To determine

To find: The limit of limx→0sinxx=1.

Answer

The value of limx→0sin5x3x is 53.

Explanation

Result used:

The value of limθ→0sinθθ=1

Calculation:

Compute limx→0sin5x3x.

Divide the numerator and denominator by 5,

limx→0sin5x3x=limx→05⋅sin5x5⋅3x=limx→05⋅sin5x3⋅5x=53(limx→0sin5x5x)

Use the Result stated above and simplify further,

limx→0sin5x3x=53(limx→0sin5x5x)=53(1)=53

Therefore, the value of limx→0sin5x3x is 53.