Chapter 1 Test Flashcards
(44 cards)
How do you know if there is a hole?
It will be 0/0
If you are looking at a limit and it says x approaches n-, what does that mean?
As x approaches n from the left
If you are looking at a limit and it says x approaches n+, what does that mean?
As x approaches n from the right
What is one thing that will always cause a limit to not exist?
An asymptote
Explain why a limit would not exist.
If you trace the function from the left and the right and your fingers don’t end in the same position
If you are asked to identify the values of c for which the limit as x approaches c for function f(x) exists what do you say?
You would say the limit exists for all points except at any holes or asymptotes
Finish this limit property: What is the limit as x approaches c for the function b? When b is a horizontal line.
B
Finish this limit property: What is the limit as x approaches c for the function x?
C
Finish this limit property: What is the limit as x approaches c for the function x^n?
C^n
How do you solve this limit with our limit properties?
Limit as x approaches c for function [b(f(x)]
Find the limit as x approaches c for f(x), then multiply the entire thing by b
How do you solve this limit with our limit properties?
Limit as x approaches c for function [f(x) +/- g(x)]
Find the limit as x approaches c for f(x) then find the limit as x approaches c for g(x) and add or subtract them together
How do you solve this limit with our limit properties?
Limit as x approaches c for function [f(x) * g(x)]
Find the limit as x approaches c for f(x) then find the limit as x approaches c for g(x) and multiply them
How do you solve this limit with our limit properties?
Limit as x approaches c for function [f(x)/g(x)]
Find the limit as x approaches c for f(x) then find the limit as x approaches c for g(x) and divide them
IMPORTANT TO NOTE THAT the limit as x approaches c for g(x) CANNOT be 0
How do you solve this limit with our limit properties?
Limit as x approaches c for function [f(x)]^n
Find the limit as x approaches c for f(x) then take that answer to the nth power
How do you solve trig function limits?
Exs: Limit as x approaches c for function sin x
or for function csc x, etc.
It would just be sin c
Csc c
Etc
Indeterminate form
When you directly plug in a c value, and you get 0 over 0.
How do you find a limit if when you directly plug in a c value you get 0?
You have to factor stuff out or figure out something to get rid of whatever is creating the hole in the denominator
Why would you get points docked on a limit question?
You need to make sure you are always including “limit as x approaches…” when you have equal signs or you are writing an incorrect statement.
How do you find the x and y values of a hole?
The x value will be the c value you got when you plugged it in and got 0/0, and the y value is when you plug in the c value to your new factored function
How do you factor down an equation with a radical?
Multiply the equation by the radical conjugate.(if its blah - 1, do blah + 1), then on the part where the radical isn’t make sure to NOT multiply that out
Squeeze Theorem
If h(x) is equal or less than f(x) is equal or less than g(x) then all of their limits are equal as well.
Special Trig Limits
The limit as x APPROACHES 0 for the function sin x over x equals 1
The limit as x APPROACHES 0 for the function 1-cos x over x equals 0
Sin
y over 1
Tan
y over x
