mt106s - Math 16A (LEC 008)., Fall 2006. October 25, 2006....

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Unformatted text preview: Math 16A (LEC 008)., Fall 2006. October 25, 2006. MIDTERM EXAM 1 NAME(sign): __________________________________________________ __ ID#: ___________________________________ __ Instructions: Each of the 4 problems is worth 25 points. Read each question carefully and answer it in the space provided. YOU MUST SHOW ALL YOUR WORK TO RECEIVE FULL CREDIT. Calculators, books or notes are not allowed. Make sure that you have a total of 5 pages (including this one) with 4 problems. Read through the entire exam before beginning work. TOTAL 2 1. (a) Find the equation of the circle with center at the point (12) which goes through the point (4,6). 2 1 0901+ ($232" U") +65”) (“330131 :2; .WM f (b) Find the equation of the line that goes through the two points (1,2) and (4,6). 6-2 3—2= a (x-i) i) g~2=%(x—Q ecéfix 4%;- 4” $2 —- 1 (1? ~ 2)” asymptotes. Determine also any points where the graph of y = f intersects its horizontal asymptote. Then sketch the graph of this function on which all obtained points and asymptotes are clearly marked. 2. Consider the function f(;r) = Determine the intercepts, and vertical and horizontal bow/wen; X¢2 Inlamfijrs: (0/ “?}‘>) C‘ 4—) 0) (4-) o) )8." z: 0Q /Q/\‘M -———- _ 00 4 3. Compute the following limits. Give each answer as a finite number, +00 or ~00. 4 1‘ I s __ I V /—~—_ (b hm Viz—r3 4 I = + 00 $—+l—— ($_1) r——$+8 q Ix—z) g Q (m - W70 ()1' “1 z (3(4) (2+ malZ—x/x-rB x—afi, (2_ T4; > CL“. V+L13 : )AM (X4) (2+ 4:?) '2- x ‘ 3$2+2$+¢5 r 2+ x + xJ/z d ——————-———I = < ) $1520 6m2+5mfi+4z /Q’“M 4. Throughout this problem, f(a;) = ix] + 2:1: and =' fi-l— 233 + 1. (3.) Sketch the graph of the funcion y = f(sv). Is y = f(:v) continuous at x = 0'? Is y = f(w) differentiable at cc = O? $Cx3= {3X X90) / x) X<Ot m wwm m Minn/«3 Ni X=O P. (-Hu, Qmu’r: W loath 'EJJJJ ext/uni ‘3 :40”) LJ if 41145.5 w‘LIdJL d‘ x: O (in 4a A 3th 4m we“ $ka- (b) What is the domain of y = g(m)? X 2 0 OT CO/ *3 l ) (c) Determine the point at which the tangent to y = 9(115) is parallel to the line y = 3:1: + 17. 8’Cx)=j——;‘+2 ) MM amp-2. __L‘_ +1=3 2J7 4 2‘1“? / —_____———r._.‘:-—-" (d) Compute WW» and f(9(0))- 60330”) = 6(0): 2: :tgtgml = *TPM—l‘: i ...
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mt106s - Math 16A (LEC 008)., Fall 2006. October 25, 2006....

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