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V63_0121_0010_2008F_Midterm_with_graphs

# V63_0121_0010_2008F_Midterm_with_graphs - MIDTERM 10/08...

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Unformatted text preview: MIDTERM 10/08 CALCULUS I - FALL 2008 Each question worths 20 points. Good luck! Have fun! (1) Take a look at the graph of this strange function f and answer the following questions (dont need to justify anything7 just mark one of the options): (a) C‘id R ,1 i (—1,0)U(1,2) iv) None of above. he domain of f is i ) i AAA .— ._. H e range of f is G v _’:H HVD- % U (—170) U "'l (-1,0)U [1.2) iv) None of above. AAA ._. .— 0—! (C) is continuous on Zea. AAA H. .— ._.. V \ PM [\D 4:. w—1 iv) None of above. ’ is well deﬁned on i the set where f is continuous, ” on a different set, ii') I don’t know. ((1) A CAR H ._. O 11 its domain, f’ is even. non negative. ii.) increasing. iv) None of above. (6) .— ._..‘ i >4 AAAA (2) Calculate the following limits. If the limit does not exist, compute the right and left limits (indicating for instance the cases where the limit is positive inﬁnity or negative inﬁnity). MIDTERM 10/08 2 (a) lim (#4 + 11t2 + t — 1 — t2 t—voo (b) 4 lim lt _ l t—t4 t — 4 (6) lim sec t tan t t—n'r/2 (3) Using the deﬁnition of derivative compute f’(a:) where f is given by Check your answer using the quocient rule. (4) Find the derivatives of the following functions: (a) (b) f(;r) = x2(cos(.r sin g(z) = (m sec 29v)3 (5) Using implicit differentiation ﬁnd the tangent line to the curve m2 +4my+y2 = 13 at the point (2,1). (6) Match the graph of f and f’. (7) (Extra - no points) The distance between the towns A and B is 1000 miles. There is 3000 apples in A, and the apples have to be delivered to B through a desert road. The available car can take 1000 apples at most. The car driver has developed an addiction to apples: when he has apples aboard he eats 1 apple with each mile made. Figure out the strategy that yields the largest amount of apples to be delivered to B. ...
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