Podcast
Questions and Answers
What can be said about the limit at negative infinity of logarithmic functions?
What can be said about the limit at negative infinity of logarithmic functions?
- It exists and is equal to 0
- It exists and is equal to a specific constant value
- It does not exist (correct)
- It exists and is equal to infinity
For polynomial functions with a leading coefficient 'a' that is greater than 0 and an odd degree 'n', what is the limit at positive infinity?
For polynomial functions with a leading coefficient 'a' that is greater than 0 and an odd degree 'n', what is the limit at positive infinity?
- Zero
- Negative infinity
- Positive infinity (correct)
- A specific constant value
When finding the limit at infinity of rational functions, what is the case if the degrees of the numerator and denominator are equal?
When finding the limit at infinity of rational functions, what is the case if the degrees of the numerator and denominator are equal?
- The limit exists and is a specific constant value (correct)
- The limit is always infinity
- The limit is always 0
- The limit does not exist
What can be concluded about the limit at infinity of exponential functions with a base 'b' greater than 1?
What can be concluded about the limit at infinity of exponential functions with a base 'b' greater than 1?
In the context of polynomial functions, what happens to the limit at negative infinity if 'a' is negative and 'n' is even?
In the context of polynomial functions, what happens to the limit at negative infinity if 'a' is negative and 'n' is even?
When dealing with rational functions, what can be said about the limit if 'n' is greater than 'm' and 'a = b'?
When dealing with rational functions, what can be said about the limit if 'n' is greater than 'm' and 'a = b'?
For a polynomial function of degree n and leading coefficient a, what happens to the limits at infinity if a is less than 0 and n is even?
For a polynomial function of degree n and leading coefficient a, what happens to the limits at infinity if a is less than 0 and n is even?
In which scenario do rational functions differ from polynomial functions in terms of end behaviors?
In which scenario do rational functions differ from polynomial functions in terms of end behaviors?
If n is odd in a polynomial function, how are the right and left ends of the graph positioned?
If n is odd in a polynomial function, how are the right and left ends of the graph positioned?
What happens to the limits at infinity of a rational function if the function has one branch?
What happens to the limits at infinity of a rational function if the function has one branch?
In a rational function with one branch, what can be said about its end behavior compared to polynomial functions?
In a rational function with one branch, what can be said about its end behavior compared to polynomial functions?
What is the end behavior of a rational function with one branch if it approaches zero at infinity?
What is the end behavior of a rational function with one branch if it approaches zero at infinity?
As 𝑥 approaches positive or negative infinity, what happens to 𝑦 in relation to the 𝑥-axis?
As 𝑥 approaches positive or negative infinity, what happens to 𝑦 in relation to the 𝑥-axis?
What is the horizontal asymptote of the function 𝑓(𝑥) as defined in the text?
What is the horizontal asymptote of the function 𝑓(𝑥) as defined in the text?
What is the limit as 𝑥 approaches positive or negative infinity of 𝑥^5?
What is the limit as 𝑥 approaches positive or negative infinity of 𝑥^5?
What is the general first step to evaluate limits at infinity of rational functions?
What is the general first step to evaluate limits at infinity of rational functions?
What is the limit as 𝑥 approaches ±∞ of a rational function where the denominator has a higher degree than the numerator?
What is the limit as 𝑥 approaches ±∞ of a rational function where the denominator has a higher degree than the numerator?
What should be done to prevent bad bacteria from multiplying each day in a human body?
What should be done to prevent bad bacteria from multiplying each day in a human body?
What value does the limit of a function approach as 𝑥 increases without bound?
What value does the limit of a function approach as 𝑥 increases without bound?
In evaluating the limit of algebraic functions, what are the end behaviors of polynomial functions dependent on?
In evaluating the limit of algebraic functions, what are the end behaviors of polynomial functions dependent on?
How can one compute the limits of exponential, logarithmic, and trigonometric functions?
How can one compute the limits of exponential, logarithmic, and trigonometric functions?
What do limits at infinity of some algebraic and transcendental functions help illustrate?
What do limits at infinity of some algebraic and transcendental functions help illustrate?
What is key in computing the limits at infinity of algebraic and transcendental functions?
What is key in computing the limits at infinity of algebraic and transcendental functions?
What is the limit of $e^x$ as $x$ approaches $- ext{infinity}$?
What is the limit of $e^x$ as $x$ approaches $- ext{infinity}$?
What is the limit of $\log_b(x)$ as $x$ approaches $\infty$, where $b > 1$?
What is the limit of $\log_b(x)$ as $x$ approaches $\infty$, where $b > 1$?
For polynomial functions of even degrees and an odd degree, what are the leading coefficients assumed to be when approaching $- ext{infinity}$?
For polynomial functions of even degrees and an odd degree, what are the leading coefficients assumed to be when approaching $- ext{infinity}$?
What is the limit of $\ln(x)$ as $x$ approaches $\infty$?
What is the limit of $\ln(x)$ as $x$ approaches $\infty$?
What happens to the limit of $\log_{b}(x)$ as $x$ approaches $-\infty$, where $0 < b < 1$?
What happens to the limit of $\log_{b}(x)$ as $x$ approaches $-\infty$, where $0 < b < 1$?
In the context of limits at infinity, what happens to the limit of exponential functions as the exponent increases towards infinity?
In the context of limits at infinity, what happens to the limit of exponential functions as the exponent increases towards infinity?
