Question

The positive integer which is just greater than $(1+0.0001{)}^{1000}$ is:

• A. $3$
• B. $4$
• C. $5$
• D. $2$

Answer 1

The correct option is D $2$

Here, $f\left(x\right)=x^{1000}$

For $x=1$, $f\left(x\right)=1^{1000}=1$

We know, $f(x+\Delta x)=f\left(x\right)+\Delta x{f}^{\prime }\left(x\right)$

Now, $f^{\prime }\left(x\right)=1000x^{999}$

So, $f^{\prime }\left(10\right)=1000$

Hence, $f(x+\Delta x)=1+0.0001\times \left(1000\right)=2$ (approx.)

Hence $D$ is correct.