Solveeit Logo

Question

Question: \(g(x) = x^{2} + x - 2\) is equal to (where a is a constant)...

g(x)=x2+x2g(x) = x^{2} + x - 2 is equal to (where a is a

constant)

A

esin2y

B

sin 2y esin2y

C

0

D

None of these

Answer

esin2y

Explanation

Solution

limx0yaesin2t+ax+yesin2tdtx\lim _ { x \rightarrow 0 } \frac { \int _ { y } ^ { a } e ^ { \sin ^ { 2 } t } + \int _ { a } ^ { x + y } e ^ { \sin ^ { 2 } t } d t } { x }

=

= limx0esin2(x+y)101=esin2y\lim _ { x \rightarrow 0 } \frac { e ^ { \sin ^ { 2 } ( x + y ) } \cdot 1 - 0 } { 1 } = e ^ { \sin ^ { 2 } y }