Answer to Question #155261 in Calculus for Ojugbele Daniel

Question #155261

Limit x approach infinity x[ ( 1 + a/x )^1+1/x - x^-1/x ( x+ a ) ]


1
Expert's answer
2021-01-13T19:38:20-0500

"\\lim \\limits_{x\\to \\infty} x[ ( 1 + \\frac{a}{x} )+ \\frac{1}{x} - \\frac{x^{-1}}{x} ( x+ a ) ]=""\\lim \\limits_{x\\to \\infty} [ ( x + a )+ 1 - ( 1+ \\frac{a}{x} ) ]=" "\\lim \\limits_{x\\to \\infty} [ x + a - \\frac{a}{x} ]=\\infty"

As we know "\\lim \\limits_{x\\to \\infty} \\frac{1}{x}=0" and "\\lim \\limits_{x\\to \\infty} x=\\infty". so the expression increases indefinitely.



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