101-2002&2003-1-M10-October2002

101-2002&2003-1-M10-October2002 - 75 minutes 1 lim...

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Kuwait University Dept. of Math. Camp. Sci. Math. 101 First Exam. October 31, 2002 Duration: 75 minutes Calculators, Mobile Phones and Pagers are not allowed. Answer the following questions. 1. Find the vertical and horizontal asymptotes for the graph of J, (if any) where (4 Points) 2. Let J(x) = xsin (x - 2) x2 - X - 2 ' Ax+ 1 x2 -1 ' if x < 2, if x> 2. Find the value of the constant A, so that the function J is continuous at x = 2. (4 Points) 3. Let J (x) = .)7 - 3x. Use the definition of the derivative to find l' (1) . 4. Find l' (x) , if J (x) = x3 tan 2x + sec (x2 + 4) . (4 Points) (4 Points) 5. Let J (x) = 5X3/5 - x + 7. Find the point at which the graph of J has a vertical tangent line. (4 Points) 6. Let J(x) = f Ix ~ :1 ix + 3) \. Find all points of discontinuity of J and classify each x-I x +x--:-6 discontinuity as removable, infinite or jump. (5 Points)
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Kuwait University Dept. of Math. Compo Sci. Math. 101 First Exam. Solution October 31, 2002 Duration:
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Unformatted text preview: 75 minutes , 1. lim f (x) = -00, lim f (x) = 00 ===::;. . I x = -3 IS VA.! x-+-3-x--->-3+ 2/xl VI + ;2 f (x) = ----: lim f (x) = -2, lim f (x) = 2 ===::;. . I y = -2 & y = 2 are Hl x + 3 x--->-oo x-+oo 2. lim! (x) = lim-x-lim sin (x-2) = ~ ! (2) _ 2A + 1 x-+2-x--->2x+Ix-+2 (x-2) 3'--. 3. lim!(x)-!(1) =lim!(x)-!(I) =lim v?-3x-2'= x-+l x-I x-+l x-I x-+l x-I , (7-3x)-4 .-3-3 1f'(1) =-3,1 hm-----:::=---:::=--=--=-~ = l1m-_------= -d 4 . x-+l (x-1) (J?-3x + 2) x-+l J?-3x + 2 4 4. !' (x) = 3x2 tan2x + 2x~ sec2 2x + 2xsec (x2 + 4) tan (x2 + 4). 5. f' (x) = 3x-2/5-1. ! is continuous at x = a and lim If' (x) I = (X) ~ the graph of f ha.s VTL ;-rt the point x-+o (0,7) . 6. The discontinuities of f are at -3, 1, 2.---==------~-------~~~~~----...
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101-2002&amp;2003-1-M10-October2002 - 75 minutes 1 lim...

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