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

your question is ....
$\displaystyle\lim_{x\to\ 0}\frac{x^2+2x}{x^4}$

Let's check form of limit ,
put x = 0 in numerator and denominator
we get, 0/0 e.g., 0/0 is the form of limit.

now, $\displaystyle\lim_{x\to\ 0}\frac{x^2+2x}{x^4}$

= $\displaystyle\lim_{x\to 0}\frac{x(x+2)}{x.x^3}$

= $\displaystyle\lim_{x\to 0}\frac{x+2}{x^3}$

now, if we put x = 0, we get 2/0 = undefined
hence, limit doesn't exist