Skip to content

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

The value of the limit of (3x² + 5x)/(2x² − 7) as x tends to infinity is:

Both numerator and denominator are quadratics, so the limit at infinity is the ratio of the leading coefficients. Dividing through by x² leaves (3 + 5/x)/(2 − 7/x²), which approaches 3/2 as x grows without bound. The limit is therefore 3/2.

  1. A3/2Correct
  2. B0
  3. C5/7
  4. D∞

Explanation

Divide numerator and denominator by x² to get (3 + 5/x)/(2 − 7/x²). As x → ∞, the terms 5/x and 7/x² tend to 0, so the limit is 3/2. Answer ∞ is wrong because both polynomials have the same degree, so the ratio of leading coefficients is the limit.

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