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Final

# final1530regular+solutions.pdf

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Department
Administrative Studies
Course Code
ADMS 3530
Professor
Barun

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Final Exam for Econ 1530 Sections C and D York University 20 December 2005 First name: Last name: SID number: Instructions: Write your name and SID number above; circle your answer below, and ﬁll out the same answer on the bubble sheet (as well as SID number and name). Problem 1. Aq uniyf K increases by 1% per year (with annual compounding). After approximately how many years has the quantity increased to 2K? (a) 70 years (b) 20 years (c) 2 years (d) 1/2ayer Problem 2. Let S = P n i.hn S equals: i=1 (a) n(n − 1)/2 (b) n(n +1) /2 (c) n (d) none of the above Problem 3. The graph of the linear function f(x) passes through the points (x ,1 )1(0 ,2) and (x 2y 2=(1 ,1). Which is the function? (a) f(x)=2 − x (b) f(x)= α − x (c) f(x)=1 − x (d) none of the above Problem 4. If f 0(x) ≥ 0and f (x) ≤ 0, what of the below describes f? (a) f is increasing and convex (b) f is decreasing and concave (c) f is decreasing and convex (d) f is increasing and concave 0 Problem 5. The function f(x) is such that f (x)= −2o frl x, and passes through the point (x1,y1)=(1 ,4). Which is the function? (a) f(x)=1 − x (b) f(x)= −x 2 (c) f(x)=2(3 − x) (d) none of the above 1 √ Problem 6. Let f(x)= x. Which of the below gives a linear approximation off(x)about 1 x =1? √ (a) f(a)+ a(x − a) (b) (1 − x)/2 (c) (1 + x)/2 (d) none of the above dy Problem 7: Let F(x)= G(y). Which one of the below options gives dx ? (a) dy/dx = G (y)/F (x)0 (b) dy/dx = −F (y)/G (x) 0 0 0 (c) dy/dx = F (x)/G (y) (d) none of the above Problem 8: Let f(x)= x(lnx−1). Which of the below gives the second derivative off(x)? (a) f (x)= 1 ¡1−x +ln x ¢ (1−x)2 x (b) f (x)= 1 x 00 (c) f (x)= x2 (d) none of the above Problem 9: Let U(C)= −e −γC ,wee γ > 0 is a constant. What below gives A(C)= −U (C) U (C) ? (a) A(C)=1 /(1 − γC) (b) A(C)= γ/(1 − γC) (c) A(C)= γ (d) none of the above Problem 10: Let F(x)=1 − e −ax ,wee a> 0s iacosn.Lt G(z)= F (lnz). Which of the below gives G (z)? 0 2 −(1+a) (a) G (z)= −a z (b) G (z)= az −a 0 2 (c) G (z)= −a (d) none of the above 1− 1−γx Problem 11: Let f(x)= x ,he γ > 0 is a constant. Which one of the below options gives lim x→0 f(x)? (a) γ (b) 1/γ (c) γ/2 (d) none of the above 1 0 Recall that a linear approximation off(x)aboux = a is given by f(a)+ f (a)[x − a]. 2 Problem 12: Let the function f(x)= −(1 +x) be deﬁn edonhenra0[ ,1]. Which of the below gives the maximum point for f(x)? (a) x = −1 (b) x =0 (c) x =1 (d) none of the above Problem 13: Figure 1 shows the graph of f (x). Which of the below statements is the correct one? [Note that the graph shows f (x), not f(x).] (a) x = 16 is a local maximum point for f(x) (b) x = 0 is a lo
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