Objective Questions

Find the derivative of y = 3 log(x - 1)

Find the derivative of y(x) = log₂ x

Find the gradient of y = (1-cos x) / (1+cos x) at x = π/2

If y = e^(ax²+b), dy/dx is

Given y = (1+x²) / (1-x²), find dy/dx

Obtain ∫(2/(2-3x))dx

Obtain ∫sec x dx

Using the Wallis formula the integral of ∫₀^π/2 cos^3<…

Find the inverse f⁻¹(x) of the function f(x) = (3x+1)/(x-5)<…

If I_n = ∫ cotⁿ x dx, the reduction formula for I_n is:

Obtain the integral ∫ (sin 2x)/(sin x) dx.

Evaluate ∫ Cos(lnx)/x dx

If y = ∫ f(x)dx+C, then f(x)dx is called the -----

If y = ∫f(x)dx + C, then ∫f(x)dx is called the -----

Evaluate ∫ Cos³x dx

Simplify ∫ (4x-5)/(x²-x-2) dx

Evaluate
∫ Cos(ln x) / x dx

If y = ∫ f(x)dx + C, then f(x)dx is called the -----.

The nth term of the Maclaurin series expansion of $\cos 3x$ is

Evaluate $\frac{d}{dx}(3x^2 \cos^{-1}x)$.

Obtain $\int \sin^2 x dx$.

Integrate $\int \sec^2 x \tan x dx$.

Given that $a$ is a positive constant, evaluate $\int_1^{3a} \frac{2x+1}{x} dx$.

Find $\frac{d}{dx}(\text{cosec}^{-1}(5x))$.

Find $\int \frac{dx}{4+9x^2}$.

The Wallis formula for $\int_0^{\frac{\pi}{2}} \sin^n x dx$, where $n \geq 2$ a…

Which of the following option best describes the reduction formula for $V_n = \…

Find $\int \frac{x}{x-1} dx$.

Given the function $f(x-5) = 3x^2 - x + 1$, evaluate $f(x)$.

Given the functions $f(x) = 3x^2-5$ and $g(x) = 5x-1$, evaluate $f(g(x))$.

Given that $y = \frac{x}{2x+5}$, find $\frac{dy}{dx}$.

Find the integral of \(\ln\left(\frac{x}{2}\right)\,dx\)

Given that \(y = \ln(x^3)+\ln(7x)\), find \(\frac{dy}{dx}\).

The \(n^{th}\) term of the Maclaurin series expansion of \(\cos 3x\) is:

Find \(\frac{d}{dx} (3x^2 \cos^{-1}x)\).

Obtain \(\int \sin^2 x\,dx\).

Integrate \(\int \sec^2 x \tan x\,dx\).

Find \(\int \frac{dx}{4+9x^2}\).

Which of the following option best describes the reduction formula for \(V_n = …

Find \(\frac{d}{dx} (\csc^{-1}(5x))\).

Integrate \(\int \frac{x}{x-1}\,dx\).

Given the function \(f(x-5) = 3x^2 - x + 1\), evaluate \(f(x)\).

Given the functions \(f(x) = 3x^2-5\) and \(g(x) = 5x-1\), evaluate \(f(g(x))\).

Given that \(y = \frac{x}{2x+5}\), find \(\frac{dy}{dx}\).

Given that \(x^3 + x + y^3 + 3y = 6\), find \(\frac{dy}{dx}\) at \((1, 1)\).

Evaluate \(\lim_{x\to3} \frac{x^5-243}{x^3-27}\).

The nth term of the Maclaurin series expansion of cos 3x is

d/dx (3x² cos⁻¹x) =...

Integrate ∫sec²x tan x dx

Given that a is a positive constant, evaluate ∫(from a to 3a) (2x+1)/x dx

The derivative of cosec⁻¹(5x) with respect to x is:

Find ∫dx / (4+9x²)

Find ∫ln(x/2) dx

The Wallis formula for ∫(from 0 to π/2) sinⁿx dx, where n ≥ 2 and n is an odd n…

Which of the following option best describes the reduction formula for V_n = ∫c…

Integrate ∫x/(x-1) dx

Given the function f(x-5) = 3x²-x+1, evaluate f(x)

Given the functions f(x) = 3x²-5 and g(x) = 5x-1, evaluate f(g(x)).

Given that y = x/(2x+5). Find dy/dx

Given that x³+x+y³+3y=6. Find dy/dx at (1,1)

Given that x³ + x + y³ + 3y = 6. Find ^dy/_dx at (1, 1)

Which of the following option best describes the reduction formula for V_n<…

Given the functions f(x) = 3x²-5, g(x) = 5x- 1 evaluate f(g(x)).

The Product rule of differentiation formula for the function V = r(x)s(x) is...

lim _x→3 ^(x5-243)/_(x³-27)…

Given the function f(x - 5) = 3x² - x + 1, evaluate f(x)

Find ^d/_dx (cosec⁻¹(5x))

Integrate ∫sec² x tan x dx

Obtain ∫sin² x dx

Find ∫^dx/_(4+9x²)

Given that a is a positive constant, evaluate ∫_a^{2a (…}

Integrate ∫^x/_(x-1) dx

Given that y = ^x/_(2x+5). Find ^dy/_dx

Given that x = a sin t and y = a cos t, what is y'?

Integrate ∫ sec x tan x dx.

Integrate ∫ dx / (x - x ln x).

Integrate ∫ sin² x dx.

Integrate ∫ xeˣ dx.

Given the function y = eˣ, find f(x+h) - f(x).

Evaluate lim _x→0 (sin x / x).

If I_n = ∫ cotⁿ x dx, the reduction formula for I_n is:

Find the area between the curve y = x³ - 6x² + 8x and the x-axis in squa…

Evaluate ∫ sin x cos x dx.

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

Given that x = a sin(t) and y = a cos(t), what is y' (dy/dx)?

Integrate ∫sec(x) tan(x) dx.

Integrate ∫1/(x - xln(x)) dx.

Integrate ∫x eˣ dx.

Evaluate lim (sin(x)/x) as x approaches 0.

Find the first derivative of sec⁻¹(5x) with respect to x.

By Wallis' formula, evaluate ∫₀^π/2 cos⁵(x) sin²(x) dx.

Obtain the integral ∫eˣ / (4+eˣ) dx.

Given that ∫₀^θ 4sin(2x)cos⁴(2x) dx = 4/5, where 0 < θ < π…

Given that ∫₀^θ 5tan(x)sec⁴(x) dx = 15/4, where 0 < θ < π/…

Obtain the integral ∫sec(x) dx.

Evaluate ∫₀^π/4 sec²(x) e^4tan(x) dx.

If f(x) = xe⁻ˣ, find f''(x).

Given that x = a sin t, y = a cos t, find the first derivative y'.

Evaluate the integral ∫sec x tan x dx.

Evaluate the integral ∫xe^x dx.