sin 2x) / cos 2x, find dy/dx

Which of the following equation is not correct?

If y = e^(2x) log (x+6), find dy/dx

Evaluate ∫ (e^(2x) + e^(-2x)) / (e^(2x) - e^(-2x)) dx

Find dy/dx if 3x^2 y + xy^2 = 5

Evaluate ∫ dx / (x^2 + 4x + 7)