Question

50 points:- plzzzzzz solve this question fast.

Answer 1

e to the power -1/6

Explanation: lim x tends to zero , so,

sinx =x−x33!+x55!+x77!+⋯

this is an alternate series and if |x|<1

x−x33!x<sinx<x−x33!+x55!x

limx→0⎛⎝x−x33!x⎞⎠1x2=limx→0(1−x26)1x2

but making y=−x26

limx→0(1−x26)1x2=limy→0((1+y)1y)−16=e−16

Therefore

limx→0⎛⎝x−x33!+x55!x⎞⎠1x2=limx→0(1−x23!+x45!)1x2=e−16

Answer 2

Answer:

e−16

Explanation:

sinx=x−x33!+x55!+x77!+⋯

this is an alternate series and if |x|<1

x−x33!x<sinxx<x−x33!+x55!x

limx→0⎛⎝x−x33!x⎞⎠1x2=limx→0(1−x26)1x2

but making y=−x26

limx→0(1−x26)1x2=limy→0((1+y)1y)−16=e−16

analogously

limx→0⎛⎝x−x33!+x55!x⎞⎠1x2=limx→0(1−x23!+x45!)1x2=e−16