Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Step 1
The given expression is:
The definite integral on interval [a, b]
So, from the given expression is:
Hence, the function is:
The definite integral is expressed as:
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- 1. (a) Draw the graphs of the functions x and x in the plane. Then find all integers n > 2 such that (0, 0) is an inflection point of the function f(x) = x". (x + 1)®x³(x – 2)ª(x – 4)³ for all x. Find all x (b) The second derivative f" of f is given by f"(x) corresponding to inflection points of the graph of f. (c) A polynomial function g has degree 18 (like the degree of f" in part (b)). What is the maximum number of inflection points that the graph of g could possibly have? Explain your answer. (d) From (a) - (c) we see that just because g"(c) = 0 does not mean that (c, g(c)) is an inflection point. What additional property must exist for (c, g(c)) to necessarily be an inflection point?arrow_forward3. Consider the function for x +0 f(x) 1 for x = 0. (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].arrow_forwardDraw the graph of f(x) = sin( in (1-x²) in the viewing rectangle [0, 1] by [0, 0.25] and let I = - $²³ (a) Use the graph to decide whether L2, R2, M₂, and T₂ underestimate or overestimate I. L2 will underestimate I. OL2 will overestimate I. OR₂ will underestimate I. • R₂ will overestimate I. M₂ will underestimate I. O M₂ will overestimate I. OT₂ will underestimate I. T₂ will overestimate I. f(x) dx. (b) For any value of n, list the numbers Ln, Rn Mnr Tn and I in increasing order. (Enter your answers as a comma-separated list.) (c) Compute L5, R 5, M5, and T5. (Round your answer to four decimal places.) L5 = R5 = M5 = T5 =arrow_forward
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