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

Answer:

0

Step-by-step explanation:

$\lim_{n \to 0}  \frac{sin^2(x)}{x}$

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

$\lim_{n \to 0}  \frac{sin(2x)}{1}$

Plug in 0 for x to find limit

sin(2*0) = 0

So limit value is 0