Limit Laws

Question 1

What are the rules for when you plug into a limit and receive an output of 0/0

Answer 1

This means this limit is an indeterminate form. You must do the following:

1) Factor, simplify, plugin,
2) Common demominator, simplify, plug in.
3) Conjugate, similify, pl.ug in.
4) Trig rules, simplify, plug in.
5) L Hopitals Rule, simplify, plug in.

Question 2

What is the trig rule for sin for indeterminate forms?

Answer 2

lim= sin^n ax/bx^n = lim sin(ax)^n/bx^n= a^n/b^n

Question 3

What is the trig rule for cos for indeterminate forms?

Answer 3

lim cos-1/x= lim 1-cosx/x= 0

Question 4

When do we use squeeze theorem

Answer 4

We use the squeeze theorem when we are given an oscillating function for which we can’t determine what the limit is approaching using other methods like factoring, common denominators, conjugation, etc.

Question 5

What is squeeze theorem and what are the steps

Answer 5

We squeeze the graph using two functions. As long as fx) lies between the two functions we can evaluate the lmit of f(x)

Steps

1) Plug in zero into f(x)
2) Determine the problem area of the equation (usually trig)
3) Place the problem area of f(x) between the range of the trig function.
4) Multiple all by the rest of the equation if applicable.
5) Evaluate the limit of the left and right side of f(x)
6) F(x) is infinity -infinity or zero by squeeze theorem.

Question 6

If deg of the ____ is ____ than the top, then f(x) = 0

Answer 6

bottom, greater

Question 7

If degree of the bottom is ____ to the top, then the limit of f(x) = division of the ________

Answer 7

= coefficients

Question 8

If the degree of the ____ is less than the degree of the ____ , then there is ____ _________ ________

Answer 8

bottom, top, no horizontal asymptote. DNE or plus in infinity to the numerator.