If $$f(x)$$ $$=$$ xsinx and $$g(x)$$ $$=$$ xtan x where $$0$$ < x ≤ $$1$$, then in this interval

Correct option is 3f(x) is an increasing function

Questions

If $f (x) = \frac{x}{\sin x} a n d g (x) = \frac{x}{\tan x} w h e r e 0 < x \leq 1$ , then in this interval

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both f(x) and g(x) are increasing functions

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detailed solution

Correct option is C

f′(x)=sin⁡x−xcos⁡xsin2⁡xg′(x)=tan⁡x−xsec2⁡xtan2⁡x Let u(x)=sin⁡x−xcos⁡x, sothatu ′(x)=xsin⁡x>0 for 0u(0). So f′(x)>0 for 0

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If f(x) = xsinx and g(x) = xtan x where 0 < x ≤ 1, then in this interval

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Ready to Test Your Skills?

free study material

If $f (x) = \frac{x}{\sin x} a n d g (x) = \frac{x}{\tan x} w h e r e 0 < x \leq 1$ , then in this interval