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241finb

241finb - Calculus I(Math 241 Final Problem 1[9 Points...

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Calculus I (Math 241) – Final Problem 1. [9 Points] Calculate the derivatives: d dx ( x 3 sin 2 (2 x +1) ) and d dx ± x 2 +1 2+sin x ² and d dx sec(1 + cos 2 x ) Problem 2. [16 Points] State in precise mathematical term what it means that lim x a H ( x )= L. This includes a statement telling what H ( x ) is, and where it needs to be deﬁned. Diﬀerentiate f ( x )= x 3 using ﬁrst principles. I.e., express f 0 ( a ) as a limit of a diﬀerence quotient and work out the limit. (Make sure to show every step. This may take you 6 lines!) Problem 3. [10 Points] Use 4 16 = 2 and approximation by diﬀerentials to ﬁnd an approximate value for 4 18. Problem 4. [10 Points] Find the equation of the tangent line t ( x )tothe graph of the function f ( x )=cos 2 x at x = π/ 3. Problem 5. [15 Points] Starting out with a disk a radius R , form a round open container (no top) whose sides are straight up. You will have to pleat the edge as you bend it up to form the sides. Find the dimensions of the

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241finb - Calculus I(Math 241 Final Problem 1[9 Points...

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