Solve c) 3. Consider the functionfor x +0f(x) =for x = 0.(a) Would you expect , f(x) dx to be defined? Explain your answer.Page 2 of 304/16/2021 WorksheetMTH 1410(b) Divide the interval [-1, 1] into 2n parts. Approximate the area under the curveby rectangles, using...i. .the left endpoint on subintervals of [-1,0] and the right endpoint on subin-tervals of [0, 1].ii. .the left endpoint on subintervals of [-1, -] and the right endpoint onsubintervals of [-;, 1].What is the limit as n goes to infinity of each of the expressions calculated above?What does this say about f f(x) dx?(c) Why can't the Fundamental Theorem of Calculus be used to calculate f, f (x) dx?(d) What result do you get if you mistakenly apply the Fundamental Theorem ofCalculus to calculate f, f(x) dx without checking the hypotheses?

The Fundamental Theorem of Calculus (FTC) shows that differentiation and integration are inverse…

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(c) Why can't the Fundamental Theorem of Calculus be used to calculate f' f(x) dx?

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

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Question

Solve c)

3. Consider the function
for x +0
f(x) =
for x = 0.
(a) Would you expect , f(x) dx to be defined? Explain your answer.
Page 2 of 3
04/16/2021 Worksheet
MTH 1410
(b) Divide the interval [-1, 1] into 2n parts. Approximate the area under the curve
by rectangles, using...
i. .the left endpoint on subintervals of [-1,0] and the right endpoint on subin-
tervals of [0, 1].
ii. .the left endpoint on subintervals of [-1, -] and the right endpoint on
subintervals of [-;, 1].
What is the limit as n goes to infinity of each of the expressions calculated above?
What does this say about f f(x) dx?
(c) Why can't the Fundamental Theorem of Calculus be used to calculate f, f (x) dx?
(d) What result do you get if you mistakenly apply the Fundamental Theorem of
Calculus to calculate f, f(x) dx without checking the hypotheses?

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