Lim x -2ecos x-1-cos x

Lim_x→π/2 e^cos x 1/cos x lim_x→π/2 e^cos x 1/cos x Let x=π/2+h ⇒ x π/2=h as x →π/2,h→ 0 =lim_x→π/2 e^ sin h 1/ sin h lim_x→π/2e^cos ( π/2+4 ) 1/cos ( ...

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Byju's Answer

Standard XII

Mathematics

Substitution Method to Remove Indeterminate Form

lim x →π/2eco...

Question

${lim}_{x \to \frac{π}{2}} \frac{e^{c o s x} - 1}{c o s x}$

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Solution

${lim}_{x \to \frac{π}{2}} \frac{e^{c o s x} - 1}{c o s x}$

${lim}_{x \to \frac{π}{2}} \frac{e^{c o s x} - 1}{c o s x}$

Let $x = \frac{π}{2} + h \Rightarrow x - \frac{π}{2} = h$

as $x \to \frac{π}{2}, h \to 0$

$= {lim}_{x \to \frac{π}{2}} \frac{e^{- s i n h} - 1}{- s i n h}$

${lim}_{x \to \frac{π}{2}} \frac{e^{c o s} (\frac{π}{2} + 4) - 1}{c o s (\frac{π}{2} + 4)}$

$= 1$

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limx→π2 ecos x−1cos x

limx→π2 ecos x−1cos x limx→π2 ecos x−1cos x Let x=π2+h ⇒x−π2=h as x →π2,h→0 =limx→π2 e−sinh−1−sin h limx→π2ecos(π2+4)−1cos(π2+4) =1

${lim}_{x \to \frac{π}{2}} \frac{e^{c o s x} - 1}{c o s x}$