Chapter Study

BCA Semester 2 – Mathematics II – Unit 1: Limits and Continuity (6Hrs)

Comprehensive questions and detailed answers for Unit 1: Limits and Continuity (6Hrs). Perfect for exam preparation and concept clarity.

Questions

Marks

A function $f(x)$ is defined as

f(x)= \begin{cases} 2x+3, & -\dfrac{3}{2} \le x < 0 \\ 3-2x, & 0 \le x \le \dfrac{3}{2} \\ -3-2x, & x > \dfrac{3}{2} \end{cases}

Show that $f(x)$ is continuous at $x=0$ and discontinuous at $x=\dfrac{3}{2}$ .

MediumNumerical5 marks2022(TU FOHSS Final)

Evaluate the limit:

\lim_{x \to \theta} \frac{x\cos\theta - \theta\cos x}{x - \theta}

MediumNumerical5 marks2023(TU FOHSS Final)

Define Indeterminate forms.

MediumNumerical5 marks2024(TU FOHSS Final)

Evaluate:

\lim_{x \to 0} \frac{\tan x - \sin x}{x^3}

MediumNumerical5 marks2024(TU FOHSS Final)

A function $f(x)$ is defined as

f(x)= \begin{cases} 2x+3, & \text{for } x<1 \\ 4, & \text{for } x=1 \\ 6x-1, & \text{for } x>1 \end{cases}

Is the function $f(x)$ continuous at $x=1$ ?
If not, how can you make it continuous at $x=1$ ?

MediumTHEORY5 marks2024(TU FOHSS Final)

Evaluate

\lim_{x \to \frac{\pi}{4}} \frac{\sin x - \cos x}{x - \frac{\pi}{4}}

MediumTHEORY5 marks2024(TU FOHSS Final)

Showing 6 questions