CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
What is the value of lim(x → 0) (e^(5x) − 1)/x?
The limit equals 5. Multiply and divide by 5 so the expression becomes 5 times (e^(5x) − 1)/(5x). Using the standard result that (e^h − 1)/h tends to 1 as h tends to 0, the limit is 5 × 1 = 5.
- A1
- B5Correct
- C0
- D1/5
Explanation
Use the standard limit lim(h → 0) (e^h − 1)/h = 1. Write (e^(5x) − 1)/x = 5 × (e^(5x) − 1)/(5x). As x → 0, 5x → 0, so the limit is 5 × 1 = 5. Option 1 forgets the coefficient 5 in the exponent.
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