Bihar Board 12th Maths Important Questions Long Answer Type Part 3 in English

Bihar Board 12th Maths Important Questions Long Answer Type Part 3 in English

BSEB 12th Maths Important Questions Long Answer Type Part 3 in English

Continuity and Differentiability

Question 1.
Find the relation b/w a & b so that the function (x) defined by

= 3b + 3
∵ f(x) is continuous at x = 3.
∴ LHX =RHL= f(3)
∵ 3a + b = 3b + 3′
⇒ 3a + b – 3b = 3
⇒ 3a – 2b = 3

Question 2.

Question 3.

Question 4.

∵ L.H.S = R.H.S at x = 3
∴ f(x) is differentiable at x = 3 and f'(3) = 12.

Question 5.
For whal choice of a & b is the function :

Solution:
It is given that f(x) is differentiable at x = c
∴ f(x) will be continuous of x = c.

f(c) = c²
∵ L.H.S. = R.H.S.=/(c)
∴ c² = ac + b = c²
Now f(x) is differentiable at x = c

∴ L.H.S. = R.H.S.
∴ a = 2c …(ii)
from eqn. (i) & eqn. (ii)
c² = 2c² + b
=> b = c² & a = 2c

Question 6.

or, 5 = b ⇒ B = 5
From eqn. (i),
a – 5 + 2 = 0
or, a – 3 = 0
∴ a = 3

Differentiation

Question 1.
Differentiate the following functions w.r. to x from 1st principles.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.

Question 11.

Question 12.

Question 13.

Question 14.