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1983

JEE Main 1983 Mathematics question on Limits Continuity and Differentiability

The function f(x)=log⁡(1+ax)−log⁡(1−bx)xf(x) = \dfrac{\log(1 + ax) - \log(1 - bx)}{x} is not defined at x=0x = 0. The value which should be assigned to ff at x=0x = 0, so that it is continuous at x=0x = 0, is
  1. A.
    a−ba - b
  2. B.
    a+ba + b
  3. C.
    log⁡a+log⁡b\log a + \log b
  4. D.
    None of these
Show answer and solution

Correct option: B

Solution

Using the standard limit lim(x→0) log(1+t)/t = 1, we get lim(x→0) [log(1+ax) - log(1-bx)]/x = lim(x→0) [log(1+ax)/(ax) · a + log(1-bx)/(-bx) · b] = a·1 + b·1 = a + b. So f(0) must be assigned the value a + b.

[1983]

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