spingo said: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.
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.