MCQ
If $y=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\ldots .$. , then $\frac{d y}{d x}=$ _________ .
- ✓$y$
- B$y-1$
- C$0$
- DDoes not exist
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$f(x)=\left\{\begin{array}{cc}e^{\min \left[x^2, x-[x]\right\}}, & x \in[0,1) \\e^{\left[x-\log _e x\right]}, & x \in[1,2]\end{array}\right.$
where [t] denotes the greatest integer less than or equal to $t$. Then the value of the integral $\int \limits_0^2 x f(x) d x$ is