Question

Find the solution for \(\lim_{x\to 0}⁡ \frac{ax}{ax+x}.\)

(a) 0

(b) a

(c) 1

(d) \(\frac{a}{a+1}\)

The question was posed to me during an online exam.

Enquiry is from First Order Nonlinear Differential Equations in chapter Ordinary Differential Equations – First Order & First Degree of Engineering Mathematics

Answer 1

The correct option is (d) \(\frac{a}{a+1}\)

For explanation I would say: The given equation can be solved using L-Hospital’s Rule,

\(\frac{d(ax)}{dx}=a,  \frac{d(ax+x)}{dx}=a+1\)

\(\lim_{x\to 0}⁡\frac{ax}{ax+x}    →    \lim_{x\to 0}⁡\frac{a}{a+1}    →    \frac{a}{a+1}\)