Question

Exact value of the limit as x goes to 0 of sinx^2/x

Answer 1

Hello from MrBillDoesMath!

Answer:

0

Regardless of question interpretation:

lim ( sin (x^2)) /x

or

lim ( sin (x) )^2 /x

Discussion:

Interpretation 1:

As x goes to 0...

lim ( sin (x^2)) /x =

lim (sin (x^2))/x^2) * x =

1 * 0 =

0

Interpretation 2:

As x goes to 0...

lim ( sin (x) )^2 /x =

lim sin(x) ( sin(x)/x) =

0 * 1 =

0

Thank you,

MrB

Answer 2

0

Explanation:

`\lim_(n \to 0)  (sin^2(x))/(x)`

When we plug in 0 we will get 0/0

so we apply L' Hopitals rule

We take derivative at the top and bottom

derivative of sin^2(x) is 2sin(x)* cos(x)

2sin(x)cos(x) is sin(2x)

Derivative of x is 1

so limit becomes

`\lim_(n \to 0)  (sin(2x))/(1)`

Plug in 0 for x to find limit

sin(2*0) = 0

So limit value is 0