The displaystyle limy → a ( sin (y-a/2)) . ( tan (π y/2a)) is

Question

The displaystyle limy → a ( sin (y-a/2)) . ( tan (π y/2a)) is (A) (a/2 π) (B) (2 a/ π) (C) (a/π) (D)  - (a/π)

Tardigrade Admin · Accepted Answer

Let L = displaystyle lim y arrow a ( sin (y-a/2))( tan (π y/2 a)) = displaystyle lim y arrow a ( sin (y-a/2)/ cot (π y)2 a) [(0/0) form ] Using by L'Hospital rule, we get = displaystyle lim y arrow a ((1/2) cos (y-a/2)/-(π)2 a textcosec2 (π y)2 a =((1/2) × 1/-(π)2 a ⋅ 1)=(-a/π)

Q. The $y \to a lim {(sin \frac{y - a}{2}) . (tan \frac{π y}{2 a})}$ is

$\frac{a}{2 π}$

$\frac{2 a}{π}$

$\frac{a}{π}$

$- \frac{a}{π}$

Q. The y→alim​{(sin2y−a​).(tan2aπy​)} is

2πa​

π2a​

πa​

−πa​

Let L=y→alim​{(sin2y−a​)(tan2aπy​)} =y→alim​cot2aπy​sin2y−a​​ [00​ form ] Using by L'Hospital rule, we get =y→alim​−2aπ​<br/><br/>cosec22aπy​21​cos2y−a​​ =−2aπ​⋅121​×1​=π−a​

Q. The $y \to a lim {(sin \frac{y - a}{2}) . (tan \frac{π y}{2 a})}$ is

$\frac{a}{2 π}$

$\frac{2 a}{π}$

$\frac{a}{π}$

$- \frac{a}{π}$