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Check Answers to my problems

  1. Nov 11, 2008 #1
    a. lim(tanx • lnx)
    x-> 0+

    I got lim = 0

    b. lim x^1/x
    x->infinity

    I got lim = 1

    c. Find (if possible) the maximum and minimum values of g(x) = x^2 + 1/x^2 for x>0. Clearly show that you have found the extrema.

    I found; no maximum value and g(1)=2 for my minimum.


    d. Use Newton's method to estimate the solution of the equation sinhx = 1-x. Display the rationale for your initial approximation and the Newton iteration formula for this particular problem.

    x_n+1_= Xn - f(x)/f'(x)

    X1=0
    X2=.5
    X3=.490085
    X4=.490073

    e. Show that for every number a, the linear approximation L(x) to the function f(x) = x^2 at a satisfies f(x) ≥ L(x). [Hint: Construct L(x) at an arbitrary a-value, then determine the sign of the difference f(x) - L(x).]

    my work:
    L(x) (approx) = f(a) +f'(a)(x-a)
    = a^2 + 2a(x-a)
    Substitute 0 in for a
    = 0^2 + 2(0)(x-0)
    L(x)=x
    Therefore f(x) ≥ L(x)
    x^2 ≥ x



    Thanks a bunch.
     
  2. jcsd
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