Dominant Terms in Calculus Limits

[spingo]

Hello, I am having issues finding the dominant terms in the following expression:

lim [(x^7)-9(e^x)] / [sqrt(10x-1)+8*ln(x)]
x->infinity

Prompt: Find the limit and the dominant term in the numerator and denominator.

 

[skeeter]

Link to a decent explanation of dominance ...

Dominance

 

[spingo]

So the dominant term in the numerator is should be (x^7)? According to my assignment this is incorrect but I'm not sure how. Additionally, by the logic used in the document sqrt(10x-1) should be dominant in the denominator.

The limit should be infinity then?

My assignment claims all of these answers are incorrect.

 

[skeeter]

So the dominant term in the numerator is should be (x^7)? According to my assignment this is incorrect but I'm not sure how. Additionally, by the logic used in the document sqrt(10x-1) should be dominant in the denominator.

The limit should be infinity then?

My assignment claims all of these answers are incorrect.

dominant term in the numerator is the exponential, as stated clearly in the link.

yes, dominant term in the denominator is the square root function

the limit is $-\infty$