# Continuity And Differentiability Class 12 Maths Chapter 5 Exercise 5.1

## Topics/Questions discussed in this video:

I am discussing about how to check continuity and discontinuity in a graph of a function through limits. I am using my own assignments to explain NCERT Exercise 5.1 Questions as well as Extra (HOTS) question for explanation and CBSE Board exam point of view. You can download assignments and all other material related to maths on my website.

Questions Discussed in this lecture:

1. f(x)=\begin{cases} kx^{2} & \text{ if } x\le 2 \\ 3& \text{ if } x>2 \end{cases}

2. f(x)=\begin{cases} kx+1& \text{ if } , x\le \pi \\ \cos x& \text{ if } , x>\pi \end{cases}

3. f(x)=\begin{cases} kx+1& \text{ if } , x\le 5 \\ 3x-5& \text{ if } , x>5 \end{cases}

4. f(x)=\begin{cases} \frac{x^{2} -2x-3}{x+1} , x\ne -1 \\ k, x=-1 \end{cases}

5. f(x)=\begin{cases} \frac{k\cos x}{\pi -2x} & \text{ if } , x\ne \frac{\pi }{2} \\ 3& \text{ if } , x=\frac{\pi }{2} \end{cases}

6. f(x)=\begin{cases} 5 & \text{ if } , x\le 2 \\ ax+b & \text{ if } , 2<x<10 \\ 21& \text{ if } , x\ge 10 \end{cases}

7. f(x)=\begin{cases} \frac{1-\cos 2x}{2x^{2} }, & \text{ if } x\ne 0 \\ k, & \text{ if } x=0 \end{cases}

8. f(x)=\begin{cases} \frac{log (1+ax)-log (1-bx)}{x}, & \text{ if } x\ne 0 \\ k, & \text{ if } x=0 \end{cases}

9. f(x)=\begin{cases} \frac{sin ^{2} kx}{x^{2} }, & \text{ if } x\ne 0 \\ 1, & \text{ if } x=0 \end{cases}

10. f(x)=\begin{cases} \frac{1-\cos 4x}{x^{2} }, & \text{ if } x<0 \\ k, & x=0 \\ \frac{\sqrt{x} }{\sqrt{16+\sqrt{x} } -4}, & \text{ if } x>0 \end{cases}

11. f(x)=\begin{cases} \frac{x}{|x|+2x^{2} }, & \text{ if } x\ne 0 \\ k, & \text{ if } x=0 \end{cases}

## Agam Sir

Teacher

Ashish Kumar a.k.a Agam Sir has vast experience of 12+ years of teaching Mathematics and Physics. He has skills (academic and vocational) that go with working alongside people, especially young people, their parent(s) and the institutes that works with him. He always seek to be an agent of positive change and progression, a mentor/ trainer/ educator for learners/students, seeing that their needs are ideally met.