Find the limit of $\sqrt{x+1}-x$ as $x$ approaches $\infty $

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Learn how to solve integral calculus problems step by step online. Find the limit of (x+1)^(1/2)-x as x approaches infinity. Applying rationalisation. Multiply and simplify the expression within the limit. As it's an indeterminate limit of type \frac{\infty}{\infty}, divide both numerator and denominator by the term of the denominator that tends more quickly to infinity (the term that, evaluated at a large value, approaches infinity faster). In this case, that term is . Rewrite the fraction, in such a way that both numerator and denominator are inside the exponent or radical.