Limits Flashcards
(21 cards)
What is the limit on a graph?
The maximum value on a graph or a table
How do you find the limit of f(x) when x approaches 3?
Look from both the positive and negative sides
What is the limit of f(x) when x approaches 3 if values from both sides approach 5?
5
What does an open circle on a graph indicate?
That the value at that point is undefined
What happens when x equals 3 in the function (x^2 - x - 6) / (x - 3)?
It results in division by 0, which is undefined
How can the function (x^2 - x - 6) / (x - 3) be rewritten?
(x + 2) when x does not equal 3
What is a reasonable estimate for h when x approaches 3 if values approach 2?
2
What is the limit of f(x) when x approaches 6 if values approach -3?
-3
What can a graph help us approximate?
The finite y value we’re approaching as x gets closer to some value
What does it mean if the limit does not exist?
It indicates that values from both sides do not approach a common number
What is the limit of f(x) when x approaches 3 if values approach 10 from both sides?
10
What happens to the limit of g(x) / f(x) when f(x) equals 0?
It is undefined
When can we say the limit of [f(x) + g(x)] exists?
If lim [f(x) + g(x)] from both sides approaches the same value
What does it mean if the limit of [f(x) + g(x)] does not exist?
The limits from both sides do not equal each other
What should you consider when approaching limits of composite functions?
The continuity of f(x) and the approach from both sides
What is the limit of (6x^2 + 5x - 1) when x approaches -1?
0
What indicates that a limit is undefined by direct substitution?
When you divide by 0
What is the limit of sin x when x approaches pi?
0
What is the limit of cos x when x approaches pi/4?
√2 / 2
What happens to the limit of tan x when x approaches pi/2?
It is undefined
What does it indicate if the limit is in the domain of a function?
It will lead to a limit, aka the value in their domain
