Answer:
1
Step-by-step explanation:
Given [tex]\lim_{x \to 0} \frac{sinxcosx}{x}[/tex]
multiply the numerator and denominator with 2
we get [tex]\lim_{x \to 0} \frac{2sinxcosx}{2x}[/tex]
We know that sin2x=2sinxcosx
[tex]\lim_{x \to0} \frac{sin2x}{2x}[/tex]
Now consider y=2x
As x→0 2x→0 y→0
Now limit changes to
[tex]\lim_{y \to0} \frac{siny}{y}[/tex]=1
