CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
What is the value of lim(x → 0) (log(1 + 4x))/x, where log denotes the natural logarithm?
The limit is 4. Multiply and divide by 4 to get 4 × log(1 + 4x)/(4x). Because log(1 + h)/h tends to 1 as h tends to 0, the whole expression tends to 4 × 1 = 4.
- A1
- B1/4
- C4Correct
- D0
Explanation
Use lim(h → 0) log(1 + h)/h = 1. Write log(1 + 4x)/x = 4 × log(1 + 4x)/(4x). As x → 0, 4x → 0, so the limit is 4 × 1 = 4. Option 1/4 comes from dividing by the coefficient instead of multiplying.
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