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 lim 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:
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:
Therefore; \lim _{x \rightarrow 1^{-}}f(x) ≠ \lim _{x \rightarrow 1^{-}}f(x)
Hence \lim _{x \rightarrow 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 = \frac{x-a}{x-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
\frac{d y}{d x} = 4a2x3 + 4abx.
3.
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
Question 3.
Find the derivatives of the following: (3 score each)
Answer:
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;
Question 5.
Evaluate: \lim _{x \rightarrow 0} \frac{(x+5)^{2}-25}{x}.
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) = \frac{\sin x}{x}.
Answer:
Question 8.
Evaluate \lim _{x \rightarrow 0} \frac{\sin a x}{b x}.
Answer: