Please answer 8b) in its entirety. a) limx+4 x²-166x²-10x - 3x²+4xg) lima) 1/8b) 3√2b) limt→xh)limx-0cos tcos x-1c) 16/5xd)x→5i) limX→012–5xsin 4xxj) limsin xx→∞ exx-0g) 2; h) 0; i) 4x2-5x5√√x-1k) limx-10x²-xj) 0k) 0x-0+ ex-11) limx→∞1) 0In xXm) ∞x-8m) lim e¹xx→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 pointsb) r(x) = x4 - 4x³ + 1 c) f (x) = xe-*In xa) f(x) =9. Solve the following optimization problems. Be sure to identify the constraint equation and the maximizing/minimizingfunction, determine the domain of the optimizing function, check the second derivative for optimum value, and write theanswer in complete sentence including appropriate unitsa) If 1200cm² of metal is available to make a box with square base and open top, find the dimensions of the box withlargest 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 ofthe 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 westends 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 circuitto be 2,000m (2Km), what will be the dimensions (r and /) that make the picnic area maximum? Give you answer inmeters.

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Given function is: rx=x4-4x3+1
Using the first and second derivative tests, we have to find the…

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