Answer:
1
Step-by-step explanation:
We are given that
[tex]f(x)=\frac{sinx}{x}[/tex]
Numbers are in radians
Substitute x=-1
[tex]f(-1)=\frac{sin(-1)}{-1}=0.84[/tex]
Substitute x=-0.25
[tex]f(-0.25)=\frac{Sin(-0.25)}{-0.25}=0.989[/tex]
Substitute x=-0.01
[tex]f(-0.01)=\frac{sin(-0.01)}{-0.01}=0.999[/tex]
Substitute x=-0.005
[tex]f(-0.005)=\frac{sin(-0.005)}{-0.005}=0.999[/tex]
Substitute x=0.005
[tex]f(0.005)=\frac{sin(0.005)}{0.005}=0.999[/tex]
Substitute x=0.01
[tex]f(0.01)=\frac{sin(0.01)}{0.01}=0.999[/tex]
Substitute x=0.25
[tex]f(0.25)=\frac{sin(0.25)}{0.25}=0.989[/tex]
Substitute x=1
[tex]f(1)=\frac{sin(1)}{1}=0.84[/tex]
Therefore, [tex]\lim_{x\rightarrow 0}\frac{sinx}{x}=1[/tex]
