Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives

Kerala State Board New Syllabus Plus One Maths Chapter Wise Previous Questions and Answers Chapter 13 Limits and Derivatives.

Kerala Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives

Plus One Maths Limits and Derivatives 3 Marks Important Questions

Question 1.
Find the derivative of y = tan x from first principles. (MARCH-2010)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 1

Question 2.
Choose the most appropriate answer from those given in the bracket (IMP-2010)
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 2
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 3

Question 3.
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 4
(IMP-2010)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 5

Question 4.
Using the first principle of derivatives, find the derivatives of \(\frac { 1 }{ x }\) (MARCH-2011)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 6

Question 5.
Using the quotient rule find the derivative mof f(x) = cot x (MARCH-2011)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 7

Question 6.
Find the derivatives of the following: (MARCH-2011)
https://i2.wp.com/www.aplustopper.com/wp-content/uploads/2019/06/Plus-One-Maths-Chapter-Wise-Previous-Questions-Chapter-13-Limits-and-Derivatives-8.png?resize=172%2C73&ssl=1
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 9

Question 7.
Prove that (MARCH-2012)
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 10
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 11

Question 8.
Find the derivative of y = cotx from first principles. (MARCH-2012)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 12

Question 9.
i) The value of \(\lim _{x \rightarrow 0} \frac{\sin x}{x}\) (MARCH-2013)
ii) Evaluate \(\lim _{x \rightarrow 0} \frac{\sin 4 x}{3 x}\)
Answer:
i) 1
ii)
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 13

Question 10.
i) The value of \(\lim _{x \rightarrow a} \frac{x^{n}-a^{n}}{x-a}\) (MARCH-2013)
ii) Evaluate \lim _{x \rightarrow 1} \frac{x^{15}-1}{x^{10}-1}
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 14

Question 11.
Find the derivative of f(x) = sin x from the first principle. (MARCH-2013)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 15

Question 12.
Find the derivative of \(\frac{x+\cos x}{\tan x}\) (MARCH-2014)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 16

Question 13.
Find the derivatives of f(x) = sinx using the first principle. (MARCH-2014)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 17

Question 14.
Find the derivative of \(\frac{x^{5}-\cos x}{\sin x}\) using the quotient rule. (MARCH-2014)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 18

Question 15.
Using the first principle, find the derivative of cosx . (IMP-2011)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 19

Question 16.
Find the derivative of \(\frac{\cos x}{2 x+3}\) (IMP-2012)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 20

Plus One Maths Limits and Derivatives 4 Marks Important Questions

Question 1.
Evaluate (MARCH-2010)
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 21
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 22

Question 2.
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 23(MARCH-2011)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 24

Question 3.
Compute the derivative of sec x with respect to x from first principle. (IMP-2010)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 25

Question 4.
Find \(\lim _{x \rightarrow 2} \frac{x^{4}-4 x^{2}}{x^{2}-4}\) (IMP-2011)
ii) If y = sin 2x .Prove that \(\frac{d y}{d x}=\) = 2cos2x
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 26

Question 5.
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 27
(IMP-2011)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 28

Question 6.
Find the derivative of y = cosec x from first principle. (IMP-2012)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 29

Question 7.
Find the derivative of y = cosec x from first principle. (IMP-2012)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 29

Question 8.
Find the derivative of \(\frac{x+1}{x-1}\) from first principle (IMP-2013)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 30
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 31

Question 9.
i) The value of \(\lim _{x \rightarrow 0} \frac{\sin 5 x}{5 x}\) (MARCH-2014)
ii) Evaluate \(\lim _{x \rightarrow 0} \frac{\sin a x}{\sin b x}, a, b \neq 0\)
Answer:
i) 1
ii)
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 32

Plus One Maths Limits and Derivatives 6 Marks Important Questions

Question 1.
Find the derivative of \(\frac{1}{x}\) from first principle. (IMP-2010)
Find the derivative of
(ax + b)n (ax + c)m
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 33

Question 2.
i) Find \(\lim _{x \rightarrow-2} \frac{x^{2}+5 x+6}{x^{2}+3 x+2}\) (IMP-2011)
ii) Find f ‘(x) given f(x) = \(\frac{x^{2}+5 x+6}{x^{2}+3 x+2}\)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 34

Question 3.
i) Evaluate \(\lim _{x \rightarrow 3}\left(\frac{x^{3}-27}{x^{2}-9}\right)\) (MARCH-2012)
ii) Evaluate \(\lim _{x \rightarrow 0} \frac{\tan x-\sin x}{\sin ^{3} x}\)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 35

Question 4.
i) Evaluate \(\lim _{x \rightarrow 0} \frac{\sin 5 x}{\sin 3 x}\) (MARCH-2013)
ii) Find the derivate of y = cosx from the first principle.
Answer:
i)
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 36
ii)
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 19

Question 5.
i) Find the derivative of \(\frac{\sin x}{x+\cos x}\) (MARCH-2014)
ii) Match the following:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 37
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 38
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 39

Question 6.
i) \(\frac{d}{d x}(\tan x)\) = ……… (IMP-2014)
ii) Find the derivative of 3 tan x + 5 sec x
iii) Find the derivative of /(x) = (x² + 1)sinx
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 40
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 41

Question 7.
i) Match the following (MARCH-2015)
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 42
ii) Find the derivative of tanx using first principle.
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 43
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 44

Question 8.
i) Match the following: (MARCH-2015)
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 45
ii)
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 46
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 47

Question 9.
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 48
iii) Using first principles, find the derivative of cos x. (IMP-2015)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 49
iii)

Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 19

Question 10.
i) Derivative of x² – 2 at x = 10 is (IMP-2016)
a) 10
b) 20
c) -10
d) -20
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 50
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 51

Question 11.
i) \(\frac{d}{d x}\left(\frac{x^{n}}{n}\right)\) = ………… (MARCH-2016)
ii) Differentiate \(y=\frac{\sin x}{x+1}\) with respect to x
iii) Use first principles, find the derivative of cosx.
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 52
iii)
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 19

Question 12.
i) \(\frac{d}{d x}(-\sin x)\) = ………….. (MARCH-2016)
ii) Find\(\frac{d y}{d x}\) if \(y=\frac{a}{x^{4}}-\frac{b}{x^{2}}+\cos x\) where a, b are constants.
iii) Using first principles, find the derivative of sinx.
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 53
iii)
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 17

Question 14.
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 54
iii) Using the first principle, find the derivative of cosx (MAY-2017)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 55
iii)
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 19

Question 15.
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 56
(MARCH-2017)
Answer:
i) cos x
ii)
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 60
iii)
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 57

Question 16.
i) \(\lim _{x \rightarrow 0} \frac{e^{\sin x}-1}{x}=\) …….(MARCH-2017)
a) 0
b) 1
c) 2
d) 3
ii) Find
\(\lim _{x \rightarrow 0} \frac{\sqrt{1+x}-1}{x}\)
iii) Find the derivative of f(x) = sin x by using first principal.
Answer:
i) b) 1
ii)
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 58
iii)
Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives 17

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