Question

Number 4 Find the limit and use the x values : -0.03, -0.02,-0.01,0,0.01,0.02,0.03

Answer 1

EXPLANATION

First, let's represent the table with some values of x and y near to the limit:

x y

-0.03 0.66

-0.02 0.65

-0.01 0.64

0.01 0.63

0.02 0.62

0.03 0.62

Now, we need to plot the function:

$\mathrm{Plug\: in\: the\: value}\: x=0$$=\frac{\sin\left(0+\frac{\pi}{2}\right)-\sin\left(0\right)}{\frac{\pi}{2}}$$\sin \mleft(0+\frac{\pi}{2}\mright)-\sin \mleft(0\mright)$$=\frac{1}{\frac{\pi}{2}}$$Applying\text{ the fraction rule:}$$=\frac{2}{\pi}$

The limit is 2/π and it does existe because It's defined at x=0