Q80.Let f(x) = { x2−1,−1, 0−2≤x≤x≤2< 0 (1) differentiable at all points (2) not continuous (3) not differentiable at two points (4) not differentiable at one point
What This Question Tests
This question tests the careful application of definitions of continuity and differentiability at the junction point of a piecewise function by comparing left and right limits and derivatives.
Concepts Tested
Formulas Used
lim(x->a-) f(x) = lim(x->a+) f(x) = f(a) for continuity
LHD = RHD for differentiability
📚 NCERT Sections This Tests
1.1 — Define The Term Solution. How Many Types Of Solutions Are Formed? Write Briefly
Chemistry Class 11 · Chapter 1
1.1 Define the term solution. How many types of solutions are formed? Write briefly about each type with an example.
9.15 — Apply Mirror Equation And The Condition:
Physics Class 12 · Chapter 9
9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
📋 Question Details
- Chapter
- Limits & Continuity
- Topic
- Continuity and Differentiability of Piecewise Functions
- Year
- 2019
- Shift
- 11 Jan Shift 1
- Q Number
- Q80
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 5: Continuity and Differentiability
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