# Ch05. Continuity and Differentiability(Part -2)

## Achievements

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## Certificate

Certificate on successful completion of this course.

The whole chapter Continuity and Differentiability is divided into three courses. This course is the part 2. In this online course, you will learn about differentiability. This course also has assignment that has questions from NCERT Exemplar, R.D. Sharma, board’s question bank etc. Please note, all three courses based on Continuity and Differentiability do not have Rolle’s Theorem, Mean Value Theorem, NCERT Exercise 5.8 and questions based on them in Miscellaneous exercise. The PDF of assignment can be downloaded within the course.

## Course Content

The following list of questions are just meant for reference before purchasing membership. The list might or might not include NCERT Questions as it depends on the chapter/course. Some chapters have NCERT questions combined in the Assignments and some chapters have separate NCERT questions and Assignments. For complete details, please check the index of the course in the "About Course".

### Assignment – 3

Check whether the following functions are differentiable at indicated points:

1. {\displaystyle f(x)=|x|\,\,\text{at }x=0}
2. {\displaystyle f(x)={{x}^{2}}\,\,\text{at}\,\,x=1}
3. {\displaystyle f(x)=x|x|\,\,\text{at}\,\,x=0}
4. {\displaystyle f(x)= \begin{cases} & x-1,x<2 \\   & 2x-3,x\ge 2 \\ \end{cases} \,\,\text{at }x=2}
5. {\displaystyle f(x)= \begin{cases} & {{x}^{2}}\sin \left( \frac{1}{x} \right),x\ne 0 \\  & 0,x=0 \\ \end{cases} \,\,\,\text{at}\,\,x=0}
6. {\displaystyle f(x)=|x-2|\,\,\text{at}\,\,x=2}
7. {\displaystyle f(x)={{x}^{2}}+2x+7\,\,\text{at}\,\,x=3}
8. {\displaystyle f(x)=[x]\,\,\text{at}\,\,x=1} and {\displaystyle x=4}
9. {\displaystyle f(x)= \begin{cases}  & x\,[x],0\le x<2 \\  & (x-1)\,x,2\le x<3 \\ \end{cases} } at x = 2
10. {\displaystyle f(x)= \begin{cases} & {{x}^{2}}\sin \frac{1}{x},x\ne 0 \\  & 0,x=0 \\ \end{cases} } at x = 0
11. Discuss the differentiability of {\displaystyle f(x)=\,|x-1|+|x-2|} .
12. If {\displaystyle f(x)= \begin{cases} & {{x}^{2}}+3x+a,x\le 1 \\  & bx+2,x>1 \\ \end{cases} } is differentiable everywhere, find the values of a and b.
Syllabus medium English Hinglish (Hindi + English) 12 Online learning Self-learning from videos Mathematics