MCQ
$\int_{}^{} {(1 + 2x + 3{x^2} + 4{x^3} + ......)\;dx = } $
- A${(1 + x)^{ - 1}} + c$
- ✓${(1 - x)^{ - 1}} + c$
- C${(1 - x)^{ - 1}} - 1 + c$
- DNone of these
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Statement$-1$ If $f R \rightarrow R$ and $c \in R$ is such that $f$ is increasing in $(c - \delta , c)$ and $f$ is decreasing in $(c, c + \delta )$ then $f$ has a local maximum at $c$. Where $\delta$ is a sufficiently small positive quantity.
Statement $-2$ Let $f (a, b) \rightarrow \,R, c \in (a, b)$. Then $f$ can not have both a local maximum and a point of inflection at $x = c.$
Statement $-3 $ The function $f (x) = x^2 | x |$ is twice differentiable at $x = 0.$
Statement $-4$ Let $f [c - 1, c + 1] \rightarrow [a, b]$ be bijective map such that $f$ is differentiable at $c$ then $f^{-1}$ is also differentiable at $f (c)$.
(where $p$ is a constant)