Objective Questions

What is the value of the trigonometric limit: \( \lim_{x \to 0} \frac{\sin x}{x…

What is the value of the trigonometric limit: \( \lim_{x \to 0} \frac{\tan x}{x…

L'Hospital's Rule can be applied when the limit of \( \frac{f(x)}{g(x)} \) resu…

Evaluate the limit of \( \frac{\cos x - 1}{x} \) as \( x \) approaches 0.

Evaluate the limit of \( \frac{\tan x}{\sin 2x} \) as \( x \) approaches \( \pi…

Evaluate the limit of \( x^2 + 2x + 5 \) as \( x \) tends to 3.

Evaluate the limit of \( \frac{x^2 - 4}{x^2 + x - 6} \) as \( x \) tends to 2.

Evaluate the limit of \( \frac{4x^2 + 3x - 1}{2x^2 + x - 2} \) as \( x \) tends…

Evaluate the limit of \( \frac{4x^2 + 2x - 1}{3x^2 + x - 2} \) as \( x \) tends…

Evaluate the limit of \( \frac{(x + 1)(2x + 1)(x - 3)}{x^3} \) as \( x \) tends…

What is the limit of \( \frac{1 - \cos x}{x} \) as \( x \) tends to 0?

Evaluate the limit of \( \frac{\tan 3x}{x} \) as \( x \) tends to 0.

What is the limit of \( \frac{\sqrt{x + h} - \sqrt{x}}{h} \) as \( h \) tends t…

Evaluate the limit of \( \frac{\sqrt{x^2 + 9} - 3}{x^2} \) as \( x \) tends to …

Evaluate the limit of \( \frac{3x^2 - 12}{x - 2} \) as \( x \) tends to 2.

According to the provided formulas, what is the limit of \( \frac{1 - \cos ax}{…

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

Evaluate the limit of \( \frac{e^{x-1} - x}{(x - 1)^2} \) as \( x \) tends to 1.

Evaluate the limit of \( \frac{e^{3x}}{x^2} \) as \( x \) tends to infinity.

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

Evaluate the limit of \( \frac{\ln x}{\sqrt{x}} \) as \( x \) tends to infinity.

Evaluate the limit of \( \frac{1 - x + \ln x}{x^3 - 3x + 2} \) as \( x \) tends…

Evaluate the limit of \( \frac{\ln(2 + e^x)}{3x} \) as \( x \) tends to infinit…

Evaluate the limit of \( \frac{x^3 - x^2 - x - 2}{x^3 - 8} \) as \( x \) tends …

Evaluate the limit of \( \frac{x^2 - x - 6}{x^2 - 9} \) as \( x \) tends to 3.

Evaluate the limit of \( \frac{x}{x+3} + \frac{x-3}{x^2-9} \) as \( x \) tends …

Evaluate the limit of \( \frac{3 - x}{6} \) as \( x \) approaches 3.

Evaluate the limit of \( \frac{3x - 7}{2x - 1} \) as \( x \) approaches \( \fra…

Evaluate the limit of \( \frac{\sqrt{4+x} - 2}{x} \) as \( x \) tends to 0.

Evaluate the limit of \( \frac{e^{2-x} - 1}{x - 2} \) as \( x \) tends to 2.

Evaluate the limit of \( \frac{x^n - y^n}{x - y} \) as \( x \) approaches \( y …

Evaluate the limit of \( \frac{x + 1}{\sqrt{x^2 + 3x - 2}} \) as \( x \) tends …

Evaluate the limit of \( \frac{2x^2 - 3}{5x^2 - x} \) as \( x \) tends to infin…

Evaluate the limit of \( \frac{3x^2 + 3ax - 2a^2}{x^2 - a^2} \) as \( x \) tend…

Evaluate the limit of \( \frac{\sqrt{x} - 2}{x - 4} \) as \( x \) approaches 4.

Evaluate the limit of \( \frac{3x^4 + 6x}{x^2 + 4} \) as \( x \) tends to infin…

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

Evaluate the limit of \( \frac{3 - \sqrt{x}}{9 - x} \) as \( x \) approaches 9.

Evaluate the limit of \( \frac{(x+3)(2x-1)}{x^2 + x - 2} \) as \( x \) approach…

Evaluate the limit of \( \frac{x^2 + \sqrt{x} + 2}{x^2 - 11} \) as \( x \) appr…

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

Evaluate the limit of \( \frac{e^x + e^{-x}}{e^x - e^{-x}} \) as \( x \) tends …

What is the limit of \( \frac{e^{\cos x} + e^{\sin 2x}}{e^{\cos x} + e^{-\sin 2…

Evaluate the limit of \( \frac{\cos x - \sin 2x}{x^2} \) as \( x \) approaches …

Evaluate the limit of \( \frac{\ln(e^{3x} - 5x)}{x} \) as \( x \) approaches 0.

