MATH 101 Exam 2, Fall 2005

AMERICAN UNIVERSITY OF BEIRUT Mathematics Department Math 101 - Quiz I Fall 2005-2006 Name:......... Ke. weceesenaee ID2. oe. eeeeeeeeeeeeeeeeceeeeeeees Ms. Diana Audi Ms. Marwa El Houri Section 3: Th 08:00 - 09:00 Section 1: T 08:00 - 09:00 Section 4: Th 02:00 - 03:00 Section 2: T 11:00 - 12:00 Section 5: Th 11:00 - 12:00 Section 6: Th 09:30 - 10:30 Time: 60 min Direction: Write your name and ID number and circle your section number. Answer the questions in the allocated spaces, if more space is needed continue on the back. NO CALCULATORS ARE ALLOWED!!! I- (25 points) Let 4-2 2£<2 f(@)={ -r-1 2<2r<3 —4 z>3 a- Draw the graph of f. b- Find its domain and range. Domain Range c- For what values i ais f ar oe ok x= 2: Loo. s - F(Z) t er Yon pte Ay 5 aot Cont ot x= . fe % Rive “be: Pen -x-le -L: be fur: (3) x73" K—y37 A~-3 $s cont ck x = % ra VS Conknuous on (- ~) a) u(2,+°0) : II- (20 points) Find the asymptotes and sketch the graph of a? + 7x +10 z*—4 f(z) = Hociyentab nes P. Yeu : 0, x Pr 10 = {. X + 0 XE? xt k Ba Wet |s a verk cab asym Verheat Asympbeless K-h=0 «> Xeite. X*,de+lo - xt be - (x #29(%-2) . ( XK ar ts nok, avertecat asymp) (blank page) A III- (20 points) Find the limit or explain why it does not exist. a lim 1 = oo ro3- 9 x? x? ~ 20 . ae x(x 2) b- lim od X+h 292 72 -—x—2 KK & (x 42) 009) petite fe t . JV- (15 points) Let f(z) = "1 — and g(x) = 25-2 a Find fo 9(z). FC ge) = rer b- Find the domain for f 0 9. 4) L- (as-xt # © =>? Lx Va5-xt o \6é *¥ 15-xt oy xt x 4 Of 25 -x' Ze V- (20 points) Let f(x) = JE a- Find the slope of the tangent line to the curve y = f(z) at r= a. odin Rar POF Jerk. JE ah d 50 4-55 VAN VE - { - . = Re a 4 aNiw Ae he hoe Be (ae ar) b- For which value of a is the tangent line to the curve parallel to the line 4y — 22 = 31? The bang ent Ore to bo Ih carve, SNe ce): Ux vs a te ee on Ly- ay-2 3 wok a Me. “ee equal | shoal Be core yo me a, Slope of Cine ; a ‘ye 2) mo F 4 . Z>? 4. = 1 => Vaz4 =o\azl ANA wa c- Write the equation of the tangent line at this point. At \P. point a-i 2 4 Stope Me je Vee vied e gales . LY -1) = 4 («- lye gx ra 7