The sine integral function $$Si(x)=\int_{0}^{\,x} {\frac{\sin(t)}{t}}\,dt$$ is important in electrical engineering. The integrand $f(t)=\sin(t)/t$ is not defined when $t = 0$, but we know that its limit is 1 when $t\to 0.$ So we define $f(0)=1,$ and this makes $f$ a continuous function everywhere.

(a) Determine all values of $x$ between -10 and 10 where this function has a local maximum value.

List all of these values in increasing order. If any blanks are unused, type an upper-case "N" in the corresponding blank.

Local maximum 1: $x =$

Local maximum 2: $x =$

Local maximum 3: $x =$

Local maximum 4: $x =$

(b) Find the coordinates of the first inflection point to the right of the origin. Make sure that each coordinate is accurate to two decimal places.

Inflection point: $(x,y) \approx$ (, )

(c) List the horizontal asymptotes of $Si(x)$ in increasing order.

If only one horizontal asymptote exists, enter it in the first answer field. Type an upper-case "N" in any unused answer field.

Horizontal asymptote 1: $y =$

Horizontal asymptote 2: $y =$

(d) Use a graph to solve the following equation for $x$, correct to one decimal place: $$\int_{0}^{\,x} {\frac{\sin(t)}{t}}\,dt=1$$

$x \approx$