Limit at Infinity| Differential and Integral Calculus| Feliciano and Uy| Exercise 1.4, Problem 3|

Evaluate

\lim\limits_{x\to \infty }\left(\frac{4x+5}{x^2+1}\right)

SOLUTION:

Divide by the highest denominator power 

\lim\limits_{x\to \infty }\left(\frac{4x+5}{x^2+1}\right)=\lim\limits_{x\to \infty }\left(\frac{4x+5}{x^2+1}\cdot \frac{\frac{1}{x^2}}{\frac{1}{x^2}}\right)

=\lim\limits_{x\to \infty }\left(\frac{\frac{4x}{x^2}+\frac{5}{x^2}}{\frac{x^2}{x^2}+\frac{1}{x^2}}\right)

=\lim\limits_{x\to \infty }\left(\frac{\frac{4}{x}+\frac{5}{x^2}}{1+\frac{1}{x^2}}\right)

=\frac{0+0}{1+0}

 

=0

 

 

 

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