Q71. (√3x+1+√3x−1) 6 +(√3x+1−√3x−1) 6 lim 6 6 x3 x→∞ (x+√x2−1) +(x−√x2−1) (1) is equal to 272 (2) is equal to 9 (3) does not exist (4) is equal to 27
What This Question Tests
This problem tests the ability to evaluate a complex limit at infinity by using the binomial expansion (or a simplification trick) for the terms in the numerator and denominator after rationalization, requiring careful algebraic manipulation.
Concepts Tested
Formulas Used
(a+b)^n + (a-b)^n = 2 [a^n + nC2 a^(n-2) b^2 + ...]
Approximation for large x
📚 NCERT Sections This Tests
1.27 — If The Solubility Product Of Cus Is 6 × 10–16, Calculate The Maximum Molarity Of
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.
3.17 — During Nuclear Explosion, One Of The Products Is 90Sr With Half-Life Of
Chemistry Class 11 · Chapter 3
3.17 During nuclear explosion, one of the products is 90Sr with half-life of 28.1 years. If 1mg of 90Sr was absorbed in the bones of a newly born baby instead of calcium, how much of it will remain after 10 years and 60 years if it is not lost metabolically.
9.23 — (A) At What Distance Should The Lens Be Held From The Card Sheet In
Physics Class 12 · Chapter 9
9.23 (a) At what distance should the lens be held from the card sheet in Exercise 9.22 in order to view the squares distinctly with the maximum possible magnifying power? (b) What is the magnification in this case? (c) Is the magnification equal to the magnifying power in this case? Explain.
📋 Question Details
- Chapter
- Limits & Continuity
- Topic
- Limits involving binomial expansion/approximation
- Year
- 2023
- Shift
- 31 Jan Shift 2
- Q Number
- Q71
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 13: Limits and Derivatives
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