Applied Mathematics Calculus and Limit Question

Question

Evaluate the question of the following limits. 

• $\lim_{x\rightarrow \infty} \frac{2x^{3}+3x-5}{5x^{3}+1}$

Answer 1

L'Hôpital's rule     6x^2+3/15x^2

                         = 12x/30x

                         = 12/30

                       = 2/5

Answer 2

Given ,

$\large \lim_{x->\infty}\frac{2x^{3}+3x-5}{5x^{3}+1}$

dividing both numerator and denominator by $x^{3}$ we get,

=$\large \lim_{x->\infty}\frac{2+\frac{3}{x^{2}}-\frac{5}{x^{3}}}{5+\frac{1}{x^{3}}}$

putting the value of limit ,

=$\large \lim_{x->\infty}\frac{2+0-0}{5+0}$              [as $\infty$ in denominator makes $\large \frac{3}{x^{2}}$,$\large \frac{5}{x^{3}}$,$\large \frac{1}{x^{3}}$ terms 0]

 =$\large \frac{2}{5}$