A calculus problem by Vighnesh Raut

$\lim _{ x\rightarrow \infty }{ \frac { 100{ x }^{ 2 }+37x+90 }{ 50{ x }^{ 2 }+80x+60 } }$

= $\lim _{ x\rightarrow \infty }{ \frac { 100+\frac { 37 }{ x } +\frac { 90 }{ { x }^{ 2 } } }{ 50+\frac { 80 }{ x } +\frac { 60 }{ { x }^{ 2 } } } }$

= $\frac { 100+0+0 }{ 50+0+0 }$

= 2

$\large\large\large\large \lim _{ x\rightarrow \infty }{ \frac { 100{ x }^{ 2 }+37x+90 }{ 50{ x }^{ 2 }+80x+60 } }$

Now just divide the two Equations by $x^2$ ,

So , $\large\large\large\large \lim _{ x\rightarrow \infty }{ \frac { 100+\frac { 37 }{( x) } +\frac { 90 }{ { x }^{ 2 } } }{ 50+\frac { 80 }{ (x) } +\frac { 60 }{ { x }^{ 2 } } } }$

Putting $x=$ $\infty$ , we know that $\large\large\frac{1}{∞} \ = \ 0$

So ultimately, $\large\large\frac{100}{50}$ $=$ $\boxed{\boxed{2}}$

When x-> ∞ and the highest degree of polynomial in numerator is same as the degree in denominator then simply divide the coefficient in numerator by coefficient in denominator. In this case, since the highest degree of polynomial is same, So 100/50 = 2