Question

can someone plz help me??

Evaluate the limit.

lim xe^(7/x) − x

x →infinity

Answer 1

Try wolfram alpha

Answer 2

http://www.wolframalpha.com/input/?i=limit

Answer 3

use substitution, or change variable and limit

\[\text {Let} \space \space t = e^{7/x} \rightarrow x = \frac{7}{\ln t}\]
problem changes to
\[\lim_{t \rightarrow 1}\frac{7t}{\ln t}-\frac{7}{\ln t}\]
\[=\lim_{t \rightarrow 1}\frac{7t-7}{\ln t} = \frac{0}{0}\]
use L'hopitals rule, differentiate top and bottom
\[\rightarrow \lim_{t \rightarrow 1}\frac{7}{1/t} = 7\]

Answer 4

http://www.wolframalpha.com/input/?i=limit&a=*C.limit-_*Calculator.dflt-&f2=xe^%287%2Fx%29+-x&x=12&y=6&f=Limit.limitfunction_xe^%287%2Fx%29+-x&f3=infinity&f=Limit.limit_infinity&a=*FVarOpt.1-_**-.***Limit.limitvariable--.**Limit.direction--.**Limit.limitvariable2-.*Limit.limit2-.*Limit.direction2---.*--

Answer 5

here's another way you might consider: