Excerpt $3$:

FGaluation kxercize ${33}^{}$

$(1)$ Consider the function $f(x)=\frac{x-1}{\sqrt[\phantom{2}]{x}-1}$ with $x0$ which is not defined for $x=1.$ Use tables to determine whether lim $f(x)$ exists or not.

$x1$

$($i$1)$ Determine whether the function

$f(x),=\frac{e^x-e^{-x}}{x},x0$

$=2,x=0$

$is$ continuous $atx=0.,$

$($i$.$ii$)$ Show that the function

$y=f(x)=-x^2+4<mn\; id="EditorElement\_843393">1</mn>$

$=2x+1x1$

is smooth at $x=1.$ Explain your resuit.

$($iv$)$ Sketch the graph of the function

$f(x)=\frac{e^x}{e^x+1}$

$$

This evaluation exercise is particularly long because, in a sense, it evaluates more than Just the work of this frame but also much of what was done before.