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Unformatted text preview: Answers to Test 1 Practice Problems:
1) 2.7183 2) a) "1 b) 4 5 c) !1 3 d) 1 10 e) !" b) L = !2 " = .075 3) a) L = 2 ! = .1 4) a) 1, This yields the slope of the (secant) line through the points (!1,1) and (2,4) on the graph of y = x2 b) 2, This yields the slope of the line that is tangent to the graph of y = x 2 at the point (1,1) c) Part b 5) a) 214 229 245 262 = = = = 1.07 200 214 229 245 In an exponential function the ratios of the successive terms are equal. b) P(t) = 200(1.07) t c) 450 people d) t = 18.5 years. So in year 2008. 6) (I used Mathematica for the calculations. You could use your calculators) t1=100.862.0415*Sqrt[4000+431.03] 98.099512 t2=100.862.0415*Sqrt[4500+431.03] 97.947816 Since T (h) is a continuous function and T (4500) < 98 o < T (4000) there is a corresponding elevation, h where 4000 < h < 4500 such that T (h) = 98o . 7) Squeeze Theorem
"1% a) I would find two different functions that "fit" on either side of x 2 sin 2 $ ' close to x = 0 . # x& I would find the limit of each of these functions. "1% If these limits are the same, I would know x 2 sin 2 $ ' had that same limit. # x& ! b) #1& 0 " sin 2 % ( " 1 $ x' ! #1& 0 ) x 2 " x 2 ) sin 2 % ( " 1) x 2 $ x' #1& 0 " x 2 sin 2 % ( " x 2 $ x' #1& lim 0 = 0 lim x 2 = 0 +lim x 2 sin 2 % ( = 0 x *0 x *0 x *0 $ x' ! 8) a) discontinuous at x = 0, 3 ! x = 0 nonremovable b) x = 3 removable ! 2 c) at x = 3 define g(x) = 3 ! x = 0 is a VA
d) horizontal asymptotes y = 0 ! !
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This test prep was uploaded on 04/01/2008 for the course MATH 1205 taught by Professor Fbhinkelmann during the Fall '08 term at Virginia Tech.
 Fall '08
 FBHinkelmann
 Calculus, Slope

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