5) lim _{x rightarrow infty} sqrt{x^{2}+2 x}-sqrt{x^{2}-8 x}

Question

Accepted Answer

Step:1 ：Given the expression (sqrt{x^{2}+2 x}-sqrt{x^{2}-8 x}), we are asked to find the limit as x approaches infinity.Step:2 ：We can simplify the expression by multiplying and dividing by the conjugate. This will allow us to cancel out terms and simplify the expression to a form that we can easily evaluate the limit of.Step:3 ：Let&#x27;s rewrite the expression as (-sqrt{x(x - 8)} + sqrt{x(x + 2)}).Step:4 ：By evaluating the limit of this expression as x approaches infinity, we find that the limit is 5.Step:5 ：So, the final answer is (boxed{5}).

Answer

Step: 1 ：Given the expression (sqrt{x^{2}+2 x}-sqrt{x^{2}-8 x}), we are asked to find the limit as x approaches infinity.Step: 2 ：We can simplify the expression by multiplying and dividing by the conjugate. This will allow us to cancel out terms and simplify the expression to a form that we can easily evaluate the limit of.Step: 3 ：Let&#x27;s rewrite the expression as (-sqrt{x(x - 8)} + sqrt{x(x + 2)}).Step: 4 ：By evaluating the limit of this expression as x approaches infinity, we find that the limit is 5.Step: 5 ：So, the final answer is (boxed{5}).

5) $\lim _{x \rightarrow \infty} \sqrt{x^{2}+2 x}-\sqrt{x^{2}-8 x}$

Answer

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