- #1

spingo

- 2

- 0

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.

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In summary, the dominant term in the numerator is the exponential (e^x) and in the denominator it is the square root function (sqrt(10x-1)). The limit is negative infinity according to the given link.

- #1

spingo

- 2

- 0

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.

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- #2

skeeter

- 1,103

- 1

- #3

spingo

- 2

- 0

The limit should be infinity then?

My assignment claims all of these answers are incorrect.

- #4

skeeter

- 1,103

- 1

spingo said:

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 $-\infty$

A dominant term in calculus limits is the term in a function that has the highest degree. It is the term that has the greatest influence on the overall behavior of the function as the independent variable approaches a certain value.

To identify the dominant term in a function, you can look at the degree of each term in the function. The term with the highest degree, whether it is a polynomial, exponential, or logarithmic function, is considered the dominant term.

The dominant term in calculus limits is important because it determines the overall behavior of the function as the independent variable approaches a certain value. It helps us understand the behavior of the function and make predictions about its limit.

The dominant term has the greatest influence on the limit of a function. As the independent variable approaches a certain value, the dominant term will determine the overall behavior of the function and ultimately the limit.

Yes, a function can have more than one dominant term. This can happen when there are multiple terms with the same highest degree. In this case, both terms will have a significant influence on the overall behavior of the function and should be considered when evaluating the limit.

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