Question

) Using the chart, approximate the limit of the function f(x) = sin x/ x as x approaches zero. Note the numbers are in radians:

Answer 1

1

Explanation:

We are given that

`f(x)=(sinx)/(x)`

Numbers are in radians

Substitute x=-1

`f(-1)=(sin(-1))/(-1)=0.84`

Substitute x=-0.25

`f(-0.25)=(Sin(-0.25))/(-0.25)=0.989`

Substitute x=-0.01

`f(-0.01)=(sin(-0.01))/(-0.01)=0.999`

Substitute x=-0.005

`f(-0.005)=(sin(-0.005))/(-0.005)=0.999`

Substitute x=0.005

`f(0.005)=(sin(0.005))/(0.005)=0.999`

Substitute x=0.01

`f(0.01)=(sin(0.01))/(0.01)=0.999`

Substitute x=0.25

`f(0.25)=(sin(0.25))/(0.25)=0.989`

Substitute x=1

`f(1)=(sin(1))/(1)=0.84`

Therefore,
`\lim_(x\rightarrow 0)(sinx)/(x)=1`