18 Questions
What does 'evaluating' in the context of limits mean?
Evaluating a function at a specific point
What is the limit of a constant function?
It is equal to the constant value
In the expression $\lim_{x \to 5}\ x$, what does the limit represent?
The function value at $x = 5$
What is the result of $\lim_{x \to 2}\ 3x$?
$6$
What does the limit of a power theorem state?
The limit of a power function is equal to the limit of the base raised to that power
Given $\lim_{x \to -1}\ (-1)$, what is the result?
$-1$
What is the definition of the limit of a function?
The value a function approaches as its input approaches a set value
When determining the existence of a limit, what must be true about the one-sided limits approaching that value?
They must be equal to each other
What is the result when an infinite limit exists?
The function approaches positive or negative infinity as x approaches a certain value
What does it mean to evaluate a limit at infinity?
Analyze the limit as x approaches positive or negative infinity
Why do we need to check one-sided limits when evaluating the limit of a function?
To ensure consistency in approaching the limit from both sides
Which term refers to a situation where the limit at a certain point cannot be determined?
'Indeterminate form' situation
What is the limit of $4x$ as $x$ approaches $-1/2$?
$-8$
If $f(x) = 3x - 2$ and $g(x) = x^2$, what is $\lim_{x \to 2} f(x) + g(x)$?
$5$
For the function $h(x) = 3x^2 - x + 5$, what is $\lim_{x \to -2} h(x)$?
$17$
Given $f(x) = x^2 + 3x$ and $g(x) = 2x - 5$, what is $\lim_{x \to -3} f(x) \cdot g(x)$?
$-54$
What is the limit of $\frac{1}{x}$ as $x$ approaches $0$?
$\infty$
If $p(x) = x^3 + x^2 + x + 1$, what is $\lim_{x \to 1} p(x)$?
$6$
Test your understanding of limits of a function in Calculus Module 2 with this quiz. Evaluate theorems on the limits of a function, including the limit of a constant, and solve examples to strengthen your knowledge.
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