I have two similar problems that I need help completing. Please show all your work.

Question: Find the limit L. Then use the å-ä definition to prove the limit is L.

1. lim (2x+5)
2. lim 3
Thank you for your anticipated help!!

  1. 👍 0
  2. 👎 0
  3. 👁 205
  1. **Note**
    Please use the Epsilon-Delta Definition.

    1. 👍 0
    2. 👎 0
  2. 1)

    f(x) = 2 x + 5

    The limit for x to 3 is 11, assuming the function is continuous. To prove this, consider the open interval

    I = (11-epsilon, 11+epsilon)

    for some arbitrary epsilon
    We want to find a delta > 0 such that the function f maps the open interval

    J =(3-delta, 3+delta)

    into I. That would then prove that for any arbitry epsilon>0 such a delta indeed exists. This means that no matter how small you take epsilon, there is always an interval containing x = 3 that will be mapped by f into the interval of size 2 epsilon containing 11.

    If we solve:

    2 x + 5 = y

    for x, we get:

    x = (y-5)/2

    If we take y = 11 +/- epsilon, we get:

    x = 3 +/- epsilon/2

    So, we can take delta = epsilon/2

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    Evaluate the expression for the given value of the variable. Show your work. [-4b-8]+[-1-b^2]+2b^3;b=-2 Solve the equation. Check for extraneous solutions. 9[9-8x]=2x+3. Show your work. I really need help with both of these

  2. Career

    QUESTION 1 -It is important to upgrade your skills as the career world is in a constant state of change. *True False QUESTION 2 -An important component of career planning is completing career research. *True False QUESTION 3 -When

  3. Spanish

    Which of the following would be the correct ending for a verb to show that “I” did the action? Group of answer choices -o -as -a -amos Flag this Question Question 21 pts Which of the following would be the correct ending for a

  4. MATH

    Terry has completed 15 homework problems, and Susan has completed 9. Terry is completing 10 problems per hour, and Susan is completing 12 per hour. After how many hours will Terry and Susan have completed the same number of

  1. Calc - help needed

    Hi, I'm stuck at this question: List all points on the graph of y=tanx on the interval [-3π/2,2π] that have a y-coordinate of (1/radical3). This is my answer, but I keep getting it wrong. Someone, please explain​ how to go

  2. Math

    Kenneth has 22 math problems to do for homework. He has 12 problems done.How many more problems does he left?if he completes 1 problem every minute,how many more minutes does he have to work?

  3. Algebra

    Use factoring and the zero-product property to solve the following problems: z(z - 1)(z + 3) = 0 x^2 - x - 10 = 2 4a^ - 11a + 6 = 0 9r^r - 30r + 21 = -4 Please show work. Thank you so much!

  4. Algebra

    A taco stand sells tacos for $3.35 easch. The stands expenses for the day are $210. Define our variables and write an inequality to represent the amount of tacos they need to sell per day to make a profit, and then solve the

  1. mathematics

    can you please solve these questions. Use completing the square to show that the vertex for f(x) = x2 + x – 2 is at (-1/2, -2 ¼). Use fractions, not decimals, in your work. 2) Show that the vertex for g(x) = 3x2 + 18x + 15 is

  2. Math

    Last year, the personal best high jumps of track athletes in a nearby state were normally distributed with a mean of 229 cm and a standard deviation of 19 cm. What is the probability that a randomly selected high jumper has a

  3. Chemistry

    Homework question? Colmanite [Ca2B6O11 * 5 H20] is a salt whose boron content gives glass high clarity. You are a buyer for an optical fiber manufacturer and want pure material. You have just received a Certificate of Analysis for

  4. compatable numbers

    use compatable numbers to estimate the answers to the following 2 problems. show work 21.98 / 2.56 28.56 / 6.95

You can view more similar questions or ask a new question.