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Graphs, Limits, Continuity, Equation of Line from Two Points

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1. Take the function f(X) = (X-1)/X

a. What does this function equal when X = 0, X = 1, and X =2 ?

b. How about when X =100, X = 1000, and X = 10,000?

c. Describe in words what a graph of this function would look like.

d. What would you say the limit of this function is as X approaches infinity? You can use logic or induction rather than a mathematical proof to answer this question. Just explain your logic.

2. Which of the following functions are continuous? Explain your answer for each part.

a. f(X) = 100

b. f(X) = 1 if X >0

f(X) = 0 if X=0 or X<0

c. f(X) = 2X

d. f(X) = 2x if X>0

f(X) = 0 if X=0

f(X) = 2x if X<0

e. f(X) = 5X2 - 3

3. Suppose a line passes through the points (4, 2) and (0,0). Write an equation for this line, and identify the slope and intercept of this line.

4. Write an equation for the line that passes through the point (5,4) and has a slope of 2.

5. Which of the following functions are linear? Explain your reasoning.

a. f(X) = 5X + 100000

b. f(X) = 2X2 - 200

c. f(X) = 5

d. f(X) = -551 + 10000X

e. f(X) = X3 - X2

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Solution Summary

Fifteen problems involving Graphs, Limits, Continuity, Equation of Line from Two Points, Equation of Line from Slope and a Point and Linearity are solved. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

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  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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