Evaluate the limit of \( \frac{\ln(\cos 3x)}{\ln(\cos 2x)} \) as \( x \) approa…

Evaluate the limit of \( \frac{e^{1/x} - e^{-1/x}}{e^{1/x} + e^{-1/x}} \) as \(…

Evaluate the limit of \( \frac{5 - \sqrt{x}}{x - 25} \) as \( x \) tends to 25.

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

Evaluate the limit of \( \frac{8^x - 2^x}{4x} \) as \( x \) tends to 0.

Evaluate the limit of \( \frac{\ln(2 + x)}{x + 1} \) as \( x \) tends to -1.

Evaluate the limit of \( \frac{e^x - 1}{\tan 2x} \) as \( x \) tends to 0.

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

Evaluate the limit of \( \frac{\ln(\sec 2x)}{\ln(\sec x)} \) as \( x \) tends t…

Evaluate the limit of \( \frac{4}{x^2 - 4} - \frac{1}{x-2} \) as \( x \) tends …

Evaluate the limit of \( \frac{\cos 2x - \cos x}{\sin^2 x} \) as \( x \) tends …

What is the limit of \( \frac{x^2 - 4}{x - 2} \) as \( x \) approaches 2 using …

In Example 5, what was the final result of evaluating the limit as \( x \) tend…

In Model Question 19, what is the derivative of the denominator \( x^3 - 3x + 2…

Evaluate the limit of \( \frac{x^3 - x^2 - x + 1}{x^3 - 2x^2 + x} \) as \( x \)…

What is the limit of \( k \) as \( x \) approaches \( a \), where \( k \) is an…

Evaluate the limit of \( \frac{x^2 - 1}{x - 1} \) as \( x \) approaches 1.

Evaluate the limit of \( \frac{x(x+1)}{2\sqrt{9x^4 + 1}} \) as \( x \) tends to…

What is the limit of \( [f(x)]^n \) as \( x \) approaches \( a \)?

Evaluate the limit of \( \frac{2x + 1}{x - \sin 2x} \) as \( x \) tends to 0.

What is the limit of \( \frac{1 + \sqrt{x+2}}{1 - \sqrt{x+2}} \) as \( x \) ten…

Evaluate the limit of \( \frac{x+3}{x+2} \) as \( x \) tends to infinity.

In the expression \( \frac{x^2-4}{x-2} \), what is the value at \( x=2 \) befor…

Evaluate the limit of \( \frac{\ln x}{x} \) as \( x \) tends to infinity.

What is the limit of \( e^{-x} \) as \( x \) tends to infinity?

Evaluate the limit of \( \frac{\sin 3x}{\sin 2x} \) as \( x \) approaches 0.

What is the limit of \( \frac{1}{x^2} \) as \( x \) tends to 0?

Evaluate the limit of \( \frac{x^2 - 9}{x + 3} \) as \( x \) tends to -3.

If \( f(x) = x^2 \), what is the limit of \( f(x) \) as \( x \) approaches -2?

What is the limit of \( \frac{\sqrt{x} - \sqrt{a}}{x - a} \) as \( x \) approac…

Evaluate the limit of \( \frac{2x + 5}{3x - 1} \) as \( x \) tends to infinity.

What is \( f'(x) \) for \( f(x) = \ln(\sin^2 x) \)?

Derivative of \( y = 8 \cos x + 3 \sin x \) is?

Evaluate \( d/dx(x^6 - 7x^3 - 6x + 4) \).

Find \( f'(x) \) if \( f(x) = x^4 + 2x^{5/2} \).

Derivative of \( y = 1/2 x^{1/3} + 5x \) is?

Find \( dy/dx \) for \( y = (8x + 1/2)^2 \).

Evaluate \( d/dt(7t^2 - 4t^{1/2}) \).

Differentiate \( y = 6x^{-3/2} + 4x + 1 \).

Find \( d/dw(w^2 - w^{-3/2}) \).

Evaluate the limit of \( \frac{x - 4}{\sqrt{x} - 2} \) as \( x \) tends to 4.

A two Farad and a four Farad capacitor are connected in series. What single cap…

Gauss's law can be applied to the following except:

A transformer has 200 turns in its primary coil and 600 turns in its secondary …

A magnetic induction of 20μT is applied to a long straight current carrying wir…

A metal ball of 10kg with 5 C charges is moving perpendicular to the magnetic f…

Which of following circuit element stores energy in electromagnetic field?

Two point charges are 6 cm apart. They are moved to a new separation of 3 cm. B…

Capacitance 15F and 5F are connected in parallel across a 20V battery. What is …

A parallel plate air capacitor with no dielectric between the plates is connect…

A galvanometer has spring constant 'k', a magnetic field 'B' and deflection ang…

Which of the following copper conductor that has the least resistance is:

Electric field is steepest in the direction in which the potential:

A two farad and a four Farad capacitor are connected in series. What single cap…

A magnetic induction of 20µT is applied to long straight current carrying wire …