MCQ
If $f(x) = x, - 1 \le x \le 1$, then function $f(x)$ is
  • Increasing
  • B
    Decreasing
  • C
    Stationary
  • D
    Discontinuous

Answer

Correct option: A.
Increasing
a
(a) It is always increasing.

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  1. y = vx

  2. v = yx

  3. x = vy

  4. x = v

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$PROPERTY 1$ if $\lim _{ h \rightarrow 0} \frac{ f ( h )- f (0)}{\sqrt{| h |}}$ exists and is finite, and $PROPERTY 2$ if $\lim _{h \rightarrow 0} \frac{f(h)-f(0)}{h^2}$ exists and is finite.

Then which of the following options is/are correct ?

$(1)$ $f(x)=x|x|$ has $PROPERTY$ $2$  $(2)$ $f(x)=x^{2 / 3}$ has $PROPERTY$ $1$  $(3)$ $f(x)=\sin x$ has $PROPERTY$ $2$  $(4)$ $f(x)=|x|$ has $PROPERTY$ $1$

$\int_{}^{} {{e^{{x^2}}}x\;dx} $ is equal to