1 answer

How do you identify all of the asymptotes of #G(x) = (x-1)/(x-x^3)#?

Question:

How do you identify all of the asymptotes of #G(x) = (x-1)/(x-x^3)#?

Answers

Find #G(x) = -1/(x(x+1))# with exclusion #x != 1#, hence vertical asymptotes #x = -1# and #x = 0# and horizontal asymptote #y = 0#.

Explanation:

#G(x) = (x-1)/(x-x^3) = -(x-1)/(x(x-1)(x+1)) = -1/(x(x+1))#

with exclusion #x != 1#

When #x = 0# or #x = -1#, the denominator is zero and the numerator is non-zero, so these are vertical asymptotes.

#G(1) = 0/0# is undefined. This is a removable singularity - not an asymptote. #lim_(x->1) G(x) = -1/2# exists.

As #x->oo, G(x)->0#, so #y = 0# is a horizontal asymptote.

.

Similar Solved Questions

1 answer
Charges in Nucleus
In an early model for the atom the nucleus of charge q wassurrounded by a circular ring of radius r = a of negative charge-q.a. Find the magnitude of the force on the nuclear charge if it isdisplaced the distance x = √(2)a along the axis of thering.b. Will this force:1. be undermined in direct...
1 answer
(1 point) Find k such that the following matrix M is singular. -2 М. 2 -1...
(1 point) Find k such that the following matrix M is singular. -2 М. 2 -1 3 -1 -3 0 -12 -2 + k k =...
1 answer
Metabolic syndrome with its cluster of factors raises a person's risk of CVD. True False
Metabolic syndrome with its cluster of factors raises a person's risk of CVD. True False...
1 answer
Newman Madison needs $238,900 in 10 years. Click here to view factor tables How much must...
Newman Madison needs $238,900 in 10 years. Click here to view factor tables How much must he invest at the end of each year, at 5% interest, to meet his needs? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to O decimal places, e.g. 458,581.) Investment amount ta $...
1 answer
This is a graded discussion: 100 points possible DQ-4 Imagine yourself an educated and religiously devout...
This is a graded discussion: 100 points possible DQ-4 Imagine yourself an educated and religiously devout person back in the 1540's. Would you have belived Copernicus? As you have learned in the readings, there were arguments both for and you would have known back then, and write about how you w...
1 answer
Using neurotransmitter signaling. Cells within a biofilm communicate aculation Aerobic bacteria can grow in either high...
using neurotransmitter signaling. Cells within a biofilm communicate aculation Aerobic bacteria can grow in either high or low oxygen environments, but usually have a slight preference for one or the other. In a parasitic relationship, one member benefits and the other member is neither harmed nor b...
1 answer
2. The most important stakeholder who has an interest or involvement in the behavioral healthcare system,...
2. The most important stakeholder who has an interest or involvement in the behavioral healthcare system, structure, process, task and/or activity is ________________. The client Policy makers Accreditors Payers 3. The _________ process encompasses initial and ongoing assessment tasks and activities...
1 answer
Is #f(x)=(-x^3+x^2+2x-11)/(x-1)# increasing or decreasing at #x=2#?
Is #f(x)=(-x^3+x^2+2x-11)/(x-1)# increasing or decreasing at #x=2#?...
1 answer
A baker is serving a new circular brownie pizza dessert (1" thick with a volume of 132.25 cubic inches). What are the dimensions of the open-topped cardboard box needed to serve the brownie pizza (assume the brownie to be inscribed in the box)?
A baker is serving a new circular brownie pizza dessert (1" thick with a volume of 132.25 cubic inches). What are the dimensions of the open-topped cardboard box needed to serve the brownie pizza (assume the brownie to be inscribed in the box)?...
1 answer
Discuss factors related to the emotional, psychological, cultural, and traditional aspects of food
Discuss factors related to the emotional, psychological, cultural, and traditional aspects of food...
1 answer
13. Which of the following would cause an employee of Hill Corp to recognize income under...
13. Which of the following would cause an employee of Hill Corp to recognize income under the economic benefit doctrine? (A) The employer places assets in a revocable trust for the future benefit of the employee. (B) The employer makes an irrevocable promise to pay a future benefit to the employee....
1 answer
4. When John enters the bank office, there are four customers waiting in line and one...
4. When John enters the bank office, there are four customers waiting in line and one g served. There is a single distributed with A10 customer per hour, independent of everything else. (a) (2 points) What is the average service time per customer? (b) (4 points) What is the distribution of John'...
1 answer
Pepsi is experimenting with a new machine that fills their cans with product three times faster...
Pepsi is experimenting with a new machine that fills their cans with product three times faster than the previous method they were using. However, they are worried that the increase in speed might be because the machine is less accurate. You want to test if the machine is not filling the cans to the...
1 answer
Train waiting time is uniformly distributed with the shortest and the longest waiting times being 7...
train waiting time is uniformly distributed with the shortest and the longest waiting times being 7 and 22 min respectively. What is the standard deviation of the average waiting time of 50 individuals...
1 answer
Nursing information competencies goals ,Write five goals related to learning informatics theory and application,try to make...
nursing information competencies goals ,Write five goals related to learning informatics theory and application,try to make these goals fairly short-term ,within the next five years ....
1 answer
1. 3 examples of good critical thinking regarding a patient diagnosed with cellulite of the right...
1. 3 examples of good critical thinking regarding a patient diagnosed with cellulite of the right lower limb 2. Mrs. John tells the nurse that a friend told her she could not visit because she has not had chickenpox. Her friend is afraid she might “catch chickenpox” from Ms. john.’...
1 answer
A condensed income statement by product line for Healthy Beverage Inc. indicated the following for Fruit...
A condensed income statement by product line for Healthy Beverage Inc. indicated the following for Fruit Cola for the past year: Sales $237,300 Cost of goods sold 110,000 Gross profit $127,300 Operating expenses 144,000 Loss from operations $(16,700) It is estimated that 16% of the cos...