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Exercise

$\lim_{x\to\infty}\left(\frac{1}{x+1}-\frac{1}{x}\right)$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to\infty }\left(\frac{1}{x+1}+\frac{-1}{x}\right)$ by replacing all occurrences of $x$ by $\infty $

$\frac{1}{\infty +1}+\frac{-1}{\infty }$
2

Any expression divided by infinity is equal to zero

$\frac{1}{\infty +1}$
3

Infinity plus any algebraic expression is equal to infinity

$\frac{1}{\infty }$
4

Any expression divided by infinity is equal to zero

0

Final answer to the exercise

0

Try other ways to solve this exercise

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  • Integrate by partial fractions
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Main Topic: Limits

In mathematics, a limit is the value that a function or sequence "approaches" as the input or index approaches some value.

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