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)
Answer:
Question 2.
Evaluate the following: (3 score each)
Answer:
ii) Put x + 1 = y, x → 0, y → 1
iii) Put 1 – x = y, x → 0, y → 1
Question 3.
Evaluate the following: (3 score each)
Answer:
= 1 × 3 × 1 × 3 = 9
iv) Put π – x = y, x → π, y → 0
vii) Put x – π2 = y, x → π2, y → 0
Question 4.
Evaluate the following: (3 score each)
Answer:
= 11 × 1 = 1.
Question 5.
Find limx→0f(x) and limx→1 f(x) where
f(x) = {2x+3,x≤03(x+1),x>0.
Answer:
Question 6.
Find limx→1f(x) where f(x) = {x2−1,x≤1−x2−1,x>1.
Answer:
Therefore; limx→1−f(x) ≠ limx→1−f(x)
Hence limx→1−f(x) does not exist.
Question 7.
Evaluate
Answer:
Plus One Maths Limits and Derivatives Practice Problems Questions and Answers
Question 1.
Evaluate the following:(2 score each)
Answer:
Question 2.
Find the derivatives of the following: (2 score each)
- y = (x – d)(x – b)
- y = (ax2 + b)2
- y = x−ax−b
- y = x-3(5 + 3x)
Answer:
1.
= (x – a) × 1 + (x – b) × 1
= x – a + x – b = 2x – a – b
2. y = a2x4 + b2 + 2abx2
dydx = 4a2x3 + 4abx.
3.
4. y = 5x-3 + 3x-2
dydx = 5(-3)x-3-1 + 3(-2)x-2-1
= -15x-4 – 6x-3
Question 3.
Find the derivatives of the following: (3 score each)
Answer:
Question 4.
If xy = c2 , prove that x2 dydx + c2 = 0.
Answer:
xy = c2 ⇒ y = c2x
Differentiating with respect to x;
Question 5.
Evaluate: limx→0(x+5)2−25x.
Answer:
Question 6.
Find the derivative of f(x) = x sin x.
Answer:
f'(x) = x × cosx + sin x × 1 = xcosx + sinx.
Question 7.
Find the derivative of f(x) = sinxx.
Answer:
Question 8.
Evaluate limx→0sinaxbx.
Answer: