Class 12 ISC Maths Continuity & Differentiability Board Questions

Continuity and differentiability in class 12 is about, if a function f(x) is said to be continuous at a point x = a, if Left hand limit of f(x) at(x = a) = Right hand limit of f(x) at (x = a) = Value of f(x) at (x = a) i.e. if at x = a, LHL = RHL = f(a)

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Important Questions

Board Questions

Cont. and Diff. BoardsQuestions

2016

Q1 Verify the conditions of Rolle's Theorem for the following function:
f(x)=log(x²+ 2) — log 3 on [-1, 1]

Find a point in the interval, where the tangent to the curve is parallel to x-axis.

solutions

Q2 Using L'Hospital's Rule, evaluate:

lim_x->0(

1 / x²

cotx / x

)

solutions

2017

Q1 Verify Langrange's mean value theorem for the function:

f(x) = x (l — log x) and find the value of 'c' in the interval [1, 2]

solutions

Q2 Using L'Hospital's Rule, evaluate:

It _{(x --> π/2)} (x tanx - π/4 . sec x)

solutions

2018

Q1 (a) Show that the function f(x) =

x²,x≤1

1 / x

,x>1

is continuous at x = 1 but not differentiable

OR
(b) Verify Rolle's theorem for the following function: f (x) = e^-x sin x on [0, π]

solutions

Q2 Find the value of constant 'k' so that the function f(x) defined as: f(x)= f(x) =

x²-2x-3 / x+1

,x ≠ -1

k,x=-1

is continuous at x=-1

solutions

2019

Q1 (a) Show that the functionf(x) = |x—4|, x ∈ R is continuous, but not differentiable at x = 4.

OR
(b) Verify the Lagrange's mean value theorem for the ftnction:
f(x)=x+ 1/x in the interval [1, 3]

solutions