Podcast
Questions and Answers
What does 'evaluating' in the context of limits mean?
What does 'evaluating' in the context of limits mean?
- Calculating the area under a curve
- Finding the constant value
- Evaluating a function at a specific point (correct)
- Determining the rate of change
What is the limit of a constant function?
What is the limit of a constant function?
- It is undefined
- It approaches infinity
- It is always zero
- It is equal to the constant value (correct)
In the expression $\lim_{x \to 5}\ x$, what does the limit represent?
In the expression $\lim_{x \to 5}\ x$, what does the limit represent?
- The constant value
- The maximum value of the function
- The function value at $x = 5$ (correct)
- The rate of change at $x = 5$
What is the result of $\lim_{x \to 2}\ 3x$?
What is the result of $\lim_{x \to 2}\ 3x$?
What does the limit of a power theorem state?
What does the limit of a power theorem state?
Given $\lim_{x \to -1}\ (-1)$, what is the result?
Given $\lim_{x \to -1}\ (-1)$, what is the result?
What is the definition of the limit of a function?
What is the definition of the limit of a function?
When determining the existence of a limit, what must be true about the one-sided limits approaching that value?
When determining the existence of a limit, what must be true about the one-sided limits approaching that value?
What is the result when an infinite limit exists?
What is the result when an infinite limit exists?
What does it mean to evaluate a limit at infinity?
What does it mean to evaluate a limit at infinity?
Why do we need to check one-sided limits when evaluating the limit of a function?
Why do we need to check one-sided limits when evaluating the limit of a function?
Which term refers to a situation where the limit at a certain point cannot be determined?
Which term refers to a situation where the limit at a certain point cannot be determined?
What is the limit of $4x$ as $x$ approaches $-1/2$?
What is the limit of $4x$ as $x$ approaches $-1/2$?
If $f(x) = 3x - 2$ and $g(x) = x^2$, what is $\lim_{x \to 2} f(x) + g(x)$?
If $f(x) = 3x - 2$ and $g(x) = x^2$, what is $\lim_{x \to 2} f(x) + g(x)$?
For the function $h(x) = 3x^2 - x + 5$, what is $\lim_{x \to -2} h(x)$?
For the function $h(x) = 3x^2 - x + 5$, what is $\lim_{x \to -2} h(x)$?
Given $f(x) = x^2 + 3x$ and $g(x) = 2x - 5$, what is $\lim_{x \to -3} f(x) \cdot g(x)$?
Given $f(x) = x^2 + 3x$ and $g(x) = 2x - 5$, what is $\lim_{x \to -3} f(x) \cdot g(x)$?
What is the limit of $\frac{1}{x}$ as $x$ approaches $0$?
What is the limit of $\frac{1}{x}$ as $x$ approaches $0$?
If $p(x) = x^3 + x^2 + x + 1$, what is $\lim_{x \to 1} p(x)$?
If $p(x) = x^3 + x^2 + x + 1$, what is $\lim_{x \to 1} p(x)$?
