Exam1 MTH251 KEY fall10

# Exam1 MTH251 KEY fall10 - x*3 pg6x t 3 Given g(x...

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Printed Name: V ZV Exam I MTH25I Wed.. October20,2010 Note: Provide exact answers in reduced form, show all work, and clearly indicate your answer. Each question is worth 10 points unless otherwise indicated. l. a) Sketch a viable graph of a function/that satisfies each of the following: Jli_/tx) - -1, J1g/(x) =2 , .f isleft-continuousatx:0, =1,and f(3):2 r<0 A<x<2 x>2 b. Determine the value (if it exists) of each of the following: 't Iiry .fG)= O limf (x)=b'n'/ lim /(x) = tl x+0+ r+0 lry.fu)= 8 ,lin1 "f(O= 8 l4r' , for 2. uiven: ,f("i : I ,', 1or ll0 - x, for a. Sketch a graph of (x). , f(0)= , "f(2)= lyyf (,) = 8' , x+2+" r+2

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ltzY For problems 3 - 6: When asked to determine a limit, use properties of limits and techniques used in class to find each or state that it doesn't exist. AII answers must be justified by sound algebra. Reduce each as much as
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Unformatted text preview: x*3 pg6x t') 3. Given g(x): ut ,t , -x -zx-J a) Find limg(x). r+J = I,n'r' Y-23 b) Find ]{9,s(") DWE-L tl 4. Find tim 3(x +2) x+0.y-gx L7 _L *5r-L O'' a 5. Find lim Ji *s x+2s x - 25 ? l,n; >(ez5 ( f, ot7 ( {* *r ) f,; Y-? ?-{ ./ {* *f "J, lO c J-{r{ ftx*t^J'3(r+L) 6lxl, nJl,7 (2, i. y = tan(O) is discontinuous at 0 = r /2 . e,/>, x-2 is discontinuous at x :2 . Is this an infinite, ajump, discontinuity? (t+3) \/ z "--t-X y = "]: is discontinuous? If so, name them. " e'*e-' y-t.Y 6. Given f (x):3x' . a. Write an expression for .f (x + h). .f (x+h)-.f(x) L l h 'r (xl:u b. Find lim h+0 t t l,u L"+ a dAj *3, l, --"^ hsv zva = 3N + txl-I l,& jump, or removable discontinuity? P"g 'l-1 )T x- +x-6 lt - -_ t-Are there any values of x such that Y-k e^( --o--Y-=) en =" gq--\o \-:/,r' X a=X-tt 12...
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