Q80.Let S = {(λ, μ) ∈R × R : f(t) = (|λ|et −μ) ⋅sin(2|t|), t ∈R, is a differentiable function } . Then S is a subest of? (1) R × [0, ∞) (2) (−∞, 0) × R (3) [0, ∞) × R (4) R × (−∞, 0)
What This Question Tests
This question assesses the condition for a product of functions to be differentiable everywhere, especially when one factor involves an absolute value and is not differentiable at a specific point.
Concepts Tested
Formulas Used
f(x) differentiable at x=a if lim h->0 [f(a+h)-f(a)]/h exists
📚 NCERT Sections This Tests
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.
9.18 — For Fixed Distance S Between Object And Screen, The Lens Equation
Physics Class 12 · Chapter 9
9.18 For fixed distance s between object and screen, the lens equation does not give a real solution for u or v if f is greater than s/4. Therefore, fmax = 0.75 m.
📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Differentiability of functions
- Year
- 2018
- Shift
- 15 Apr Shift 1 Online
- Q Number
- Q80
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 5: Continuity and Differentiability
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