Understanding Limits of Functions

The video tutorial explores finding the limits of functions as x approaches infinity or negative infinity. It emphasizes identifying dominant terms in the numerator and denominator to simplify the problem. The tutorial covers examples where the limit results in a finite number, zero, or infinity, depending on the growth rates of the terms involved. The key takeaway is understanding how the highest degree terms influence the limit as x becomes very large or very small.

What is the key to finding the limit of a function as x approaches infinity?

• Identifying the constant terms

• Focusing on the dominating terms

• Calculating the derivative

• Using the quadratic formula

In the example function, which term dominates in the numerator as x approaches infinity?

• 17x to the sixth

• 15 square roots of x

• log base 2 of x

• 9x to the seventh

What is the limit of the function as x approaches infinity in the first example?

• 0

• 1

• 3

• Infinity

When finding the limit as x approaches negative infinity, what happens to 1 over a very large negative number?

• It approaches 1

• It approaches 0

• It becomes undefined

• It approaches infinity

What is the horizontal asymptote of the function as x approaches negative infinity?

• y = 0

• y = -1

• y = 1

• y = infinity

In the second example, which term dominates in the denominator as x approaches negative infinity?

• 3x to the third

• 6x to the fourth

• log base 2 of x

• 15 square roots of x

What is the limit of the function as x approaches infinity in the third example?

• Infinity

• 1

• 3

• 0

Why does the function in the third example approach infinity as x approaches infinity?

• The numerator grows slower than the denominator

• The denominator grows faster than the numerator

• The numerator and denominator grow at the same rate

• The numerator grows faster than the denominator

What is the degree of the dominating term in the numerator in the third example?

• Second degree

• Third degree

• Fifth degree

• Fourth degree

What is the key insight for determining the limit behavior of a function?

• Comparing the growth rates of the numerator and denominator

• Calculating the derivative

• Finding the constant terms

• Using the quadratic formula