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Published on: 27/08/2019
Continuity and Differentiability
Download CBSE Class 12th Standard CBSE Maths question papers, sample papers, important questions, and previous year solved papers in PDF format. Get free study materials, NCERT solutions, and exam preparation resources for Class 12th Standard CBSE Maths
Questions + Answers key
Take MCQ Maths Test
1.
Write the points of discontinuity of the function f(x) = [x] where [x] denotes the gretest integer function less than or equal to x.
2.
Examine the continuity of the function f(x) = |x|
3.
Check the continuity of the function f(x) = sinx + x2 at x = 0
4.
Check the continuity of the function f (x) = |x| at x = 0
5.
Check the continuity of the function f(x) = {\(\begin{matrix} 1, & if & x\le 0 \\ 2, & if & x>0 \end{matrix}\)
6.
Discuss the continuity of the function defined by f(x) = \(\frac { 1 }{ x } ,\quad x\neq 0\)
7.
State the points of discountinuity for the function \(f(x)= [x]\) in \(-3 < x < 3.\)
8.
Give an example of a function which is continuous at x = 1, but not differentiable at x = 1.
9.
Examine the continuity of the function f (x) = \(\frac { 1 }{ x+3 } , x\ \in \ R\).
10.
Examine the continuity of the function f (x) = x2+5 at x = -1
1.
{All Integers}
2.
{continuous}
3.
{continuous}
4.
{continuous}
5.
{Not continuous}
6.
Continuous at x = a (\(\neq \)0) \(\in \) R.
7.
f(x) = [x] is not continuous for integers.Hence not continuous at x = ±2, ±1, 0
8.
Absolute value function f(x) = Ix - 1I is continuous at x = 1 but not differentiable at x = 1.
9.
For x = -3 function is not defined. Hence, not continuous for x ∈ R.
10.
f( -1 ) = 1 + 5 = 6,
\(\lim _{x \rightarrow-1} f(x)=\lim _{x \rightarrow-1}\left(x^{2}+5\right)=1+5=6 \)
\(\text { As } \lim _{x \rightarrow-1} f(x)=f(-1)\)
Hence, continuous at x = -1.
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