Q80.Let f : R →R be a function such that |f(x)| ≤x2, for all x ∈R. Then, at x = 0, f is (1) differentiable but not continuous (2) neither continuous nor differentiable (3) continuous as well as differentiable (4) continuous but not differentiable
What This Question Tests
This question tests the understanding of continuity and differentiability at a point, particularly when bounds are given, requiring the application of the Squeeze Theorem.
Concepts Tested
Formulas Used
Definition of continuity: lim(x->a) f(x) = f(a)
Definition of derivative: f'(a) = lim(h->0) [f(a+h) - f(a)]/h
Squeeze Theorem
📚 NCERT Sections This Tests
1.3 — Define The Following Terms:
Chemistry Class 11 · Chapter 1
1.3 Define the following terms: (i) Mole fraction (ii) Molality (iii) Molarity (iv) Mass percentage.
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.
14.2 — Which Of The Statements Given In Exercise 14.1 Is True For P-Type
Physics Class 12 · Chapter 14
14.2 Which of the statements given in Exercise 14.1 is true for p-type semiconductos.
📋 Question Details
- Chapter
- Limits & Continuity
- Topic
- Differentiability
- Year
- 2014
- Shift
- 19 Apr Online
- Q Number
- Q80
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 5: Continuity and Differentiability
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