Pi/2) ("X" "Tan""X" - Pi/4 . "Sec" "X") - Mathematics | Shaalaa.com" />Pi/2) ("X" "Tan""X" - Pi/4 . "Sec" "X") " />Pi/2) ("X" "Tan""X" - Pi/4 . "Sec" "X")" />
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Using L ‘Hospital’S Rule, Evaluate: Lim_("X"->Pi/2) ("X" "Tan""X" - Pi/4 . "Sec" "X") - Mathematics

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Sum

Using L ‘Hospital’s Rule, evaluate: 

`lim_("x"->pi/2) ("x"  "tan""x" - pi/4 . "sec"  "x")`

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Solution

`lim_("x"->pi/2) ["x"  "tan""x" - pi/4 . "sec"  "x"]` 

`= lim_(x->pi/2)[("x sin x" - pi/4)/"cos x"]`


`= lim_(x->pi/2) [("x cos x" + "sin x".1 - 0)/-"sin x"]`


`= lim_(x->pi/2) = ("x cos x"  +  "sin x")/-"sin x"`


`= (0 + 1)/-1 = -1`

Concept: L' Hospital'S Theorem
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