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 exercise5-3
Continuity & Differentiability
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Q1 If a function is derivable at a point, is it necessary that it must be continuous at that point?
Q2 If a function is continuous at a point, is it necessary that it must be derivable at that point?
Q9 Examine the following function for continuity at x = 1 and differentiability at x = 2.
f(x)= 5x-4 ,0< x< 1 4x2-3x ,1< x< 2 3x+4 ,x≥2
| 5x-4 ,0< x< 1 |
| 4x2-3x ,1< x< 2 |
| 3x+4 ,x≥2 |
Q10 Show that the function f(x) = 2x — |x| is continuous at x = 0 but not differentiable at x=0.
Q12 If the function f(x) = |x-3| + |x-4|, then show that f is not differentiable at x = 3 and x = 4.
Q13 Show that the function f is continuous at x = 1 for all values of a where
f(x)= ax2+1,x≥1 x+a ,x< 1
Find its right and left hand derivatives at x = 1. Hence, find the condition for the existence of the derivative at x = 1.
| ax2+1,x≥1 |
| x+a ,x< 1 |
