Question

If the function $g(x)$ is defined by $g(x)=\frac{x^{200}}{200}+\frac{x^{199}}{199}+\frac{x^{198}}{198}+.....+\frac{x^2}{2}+x+5$ then $g^{\prime }(0)$ =

• A. 1
• B. 200
• C. 100
• D. 5

Answer 1

Answer: (A)

We have,
$g(x)=\frac{x^{200}}{200}+\frac{x^{199}}{199}+\frac{x^{198}}{198}+\dots +\frac{x^2}{2}+x+5$
$\Rightarrow g^{\prime }(x)=x^{199}+x^{198}+x^{197}+\dots +x+1$
$\Rightarrow g^{\prime }(0)=0+0+0+\dots +0+1=1$