a. lim(tanx • lnx)(adsbygoogle = window.adsbygoogle || []).push({});

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.

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