Q73.If the function f(x) = , x ≠0 √2−√1+cos x is continuous at x = 0, then the value of a2 is equal to { a loge 2 loge 3 , x = 0 (1) 968 (2) 1152 (3) 746 (4) 1250
What This Question Tests
This problem requires evaluating a limit to ensure continuity at x=0. It involves using standard trigonometric limits, properties of logarithms, and potentially L'Hopital's rule or series expansions.
Concepts Tested
Formulas Used
lim x→c f(x) = f(c)
1 - cos x = 2 sin²(x/2)
lim x→0 sin x / x = 1
loge(1+x) ≈ x for small x
a^x - 1 ≈ x log_e a for small x
📚 NCERT Sections This Tests
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1.3 Define the following terms: (i) Mole fraction (ii) Molality (iii) Molarity (iv) Mass percentage.
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Physics Class 12 · Chapter 12
12.5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
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Chemistry Class 11 · Chapter 1
1.27 If the solubility product of CuS is 6 × 10–16, calculate the maximum molarity of CuS in aqueous solution.
📋 Question Details
- Chapter
- Limits & Continuity
- Topic
- Continuity of a function at a point
- Year
- 2024
- Shift
- 04 Apr Shift 2
- Q Number
- Q73
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 5: Continuity and Differentiability
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