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

Students can Download Chapter 13 Limits and Derivatives Questions and Answers, Plus One Maths Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

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

Plus One Maths Limits and Derivatives Three Mark Questions and Answers

Question 1.
Evaluate the following: (3 score each)
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 1
Answer:
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 2

Plus One Maths Chapter Wise Questions and Answers Chapter 13 Limits and Derivatives
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 3
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 4

Question 2.
Evaluate the following: (3 score each)
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 5
Answer:
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 6

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

ii) Put x + 1 = y, x → 0, y → 1
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 7

iii) Put 1 – x = y, x → 0, y → 1
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 8
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 9
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 10

Question 3.
Evaluate the following: (3 score each)
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 11
Answer:
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 12
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 13
= 1 × 3 × 1 × 3 = 9
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 14

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

iv) Put π – x = y, x → π, y → 0
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 15
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 16
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 17

vii) Put x – \(\frac{\pi}{2}\) = y, x → \(\frac{\pi}{2}\), y → 0
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 18

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

Question 4.
Evaluate the following: (3 score each)
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 19
Answer:
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 20
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 21
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 22
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 23
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 24
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 25
= \(\frac{1}{1}\) × 1 = 1.

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

Question 5.
Find \(\lim _{x \rightarrow 0} f(x)\) and \(\lim _{x \rightarrow 1}\) f(x) where
f(x) = \(\left\{\begin{array}{cc}{2 x+3,} & {x \leq 0} \\{3(x+1),} & {x>0} \end{array}\right.\).
Answer:
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 26

Question 6.
Find \(\lim _{x \rightarrow 1}\)f(x) where f(x) = \(\left\{\begin{array}{cc}
{x^{2}-1,} & {x \leq 1} \\{-x^{2}-1,} & {x>1}\end{array}\right.\).
Answer:
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 27
Therefore; \(\lim _{x \rightarrow 1^{-}}\)f(x) ≠ \(\lim _{x \rightarrow 1^{-}}\)f(x)
Hence \(\lim _{x \rightarrow 1^{-}}\)f(x) does not exist.

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

Question 7.
Evaluate
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 28
Answer:
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 29

Plus One Maths Limits and Derivatives Practice Problems Questions and Answers

Question 1.
Evaluate the following:(2 score each)
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 30
Answer:
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 31
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 32
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 33

Plus One Maths Chapter Wise Questions and Answers Chapter 13 Limits and Derivatives
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 34
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 35

Question 2.
Find the derivatives of the following: (2 score each)

  1. y = (x – d)(x – b)
  2. y = (ax2 + b)2
  3. y = \(\frac{x-a}{x-b}\)
  4. y = x-3(5 + 3x)

Answer:
1.
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 36
= (x – a) × 1 + (x – b) × 1
= x – a + x – b = 2x – a – b

2. y = a2x4 + b2 + 2abx2
\(\frac{d y}{d x}\) = 4a2x3 + 4abx.

3.
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 37

4. y = 5x-3 + 3x-2
\(\frac{d y}{d x}\) = 5(-3)x-3-1 + 3(-2)x-2-1
= -15x-4 – 6x-3

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

Question 3.
Find the derivatives of the following: (3 score each)
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 38
Answer:
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 39
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 40
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 41
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 42

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

Question 4.
If xy = c2 , prove that x2 \(\frac{d y}{d x}\) + c2 = 0.
Answer:
xy = c2 ⇒ y = \(\frac{c^{2}}{x}\)
Differentiating with respect to x;
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 43

Question 5.
Evaluate: \(\lim _{x \rightarrow 0} \frac{(x+5)^{2}-25}{x}\).
Answer:
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 44

Question 6.
Find the derivative of f(x) = x sin x.
Answer:
f'(x) = x × cosx + sin x × 1 = xcosx + sinx.

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

Question 7.
Find the derivative of f(x) = \(\frac{\sin x}{x}\).
Answer:
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 45

Question 8.
Evaluate \(\lim _{x \rightarrow 0} \frac{\sin a x}{b x}\).
Answer:
Plus One Maths Limits and Derivatives Three Mark Questions and Answers 46

Leave a Comment