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8. Use the strategy discussed in class (first and second derivative tests, critical points, concavity, x- and y-intercepts, asymptotes, etc.) to analyze each given function and sketch its graph. Label all critical and inflection points b) r(x) = x4 - 4x³ +1 c) f(x) = xe-* a) f(x) = lnx x

8. Use the strategy discussed in class (first and second derivative tests, critical points, concavity, x- and y-intercepts, asymptotes, etc.) to analyze each given function and sketch its graph. Label all critical and inflection points b) r(x) = x4 - 4x³ +1 c) f(x) = xe-* a) f(x) = lnx x

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please answer 8b) in its entirety.
a) lim x+4 x²-16 6x²-10 x - 3x²+4x g) lim a) 1/8 b) 3√2 b) lim t→ x h)lim x-0 cos t cos x-1 c) 16/5 x d) x→5 i) lim X→0 12–5x sin 4x x j) lim sin x x→∞ ex x-0 g) 2; h) 0; i) 4 x2-5x 5√√x-1 k) lim x-10x²-x j) 0 k) 0 x-0+ ex-1 1) lim x→∞ 1) 0 In x X m) ∞ x-8 m) lim e¹x x→0+ 8. Use the strategy discussed in class (first and second derivative tests, critical points, concavity, x- and y-intercepts, asymptotes, etc.) to analyze each given function and sketch its graph. Label all critical and inflection points b) r(x) = x4 - 4x³ + 1 c) f (x) = xe-* In x a) f(x) = 9. Solve the following optimization problems. Be sure to identify the constraint equation and the maximizing/minimizing function, determine the domain of the optimizing function, check the second derivative for optimum value, and write the answer in complete sentence including appropriate units a) If 1200cm² of metal is available to make a box with square base and open top, find the dimensions of the box with largest possible volume. Determine the maximum volume. b) A printed page is to have 1 in. margin on all sides. The page should contain 80 sq inches of type. What dimensions of the page will minimize the area of the page while still meeting the other requirements? c) A running circuit is to be constructed in the shape of a rectangle with two semicircles attached at the east and west ends of the path (see figure). A picnic area will be set in the center of the circuit. If we want the total length of the circuit to be 2,000m (2Km), what will be the dimensions (r and /) that make the picnic area maximum? Give you answer in meters.
Transcribed Image Text:a) lim x+4 x²-16 6x²-10 x - 3x²+4x g) lim a) 1/8 b) 3√2 b) lim t→ x h)lim x-0 cos t cos x-1 c) 16/5 x d) x→5 i) lim X→0 12–5x sin 4x x j) lim sin x x→∞ ex x-0 g) 2; h) 0; i) 4 x2-5x 5√√x-1 k) lim x-10x²-x j) 0 k) 0 x-0+ ex-1 1) lim x→∞ 1) 0 In x X m) ∞ x-8 m) lim e¹x x→0+ 8. Use the strategy discussed in class (first and second derivative tests, critical points, concavity, x- and y-intercepts, asymptotes, etc.) to analyze each given function and sketch its graph. Label all critical and inflection points b) r(x) = x4 - 4x³ + 1 c) f (x) = xe-* In x a) f(x) = 9. Solve the following optimization problems. Be sure to identify the constraint equation and the maximizing/minimizing function, determine the domain of the optimizing function, check the second derivative for optimum value, and write the answer in complete sentence including appropriate units a) If 1200cm² of metal is available to make a box with square base and open top, find the dimensions of the box with largest possible volume. Determine the maximum volume. b) A printed page is to have 1 in. margin on all sides. The page should contain 80 sq inches of type. What dimensions of the page will minimize the area of the page while still meeting the other requirements? c) A running circuit is to be constructed in the shape of a rectangle with two semicircles attached at the east and west ends of the path (see figure). A picnic area will be set in the center of the circuit. If we want the total length of the circuit to be 2,000m (2Km), what will be the dimensions (r and /) that make the picnic area maximum? Give you answer in meters.
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