Chapter 1 Test Flashcards
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
How do you get from radians to degrees?
Multiply by 180 over pi
What are the two special right triangles?
For 60-30-90, across from the 60 is sq rt 3 over 2, and across from 30 is 1/2
For 45-45-90, both legs are sq rt 2 over 2
Sec
1/x
Cos
x/1
What’s important to remember with radicals?
DON’T LEAVE THEM IN THE DENOMINATOR
How do you solve something to a fraction power?
ex: 16 ^3/2
It would be 16 squared and then the answer to that cubed
Practice 57 on 1.3 PS B
66
67
68
71
Ans: -1/9
1
0
0
0
What makes a function continuous?
If you can draw its entire graph without lifting your pencil and if all 3 of these things are true
a) f(c) exists
b) limit as x approaches c for the function f(x) exists
c) f(c) equals limit as x approaches c for the function f(x) exists
What is an infinite discontinuity?
When there is a VA
What is a jump discontinuity?
When the limits from the left and right aren’t the same, if you were walking along the graph, you’d have to jump to the next part
What is a removable discontinuity?
There are two types:
BOTH WILL HAVE A LIMIT as x approaches b but that limit does not equal f(b).
So the two types are when b has an output but it doesn’t equal the limit and the other is when b has no outputs at all.
Ex: Discuss the continuity of f(x)= 1/x
Since f(0) is undefined, f is continuous on (-infinity, 0) and on (0, infinity)
How do you determine continuity with a piecewise?
Plug in whatever x equals, and make sure that whatever it equals is true for all equations in the piecewise, if that’s true then it is continuous bc all limits are equal
What’s the quickest way to explain if a limit exists?
Use symbols to say left and right limit are the same
Practice 39-52 in 1.4 PS
Csc
1/y
Cot
x/y
When is the only time limit properties work?
IF THE LIMIT EXISTS
When do you know you have an asymptote?
X over 0
What trig identity do you have to memorize?
Sin sq x + cos sq x= 1
Sq= squared/^2
