CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
The value of lim (x→0) (e^(3x) − 1)/(5x) is:
The limit is 3/5. Using the standard result that (e^t − 1)/t tends to 1 as t tends to 0, put t = 3x and rewrite the expression as three-fifths times that ratio. The limit is therefore 3/5.
- A3/5Correct
- B5/3
- C0
- D1/5
Explanation
Write the expression as (3/5)·(e^(3x) − 1)/(3x). Since (e^t − 1)/t → 1 as t → 0, with t = 3x, the limit is 3/5. Option 5/3 inverts the constants.
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