Class XII ISC Chapter Continuity and Differentiability
Explore our extensive collection of Continuity and Differentiability questions, tailored for class 12 students following the ISC curriculum. This topic is vital for understanding how to optimize a particular outcome given certain constraints. Our practice questions cover various aspects of Linear Programming, including formulating linear inequalities, graphical methods, and finding optimal solutions. Whether you're looking to strengthen your problem-solving skills or prepare for your exams, these questions provide the perfect resource to master Continuity and Differentiability concepts with ease.
class 12 C&D exercise5-2
Continuity & Differentiability
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Q1 Is the function f defined by f(x) = [x] continuous at
(i) x = 0
(ii) x = 1
(iii) x = 1/2
Examine the following (2 to 7) functions for continuity :
Q3 (i) If f(x) =
2x - 1 if x<2 3 / 2 x , if x ≥ 2
(ii) If f(x) = sinx - cosx , if x≠0 -1, if x = 0
| 2x - 1 if x<2 |
| 3 / 2 x , if x ≥ 2 |
| sinx - cosx , if x≠0 |
| -1, if x = 0 |
Q7 Is the function f defined by f(x)= x10 - 1, if x ≤ 1 x2, if x > 1
(ii) f(x) = tan x, 0 ≤ x ≤ π/4.
| x10 - 1, if x ≤ 1 |
| x2, if x > 1 |
Locate the points of discontinuity (if any) of the following (8 to 10) functions :
Q9 (i) f(x)= x4 - 16 / x - 2 , x ≠ 2 16, x = 2
(ii) f(x)= sin3x / x + cosx , x > 0 4 - 3x, x ≤ 0
| x4 - 16 / x - 2 , x ≠ 2 |
| 16, x = 2 |
| sin3x / x + cosx , x > 0 |
| 4 - 3x, x ≤ 0 |
Q10 (i) f(x) = 2x , if x < 0 0, if 0 ≤ x ≤ 1 4x, if x > 1
(ii) f(x) = x + 2 , x ≤ 1 x - 2, 1 < x < 2 0, x ≥ 2
| 2x , if x < 0 |
| 0, if 0 ≤ x ≤ 1 |
| 4x, if x > 1 |
| x + 2 , x ≤ 1 |
| x - 2, 1 < x < 2 |
| 0, x ≥ 2 |
Q11 Find the value of the constant k so that the function f defined by
f(x) = kx2 , x ≤ 2 x - 3, x > 2
continuous at x = 0.
| kx2 , x ≤ 2 |
| x - 3, x > 2 |
Q12 For what choice of a and b are the following functions continuous :
(i) f(x) = -5, if x ≤ -1 ax - b, if -1 < x < 3 7, if x ≥ 3
(ii) f(x) = x2 , x ≤ 0 ax + b, x > 0
| -5, if x ≤ -1 |
| ax - b, if -1 < x < 3 |
| 7, if x ≥ 3 |
| x2 , x ≤ 0 |
| ax + b, x > 0 |
