question_answer

If x changes from 3 to 3.3, find the approximate change in log e (1 + x).

Answer:

Let \[y={{\log }_{e}}(1+x),\] x = 3 and \[\Delta x=0.3\] Now, \[\frac{dy}{dx}=\frac{1}{1+x}\] \[\therefore \] \[dy={{\left( \frac{dy}{dx} \right)}_{x\,=\,3}}\times \Delta x=\frac{1}{1+3}\times 0.3=\frac{0.3}{4}\] \[=0.075\]