Directions: For each category of problem type you are provided several problem q

Question

Directions: For each category of problem type you are provided several problem questions and the correct answer. Look at the example questions and answers you are provided and determine how the answers were arrived at. Then, devise a rule you could use that could be used to solve any such problem of that type. Once you have completed all 4 categories use the rules/processes you have devised to solve the 4 additional problems at the end of the worksheet.

Category 2:

1) Q: lim?(x?3)??(x^2-9)/(x-3)?

A: lim?(x?3)??(x^2-9)/(x-3)?=6

2) Q: lim?(x?-1)??(x^2+3x-4)/(x^2-6x+5)?

A: lim?(x?-1)??(x^2+3x-4)/(x^2-6x+5)?=-1/2

3) Q: lim?(x?0)??(x^2+4x)/(x^3-2x)?

A: lim?(x?0)??(x^2+4x)/(x^3-2x)?=-2

What process can you develop that can be used to solve any category two problem? What issues

arise when you try to use the rule developed for category one problems? If you were to graph these functions what feature might exist in the graph at the limiting value? Why?

Category 3:

1) Q: lim?(x??)??(3x^2+5x-7)/(5x^2-4x+1)?

A: lim?(x??)??(3x^2+5x-7)/(5x^2-4x+1)?=3/5

2) Q: lim?(x??)??(-x^2+5)/(2x^3-8x^2 )?

A: lim?(x??)??(-x^2+5)/(2x^3-8x^2 )?=0

3) Q: lim?(x??)??(9x^4+2x-11)/(4x-5)?

A: lim?(x??)??(9x^4+2x-11)/(4x-5)?=?

What seems to be the most important factor when dealing with limits as x approaches infinity? What do the degrees of the polynomials in the numerator and denominator have to do with it? What rules or process can you devise to solve any category 3 problem? If you were to graph these functions, what feature would appear in the graph at the limiting value? Why?

Category 4:

1) Q: lim?(x?1)??4/(x^2-1)?

A: lim?(x?1)??4/(x^2-1)?= does not exist

2) Q: lim?(x?4)??(x+2)/(x^2-16)^2 ?

A: lim?(x?4)??(x+2)/(x^2-16)^2 ?=?

3) Q: lim?(x?1)??6-7/(x^2-1)^2 ?

A: lim?(x?1)??6-7/(x^2-1)^2 ?=-?

What happens when you try to apply the method for category 1 problems to these limits? What seems to dictate when a limit such as this does not exist and when it is either infinity or negative infinity? What process can we use to determine the answer for any category 4 problem? If you were to graph these functions, what feature would appear in the graph at the limiting value? Why?

Can anyone please explain with details how it is done? Thanks.

Explanation / Answer

all the operators are messed up plz check!!

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