UPSC Exam > UPSC Questions > Let sm,n=m^3-n^3/m^3+n^3,m,n below to N. Then...
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Let sm,n=m^3-n^3/m^3+n^3,m,n below to N. Then the value of the limit lim n desk to infinity lim m desk to infinity sm,n is A.0 B.1 C.3 D.2?
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Let sm,n=m^3-n^3/m^3+n^3,m,n below to N. Then the value of the limit l...
Understanding the Problem
- We are given the expression sm,n = (m^3 - n^3) / (m^3 + n^3), where m and n are natural numbers.
- We need to find the limit of sm,n as both m and n tend to infinity.
Solution
Step 1: Simplifying the Expression
- Let's simplify the expression sm,n = (m^3 - n^3) / (m^3 + n^3).
- Factorizing the numerator and denominator, we get sm,n = [(m - n)(m^2 + mn + n^2)] / [(m + n)(m^2 - mn + n^2)].
- Canceling out common terms, we get sm,n = (1 - n/m) / (1 + n/m).
Step 2: Finding the Limit
- As m and n tend to infinity, n/m tends to 0.
- Therefore, the limit of sm,n as m and n tend to infinity is (1 - 0) / (1 + 0) = 1.
Conclusion
- The value of the limit lim n desk to infinity lim m desk to infinity sm,n is 1.
- So, the correct answer is B. 1.
- We are given the expression sm,n = (m^3 - n^3) / (m^3 + n^3), where m and n are natural numbers.
- We need to find the limit of sm,n as both m and n tend to infinity.
Solution
Step 1: Simplifying the Expression
- Let's simplify the expression sm,n = (m^3 - n^3) / (m^3 + n^3).
- Factorizing the numerator and denominator, we get sm,n = [(m - n)(m^2 + mn + n^2)] / [(m + n)(m^2 - mn + n^2)].
- Canceling out common terms, we get sm,n = (1 - n/m) / (1 + n/m).
Step 2: Finding the Limit
- As m and n tend to infinity, n/m tends to 0.
- Therefore, the limit of sm,n as m and n tend to infinity is (1 - 0) / (1 + 0) = 1.
Conclusion
- The value of the limit lim n desk to infinity lim m desk to infinity sm,n is 1.
- So, the correct answer is B. 1.
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Let sm,n=m^3-n^3/m^3+n^3,m,n below to N. Then the value of the limit lim n desk to infinity lim m desk to infinity sm,n is A.0 B.1 C.3 D.2?
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Let sm,n=m^3-n^3/m^3+n^3,m,n below to N. Then the value of the limit lim n desk to infinity lim m desk to infinity sm,n is A.0 B.1 C.3 D.2? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Let sm,n=m^3-n^3/m^3+n^3,m,n below to N. Then the value of the limit lim n desk to infinity lim m desk to infinity sm,n is A.0 B.1 C.3 D.2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let sm,n=m^3-n^3/m^3+n^3,m,n below to N. Then the value of the limit lim n desk to infinity lim m desk to infinity sm,n is A.0 B.1 C.3 D.2?.
Let sm,n=m^3-n^3/m^3+n^3,m,n below to N. Then the value of the limit lim n desk to infinity lim m desk to infinity sm,n is A.0 B.1 C.3 D.2? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Let sm,n=m^3-n^3/m^3+n^3,m,n below to N. Then the value of the limit lim n desk to infinity lim m desk to infinity sm,n is A.0 B.1 C.3 D.2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let sm,n=m^3-n^3/m^3+n^3,m,n below to N. Then the value of the limit lim n desk to infinity lim m desk to infinity sm,n is A.0 B.1 C.3 D.2?.
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