Question $4$

Let $f(x)$ be a function and binR. f is continuous at $x=b$ if and only if :

$4\mathrm{.}1q,$

$(1)$

$4\mathrm{.}2q,$

$(1)$

$4\mathrm{.}3q,$

$(1)$

Hint: $4\mathrm{.}1,4\mathrm{.}2,4\mathrm{.}3$ require you to state the conditions that must be satisfied for $f$ to be continuous at $x=b$

Question $5$

Let

$f(x)=\{\begin{array}{ccc}4-x^2& if& x>1\\ 3x^2& if& x<mn>1</mn>\end{array}$

Determine whether or not $f(x)$ is continuous at $x=1.$

$(5)$

Question $6$

Use the first principle to determine $f^{\text{'}}(x)$ of the following functions:

$6\mathrm{.}1f(x)=x^2.$

$(3)$

$6\mathrm{.}2f(x)=x^2-4x+7.$