Question 2:
True or False. To find the linear approximation to a function at x = a you need to know the first derivative of that function.
Answer :
True. The linear approximation L(x) to a function f(x) is given by
L(x) = f(a) + (x - a) f '(a) , where f ' is the derivative of f
Question 3:
True or False. Newton's method is used to approximate the extrema of a function.
Answer :
False. Newton's method is used to approximate the zeros of a function.
Question 4:
True or False. Newton's methods fails if f '(a) is equal to zero and a is used as an initial value in the iteration process.
Answer :
True.
Question 5:
True or False. L'Hopital's rule states that the limit of a function of the form f(x) / g(x) is equal to the limit of the derivative of
f(x) / g(x).
Answer:
False. L'Hopital's rule states that the limit of a function of the form f(x) / g(x) is equal to the limit of
f '(x) / g '(x).
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