Question

Find the limit of the function algebraically.
limit as x approaches zero of quantity x squared plus two x divided by x to the fourth power.

Answer 1

\[\lim_{x \rightarrow 0}\frac{ x^{2}+2x }{ x^{4} }\]

factor out x from the numerator, then cancel out x in the numerator and denominator to get (x+2)/x^3

the numerator becomes 0 + 2 by substitution. think about what happens to expression as the denominator approaches 0.