V63_0121_0010_2008F_Midterm

# V63_0121_0010_2008F_Midterm - f x where f is given by f x =...

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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 anything, just mark one of the options): (a) The domain of f is (i) R (ii) ( - 1 , 0) (1 , 2) (iii) ( - 1 , 0) [1 , 2) (iv) None of above. (b) The range of f is (i) R (ii) ( - 1 , 0) (1 , 2) (iii) ( - 1 , 0) [1 , 2) (iv) None of above. (c) f is continuous on (i) R . (ii) R / { 2 } (iii) R / { 2 , 4 } . (iv) None of above. (d) f 0 is well deﬁned on (i) the set where f is continuous, (ii) on a diﬀerent set, (iii) I don’t know. (e) On its domain, f 0 is (i) even. (ii) non negative. (iii) increasing. (iv) None of above. (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). 1

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MIDTERM 10/08 2 (a) lim t →∞ p t 4 + 11 t 2 + t - 1 - t 2 (b) lim t 4 | t - 4 | t - 4 (c) lim t π/ 2 sec t tan t (3) Using the deﬁnition of derivative compute
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Unformatted text preview: f ( x ) where f is given by f ( x ) = x + √ x x + 1 Check your answer using the quocient rule. (4) Find the derivatives of the following functions: (a) f ( x ) = x 2 (cos( x sin x )) (b) g ( x ) = ( x sec 2 x ) 3 (5) Using implicit diﬀerentiation ﬁnd the tangent line to the curve x 2 + 4 xy + y 2 = 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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V63_0121_0010_2008F_Midterm - f x where f is given by f x =...

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