Results 1 to 2 of 2

Math Help - Determining a δ

  1. #1
    Newbie Rker's Avatar
    Joined
    Mar 2009
    Posts
    6

    Determining a δ

    I have absolutely no idea how to solve these type of problems. My teacher gave a lecture about this subject two days ago, and I took a look at this stickied thread, but I'm still stuck. :s


    In exercises 18, numerically and graphically determine a δ corresponding to (a) ε = 0.1 and (b) ε = 0.05. Graph the function in the ε δ window [x-range is (a δ, a δ) and y-range is (L ε, L + ε)] to verify that your choice works.

    1.
    limx0 (x^2 + 1) = 1


    In exercises 920, symbolically find δ in terms of ε.

    15.
    limx1 (x^2 + x 2)/(x 1) = 3


    52.
    A fiberglass company ships its glass as spherical marbles. If the volume of each marble must be within ε of π/6, how close does the radius need to be to 1/2?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Quote Originally Posted by Rker View Post
    I have absolutely no idea how to solve these type of problems. My teacher gave a lecture about this subject two days ago, and I took a look at this stickied thread, but I'm still stuck. :s


    In exercises 18, numerically and graphically determine a δ corresponding to (a) ε = 0.1 and (b) ε = 0.05. Graph the function in the ε δ window [x-range is (a δ, a δ) and y-range is (L ε, L + ε)] to verify that your choice works.

    1.
    limx0 (x^2 + 1) = 1


    In exercises 920, symbolically find δ in terms of ε.


    15.
    limx1 (x^2 + x 2)/(x 1) = 3




    52.


    A fiberglass company ships its glass as spherical marbles. If the volume of each marble must be within ε of π/6, how close does the radius need to be to 1/2?
    For 1.

    You wish to show that

    \lim_{x\to0}(x^2+1)=1.

    To do this we must have

    |f(x)-L| whenever |x-a|<\delta.

    So, given that \epsilon=0.1we proceed

    |(x^2+1)-1|<0.1

    |x^2|<0.1. Since x^2>0 for all x,

    x^2<0.1

    Can you see how to find delta?

    PS Finding a delta graphically is easy. Just draw the graph. then draw the lines L+\epsilon and L-\epsilon. Where those lines intesect the graph, draw vertical lines down to the x-axis. the line which is closest to x=a is \delta.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Determining dy/du, du/dx, dy/dx
    Posted in the Calculus Forum
    Replies: 6
    Last Post: May 17th 2010, 07:03 PM
  2. determining a and b
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 19th 2010, 02:45 PM
  3. Determining GDP
    Posted in the Business Math Forum
    Replies: 0
    Last Post: March 3rd 2009, 06:36 PM
  4. Determining pH
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: January 30th 2008, 11:54 AM
  5. nid Help on determining A, B, C, and D T_T
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 29th 2006, 08:22 AM

Search Tags


/mathhelpforum @mathhelpforum