Question

Find : $\lim_{x \to \infty} \frac{39 x^{2}+7x }{54x^2+19}$

Please show detailed steps, thank you sir/madam

Answer 1

Let x = 1/y
As x tends to infinity,  y tends to 0.

$\lim_{x \to \infty} \frac{39x^2+7x}{54x^2+19}\\\\ \lim_{y \to 0} \frac{\frac{39}{y^2}+\frac{7}{y}}{\frac{54}{y^2}+19} \\\\\lim_{y \to 0} \frac{39+7y}{54+19y^2}\\\\\frac{39}{54}$
by substituting the value of y =0 in the expression in the numerator and denominator.