The correct option is D does not exist L.H.L.=lim_x→(π2)^ tan x=+∞ R.H.L.=lim_x→(π2)^+tan x= ∞ Clearly left hand limit ≠ right hand limit.Hence ...

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Existence of Limit

limx→π/2tan x...

Question

$lim x \to \frac{π}{2} tan x =$

1

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0

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\frac{1}{π}

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does not exist

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Solution

The correct option is D does not exist
$L.H.L. = lim x \to {(\frac{π}{2})}^{-} tan x = + \infty$
$R.H.L. = lim x \to {(\frac{π}{2})}^{+} tan x = - \infty$
Clearly left hand limit $\neq$ right hand limit.
Hence given limit does not exist.

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