Evaluate the following limits: `lim_(xrarr(pi)/(2))(sqrt2-sqrt(1+sinx)

1.	Evaluate the following limits: `lim_(xrarr(pi)/(2))(sqrt2-sqrt(1+sinx))/(sqrt2cos^(2)x)`
Answer» Correct Answer - `1/8` Given limit `=lim_(xto(pi)/(2))((sqrt2-sqrt(1+sinx)))/(sqrt2cos^(2)x)xx((sqrt2+sqrt(1+sinx)))/((sqrt2+sqrt(1+sinx)))` `=lim_(xto(pi)/(2))(2-(1+sinx))/(sqrt2(1-sin^(2)x))xx(1)/((sqrt2+sqrt(1+sinx)))` `lim_(x to(pi)/(2))((1-sinx))/(sqrt2(1-sinx)(1+sinx))xx(1)/((sqrt2+sqrt(1+sinx)))` `=(1)/(sqrt2).lim_(xto(pi)/(2))(1)/((1+sinx)(sqrt2+sqrt(1+sinx)))` `=(1)/(sqrt2)xx(1)/(2xx2sqrt2)=1/8.`

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