Monotonic Function?

Question

Is #tan^-1x# a monotonically increasing function for all #x# belongs to #R# ?

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Answer 1 · 2017-05-06T15:53:12

Yes. See the Explanation.

Let #f(x)=tan^-1x, x in RR.#

#:. f'(x)=1/(1+x^2).#

Now, #AA x in RR, x^2 ge 0 rArr 1+x^2 ge 1.#

# rArr f'(x)=1/(1+x^2) gt 0, aa x in RR.#

We coclude that, #f(x)=tan^-1x, x in RR" is "uarr.#

Answer 2 · 2017-05-06T15:54:32

Yes.

Yes it is, because deriving it

#d/(dx) arctan(x) = 1/(1+x^2) > 0# so

#f(x) = int_a^x (d xi)/(1+ xi^2)# is a monotonically increasing function from #a# to #oo#