Limit values

[helge]

The task is: Use this information to determine the following limit values



This should be the right soulution. Problem is, I dont see how they go from step red to step orange. May be that shortcuts are taken here, but I dont see how they progress to the orange step. Can someone post a detailed calculation about what is going between these two steps?

 

[Deleted member 4993]

View attachment 31149

The task is: Use this information to determine the following limit values

View attachment 31150

This should be the right soulution. Problem is, I dont see how they go from step red to step orange. May be that shortcuts are taken here, but I dont see how they progress to the orange step. Can someone post a detailed calculation about what is going between these two steps?

Multiply the numerator and the denominator by 5^(-1/x).

 

[Steven G]

SK gave you the answer. I will try to motivate how you can see it on your own.

The first term in the numerator in the red is 1, while the 1st term in the numerator in orange is 5^(-1/x).
What do you do to 1 to get 5^(-1/x)?

The 2nd term in the numerator in the red is 5^(1/x), while the 1st term in the numerator in orange is 1.
What do you do to to 5^(1/x) to get 1?

The first term in the denominator in the red is 2, while the 1st term in the denominator in orange is 2*5^(-1/x).
What do you do to 2 to get 2*5^(-1/x)?

The 2nd term in the denominator in the red is 5^(1/x), while the 2nd term in the denominator in orange is 1.
What do you do to 5^(1/x) to get 1?

Answering any of the above questions will answer your initial question!