Evaluate using transformations of \lim _ { x \rightarrow \infty } \frac { ( 2 x ^ { 4 } - 137 ) ^ { 5 } } { ( x ^ { 2 } + 429 ) ^ { 10 } } =

Solve lim _ x goes to infinity frac ( 2 x ^ { 4 - 137 ) ^ 5 } ( x ^ { 2 + 429 ) ^ 10 } =

Evaluate

x \to + \infty lim \frac{( 2 x ^{4} - 137 ) ^{5}}{( x ^{2} + 429 ) ^{10}}

Rewrite the expression

x \to + \infty lim \frac{( x ^{4} ( 2 - \frac{137}{x ^{4}} ) ) ^{5}}{( x ^{2} ( 1 + \frac{429}{x ^{2}} ) ) ^{10}}

Calculate

x \to + \infty lim \frac{x ^{20} ( 2 - \frac{137}{x ^{4}} ) ^{5}}{x ^{20} ( 1 + \frac{429}{x ^{2}} ) ^{10}}

Reduce the fraction

x \to + \infty lim \frac{( 2 - \frac{137}{x ^{4}} ) ^{5}}{( 1 + \frac{429}{x ^{2}} ) ^{10}}

Rewrite the expression

\frac{lim _{x \to + \infty} ( ( 2 - \frac{137}{x ^{4}} ) ^{5} )}{lim _{x \to + \infty} ( ( 1 + \frac{429}{x ^{2}} ) ^{10} )}

Calculate

More Steps

\frac{32}{lim _{x \to + \infty} ( ( 1 + \frac{429}{x ^{2}} ) ^{10} )}

Calculate

More Steps

\frac{32}{1}

Solution

32