Finite Limits and Horizontal Asymptotes Quiz

This video tutorial by Mr. Baker explores finite limits as x approaches positive and negative infinity. It begins with an analysis of the function f(x) = 1/x, demonstrating how the graph flattens out around the x-axis, indicating a horizontal asymptote at y=0. The tutorial then examines other functions, such as 2x/(x+1) and x/sqrt(x^2+1), to identify horizontal asymptotes. The squeeze theorem is applied to the function sin(x)/x, showing how it approaches zero. Finally, the video covers properties of limits, including sum, difference, product, quotient, and power rules, using examples to illustrate these concepts.

What happens to the function f(x) = 1/x as x approaches positive infinity?

• It approaches 1

• It approaches negative infinity

• It approaches 0

• It approaches infinity

What is the y-value of the horizontal asymptote for the function f(x) = 1/x?

• Infinity

• 0

• Negative infinity

• 1

For the function 2x/(x+1), what is the limit as x approaches negative infinity?

• 1

• Negative infinity

• 0

• 2

What is the horizontal asymptote for the function x/sqrt(x^2+1) as x approaches positive infinity?

• Negative 1

• 0

• 1

• Infinity

How many horizontal asymptotes does the function x/sqrt(x^2+1) have?

• None

• Three

• One

• Two

What is the limit of sin(x)/x as x approaches positive infinity?

• Negative infinity

• 1

• Infinity

• 0

Which rule allows you to find the limit of a sum of two functions by finding their individual limits first?

• Product rule

• Power rule

• Sum rule

• Quotient rule

What is the limit of a constant as x approaches infinity?

• Negative infinity

• Infinity

• Zero

• The constant itself

Which rule allows you to find the limit of a product of two functions by finding their individual limits first?

• Sum rule

• Product rule

• Quotient rule

• Difference rule

What is the limit of 5x + sin(x) all over x as x approaches infinity?

• 0

• Negative infinity

• 5

• Infinity