Question

Find the limit: lim x goes to 0 (x^2/arctan(x))

Answer 1

Answer:

$\lim_{x \to 0} \frac{2x}{\frac{1}{1+x^{2} } }$  =0

Step-by-step explanation:

$\lim_{x \to 0} \frac{x^{2} }{tan^{-1} (x)}$

the x value for which tan(x)=0 is 0

we get an indefinite form, so we use l'hopital's rule

(l'hopitals rule: the limit of an indefinite form is equal to the limit of the derivative of the numerator divided by the derivative of the denominator)

$\lim_{x \to 0} \frac{2x}{\frac{1}{1+x^{2} } }$ = 0/1 =0

when we graph the function$\frac{x^{2} }{tan^{-1} (x)}$, the graph seems to pass the point (0,0)