Analyzing One-Sided Limits in e^(1/(6-x)) as x Approaches 6+

[tsaitea]

lim e^(1/(6-x))
x->6+

Was wondering how to solve for this limit analytically. I plotted it and see it going to 0, but that is not the answer in the book.

 

[SammyS]

lim e^(1/(6-x))
x->6+

Was wondering how to solve for this limit analytically. I plotted it and see it going to 0, but that is not the answer in the book.

Hello tsaitea. Welcome to PF !

What is $\displaystyle \lim_{x\to6^{+}}\,\frac{1}{6-x}\ ?$

 

[tsaitea]

oh -infinity, but the answer is e^(17/3)?, maybe the book is wrong then?

 

[SammyS]

oh -infinity, but the answer is e^(17/3)?, maybe the book is wrong then?

Actually $\displaystyle \ \ \lim_{x\to6^{+}}\,\frac{1}{6-x}=-\infty\ .$

If the problem you were given was to find $\displaystyle \ \ \lim_{x\to6^{+}}\,e^{1/(6-x)}\,,\$ then the book is wrong if it gives the answer as e^(17/3) . You were right in your original post to say the answer is zero.

 

[tsaitea]

Okay, thanks so much!