Skip to content

CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity

The value of lim(x → 0) (a^x − b^x)/x, where a, b > 0, is:

The limit is log a − log b, which equals the natural log of a/b. Subtract and add 1 to split the expression into (a^x − 1)/x minus (b^x − 1)/x, then apply the standard limit (c^x − 1)/x → log c to each part.

  1. Alog a − log bCorrect
  2. B(log a)(log b)
  3. Clog a + log b
  4. Da − b

Explanation

Write (a^x − b^x)/x = (a^x − 1)/x − (b^x − 1)/x. By the standard limit lim(a^x − 1)/x = log a (natural log), this tends to log a − log b, i.e. log(a/b). Option a − b results from treating the expression as a simple difference without the logarithm.

Did you get it right without looking?

One question tells you little. A timed set on Sets, Relations and Functions, Limits and Continuity shows your real accuracy, how long you take and where you lose marks.

Practise Sets, Relations and Functions, Limits and ContinuityFree diagnostic mock

More Sets, Relations and Functions, Limits and Continuity questions