Evaluate the limit as x goes to infinity using L'Hospital's rule

[Loopas]

(1)

Evaluate the limit as x goes to infinity using L'Hospital's rule:

8xe^(1/x)-8x

(2)

L'Hopital's Rule

(3)

How can I use L'Hopital's Rule for this problem if the denominator is 1? Wouldn't that just give me an undefined limit? This may be a pretty stupid question, but I'm new to this.

 

[Curious3141]

(1)

Evaluate the limit as x goes to infinity using L'Hospital's rule:

8xe^(1/x)-8x

(2)

L'Hopital's Rule

(3)

How can I use L'Hopital's Rule for this problem if the denominator is 1? Wouldn't that just give me an undefined limit? This may be a pretty stupid question, but I'm new to this.

Hint: factorise first. Also, $x = \displaystyle \frac{1}{\frac{1}{x}}$.

 

[Loopas]

How do you you know that x=(1)/(1/x)?

 

[ehild]

$$\frac{1}{(\frac{1}{x})}$$

is the reciprocal of 1/x...

ehild

 

[Loopas]

Ahhh ok so I can rewrite as (8x(e^(1/x)-1))/(1/x)?

 

[FeDeX_LaTeX]

Not quite.

 

[Curious3141]

Ahhh ok so I can rewrite as (8x(e^(1/x)-1))/(1/x)?

That x is replaced by the 1/(1/x) term. So why does it appear again?

Sorry no latex. On my phone at the moment.