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# 04faex1 - MATH 221 NAME T A.’s NAME FIRST EXAM Do all 6...

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Unformatted text preview: MATH 221 NAME T. A.’s NAME FIRST EXAM Do all 6 problems and show all work. Otherwise full credit will not be given. Only use techniques already covered in class. 2 20 pts PASSMAN 1. a) (10 pts) Find the equation of the line perpendicular to y :— 22: — 1 and passing through the point P(6,1). Where do the two lines intersect? Use this information to ﬁnd the perpendicular distance from P to the original line. b) (10 pts) Find the center and radius of the circle 2 2 _ a: +y —4:r+2y—20—0 Find the point on the circle diametrically opposite to (—1, 3). 2. a) (10 pts) Use the 5, 6 deﬁnition of limit (only method allowed) to ShOW that lim (:52 +5\$+ 1) = 25 :E—->3 b) (10 pts) Compute . m3—m2+4a:—12 11m ——-——-——~ m->2 :62 — 4 Indicate how continuity is used in your argument. 3. a) Compute , x sinm hm ————-—2— m-+0 cosa: — cos a: b) For what constant c will the function f(\$)_ 5w+c, formg2 ﬂ \$2+3c, forzc>2 be continuous for all values of :12. Explain your answer, including Why continuity holds for all real numbers :13. e the two functions below and simplify your answers. 5. Differentiat a) (10 pts) f(a;) : 33(513 + 1)”4(m + 2)?’ b) (10 pts) t anm gm) ﬂ 1 + seem 6. Differentiate the two functions below. a) (10 pts) . 7 sma: ] 1+3:2 me) = [ b) (10 pts) g(x) = cos [(1)3 + sin 21v)5] ...
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