Question

If x changes from 3 to 3.3, find the approximate change in ${\log }_e(1+x)$.

Answer 1

Let $y={\log }_e(1+x)$

$x=3$ and $△x=0.3$

Now, $\frac{dy}{dx}=\frac{1}{1+x}$

Therefore,

$dy=(\frac{dy}{dx}{)}_{x=3}\times △x=\frac{1}{1+3}\times 0.3=0.075$

$\therefore$Approximate change $=0.075$