#### To determine

**To evaluate:** The value of
limx→0xsin1x and graph of the function
y=xsin(1x).

#### Answer

The value of
limx→0xsin1x is 0.

#### Explanation

**Theorem used:** Squeeze Theorem:

If
xn≤yn≤zn for
n≥N and
limn→∞xn=limn→∞yn=L then the value of
limn→∞zn=L. (1)

**Calculation:**

Let
f(x)=xsin1x.

Known fact,

−1≤sin(1x)≤1 (2)

Multiply the inequality (2) by *x,*

−x≤xsin(1x)≤x

Apply the squeeze theorem as shown in equation (1),
limx→0(−x)=0 and
limx→0(x)=0.

Therefore, the value of
limx→0(xsin1x)=0

**Graph:**

Use online graphing calculator and draw the graph of the function as shown below in Figure 1 and Figure 2.

From Figure 1, it is observed that the function
y=xsin(1x) is close to 0 as *x* approaches to zero.