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final_1041

# final_1041 - 1 Find the fullﬂwing limits Shaw all your...

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Unformatted text preview: 1. Find the fullﬂwing limits. Shaw all your work. (In) Hm F +1 m—rm 5"“: + 5 (.1) lim Elba: 1—40 (2) 53% (1 — mu“ fer 23:11 1&1: 2. L313 I a far 3;: 272—333: for 2:22-11 (:1) Find lirn f and liIn m—Il— z—el-i' (1)) Find the value sf 3?, if any, fer which the limit lini ﬁre) exists. Sheer your war-k. (c) Find the values sf :1 and b, if any, that make f eentinneus at a: : 1. 3.. Circle each expression beiew that represents f’(3). Hm M) + h — H3) . f(3 + 21"») - H3) h—rﬂ h. m H3 + h) '- K3) he flu-+0 4.. Find Simplify your answers when possible. m2—1 19+] (a) y: (b) y = a: sift-“FINE 5. The graph ef the f’(a:) of a functien f is ehewn helew. Answer the fellewing queetiene. (a) Find the critical points of He) and determine whether they are lecal minima, leeal meantime, er neither. (b) Find the points, if any, where f"(e:) deee net exist. (c) On which intervals in the graph of f(:'e) eeneave up? (d) What are the inﬂection peinte ef the graph ef f(:e), if any? 3. Sketch the graph ef a funetien satisfying all ef the given eenditiens. I linti ﬂat) = no ' in M) =0 I Iii—lgnf(m)=3 e f(4)=0 7. A rectanglﬂar pint ef farmland with the area ef 800 m2 will be bounded en ene side by a river and en the ether three sides by a fenee (see the picture belnw). (a) Exprms the length of the fenee L in terms ef :a Rim (1:) Find the dimensiens, s: and y, that minimize the length L ef the fence. Justify yen:- answer. 3. Answer the fellewing questiens. (a) Evaluate the indeﬁnite integral. [wagers (b) Selve the djﬂerentisl equetien with initial eenditien. yes 9. Evsluste the integrals fer the fuse-ties f (3:) whose graph is shewn at right (the part ef the graph fer 3 5 :1: ﬂ 5 is s. semicircle). (b) a] f(\$)dx ﬂ ' 0' The graph ef the functien f (e) = «:3 en the interval [1, 5] is shewn belew. (a) 0n the graph, draw and shade the rectangles whese sree represents Mg, the midpeint appreximetien ef the area. under the curve 3; :2 f(s:) ever the interval [1, 5] using two snbinter— vale. 0:) Determine the: end eempnte M2. (e) Find the area under the graph 3; = Her), 1 5; s: 5 5, usng the Emdsmentsl Theeren1 ef Celeulus. ...
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