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CBSE - Class 11 > Mathematics > Limits and Derivatives Worksheets

Free CBSE - Class 11 Mathematics - Limits and Derivatives worksheets

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Here is a Sample Worksheet for you to Practice. Download this worksheet to see the answers.

1.

Fill in the blanks 

2.
If $f(x) = \begin{cases} \frac{sin[x]}{[x]} & [x] \neq 0 \\ 0 & [x]=0 \end{cases}$, where [.] denotes the greatest integer function, then $lim_{x->0} f(x)$ is equal to
1. 1 2. 0 3. –1 4. None of these
3.
$lim_{x->0} \frac{|sin(x)|}{x}$ is
1. 1 2. –1 3. does not exist 4. None of these
4.
Let $ f(x) = \begin{cases} x^2-1, & 0 < x < 2 \\ 2x+3, & 2 \leq x < 3 \end{cases} $, the quadratic equation whose roots are $lim_{x->-2} f(x)$ and $lim_{x->2^+} f(x)$ is
1. $x^2 – 6x + 9 = 0$ 2. $x^2 – 7x + 8 = 0$ 3. $x^2 – 14x + 49 = 0$ 4. $x^2 – 10x + 21 = 0$
5.
$lim_{x->0} \frac{tan(x) - x}{x^2 tan(x)}$ is
1. 2 2. $\frac{1}{2}$ 3. –$\frac{1}{2}$ 4. $\frac{1}{4}$
6.
Let $f(x) = x – [x]$; $x \in R$, then $f'(\frac{1}{2})$ is
1. $\frac{3}{2}$ 2. 1 3. 0 4. –1
7.
If $y = \sqrt{x} + \frac{1}{\sqrt{x}}$, then $\frac{dy}{dx}$ at x = 1 is
1. 1 2. $\frac{1}{2}$ 3. $\frac{1}{\sqrt{2}}$ 4. 0
8.
If $y = \frac{1-x^2/2}{1+x^2/2}$, then $\frac{dy}{dx}$ is
1. $\frac{-4x}{(1-x^2)^2}$ 2. $\frac{-4x}{1-x^4}$ 3. $\frac{1-x^2}{4x}$ 4. $\frac{-4x}{1-x^2}$
9.
If $y = \frac{sin(x) + cos(x)}{sin(x) - cos(x)}$, then $\frac{dy}{dx}$ at x = 0 is
1. –2 2. 0 3. $\frac{1}{2}$ 4. does not exist
10.
If $y = \frac{sin(x+9)}{cos(x)}$, then $\frac{dy}{dx}$ at x = 0 is
1. cos 9 2. sin 9 3. 0 4. 1
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Chapters in CBSE - Class 11 Mathematics

Mathematics Worksheet Sets Worksheet Relations and Functions Worksheet Trigonometric Functions Worksheet Complex Numbers Worksheet Linear Inequalities Worksheet Permutations and Combinations Worksheet Binomial Theorem Worksheet Sequences and Series Worksheet Straight Lines Worksheet Conic Sections Worksheet Introduction to Three Dimensional Geometry Worksheet Statistics Worksheet Probability Worksheet

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Rahul Verma Limits and Derivatives in Delhi

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