CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
The value of lim(x → 0) (log(1 + 3x))/(2x), where log is the natural logarithm, is:
The limit is 3/2. Rewrite the expression as (3/2) times log(1 + 3x)/(3x). The standard limit log(1 + h)/h tends to 1 as h tends to 0, so the limit equals 3/2 × 1 = 3/2.
- A3/2Correct
- B2/3
- C3
- D1
Explanation
Use lim(h → 0) log(1 + h)/h = 1. Write log(1 + 3x)/(2x) = (3/2) × log(1 + 3x)/(3x). As x → 0 the second factor tends to 1, so the limit is 3/2. The option 2/3 inverts the ratio of coefficients.
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