Q86.Let a, b ∈R, b ≠0 . Defined a function, f(x) = tansin2x−sinπ 2x , for x > 0 {a bx3 If f is continuous at x = 0, then 10 −ab is equal to x = 0 is equal to
What This Question Tests
This question tests the continuity of a piecewise function at x=0, requiring the evaluation of the limit using L'Hôpital's rule or standard trigonometric limits and then solving for constants a and b.
Concepts Tested
Formulas Used
lim (x→0) sin(ax)/x = a
lim (x→0) tan(ax)/x = a
L'Hôpital's Rule
📚 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.
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.
2.2 — A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 · Chapter 2
2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
📋 Question Details
- Chapter
- Limits & Continuity
- Topic
- Continuity of piecewise function
- Year
- 2021
- Shift
- 26 Aug Shift 1
- Q Number
- Q86
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 5: Continuity and Differentiability
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