Limits, by hand

Easy0 of 6 parts

Work these on paper, then type the answer in the box. Answers are marked by agreement, not by spelling, so 1/2 and 0.5 are the same answer and so are 2x+3 and 3+2x. Where a limit does not settle on a number, write inf, -inf or dne.

The method for every one of these is the same. Try substituting. If you get a number, and the expression is built from polynomials, roots and quotients with a bottom that is not zero, that number is the answer. If you get zero over zero, rewrite until the offending factor cancels, then substitute.

Evaluate $\lim_{x \to 4} \dfrac{x^2 - 16}{x - 4}$ .

Evaluate $\lim_{x \to 5} \dfrac{x^2 + 2x}{x + 1}$ .

Evaluate $\lim_{h \to 0} \dfrac{(2+h)^3 - 8}{h}$ .

Evaluate $\lim_{x \to 0^+} \dfrac{1}{x}$ .

Evaluate $\lim_{x \to 0} \dfrac{|x|}{x}$ .

$f(x) = x + c$ for $x < 1$ and $f(x) = 4x$ for $x \ge 1$ . Find the value of $c$ that makes $f$ continuous at $x = 1$ .