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CBSE - Class 11 Mathematics Limits and Derivatives Worksheet

If $f(x) = 1 + x + \frac{x^2}{2} + ... + \frac{x^{100}}{100}$, then $f'(1)$ is equal to

a. $\frac{1}{100}$ b. 100 c. does not exist d. 0

This is an intraday chart of Bank Nifty on expiry day. What aspect is so prominent on expiry days (especially the second half)?

The momentum is very high

The trend is clear

The volatility is very high

The volume is very high

Evaluate each of the following limits in Exercises 47 to 53. \n $lim_{x->\pi} \frac{1-sin(\frac{x}{2})}{cos(\frac{x}{2})(cos(\frac{x}{4}) - sin(\frac{x}{4}))}$

Differentiate each of the functions w. r. to x in Exercises 29 to 42. \n $ (sin(x) + cos(x))^2 $

Show that $lim_{x->4} \frac{|x-4|}{x-4}$ does not exists

Evaluate : $lim_{x->0} \frac{sin(x) - 2sin(3x) + sin(5x)}{x}$

Evaluate : $lim_{x->0} \frac{\sqrt[3]{1+x} - \sqrt[3]{1-x}}{x}$

Evaluate : $lim_{x->-3} \frac{x^3 + 27}{x^5 + 243}$

Let $ f(x) = \begin{cases} \frac{k \cos(x)}{\pi - 2x} & \text{when } x \neq \frac{\pi}{2} \\ 3 & \text{when } x = \frac{\pi}{2} \end{cases} $ and if $lim_{x->\frac{\pi}{2}} f(x) = f(\frac{\pi}{2})$, find the value of k.

10.

Differentiate each of the functions w. r. to x in Exercises 29 to 42. \n $ x^2 sin(x) + cos(2x) $

11.

If $lim_{x->1} \frac{x^4-1}{x-1} = lim_{x->k} \frac{x^3 - k^3}{x^2 - k^2}$, then find the value of k.

12.

Fill in the blanks

13.

$lim_{x->\frac{\pi}{4}} \frac{sec^2(x) - 2}{tan(x) - 1}$ is

a. 3 b. 1 c. 0 d. 2

14.

A Trader sold a call on share of strike price Rs 200 and received a premium of Rs 12 from option buyer. What can be his maximum loss of this position.

Rs 200

Rs 188

Rs 12

Ultimated

15.

Evaluate : $lim_{x->0} \frac{1-cos(mx)}{1-cos(nx)}$

16.

Evaluate : $lim_{x->\frac{\pi}{6}} \frac{cot^2(x) - 3}{cosec(x) - 2}$

17.

Differentiate each of the functions with respect to ‘x’ in Exercises 43 to 46 using first principle. \n $ \frac{ax+b}{cx+d} $

18.

$lim_{x->1} \frac{(x+x^2+x^3) - 3}{x-1}$ is

a. $\frac{1}{10}$ b. –$\frac{1}{10}$ c. 1 d. None of these

19.

Fill in the blanks in Exercises 77 to 80. \n if $y = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + ...$, then $\frac{dy}{dx}$ = ______________

20.

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

a. 1 b. 0 c. –1 d. None of these

Worksheet Answers

Option C

13.

14.

Option D

18.

20.

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