CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
The value of lim(x → 0) (e^(3x) − 1)/x is:
The limit equals 3. Multiply and divide by 3x so the expression becomes 3 times (e^(3x) − 1)/(3x), and the standard limit (e^h − 1)/h → 1 as h → 0 applies. Hence the result is 3 × 1 = 3, not 1.
- A0
- B1
- C3Correct
- D∞
Explanation
Using the standard limit lim(h → 0) (e^h − 1)/h = 1, write (e^(3x) − 1)/x = 3 × (e^(3x) − 1)/(3x). As x → 0, 3x → 0, so the limit is 3 × 1 = 3. The option 1 forgets the factor 3 that comes from the coefficient of x in the exponent.
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