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Disc1 - Math 170 Kouba Discussion Sheet 1 1 Graph each of...

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Unformatted text preview: Math 170 Kouba Discussion Sheet 1 1.) Graph each of the following equations in two-dimensional space. a.)y=3 b.).r=—2 c.)y=x d.)y=3—a: e.)y=w3 1 ac (I: f-)y=e g-)y=1n$ h-)y=\/55 i-)flc=y2 j~)y= 2.) Sketch the level curves for each of the following equations (surfaces) using the following values ofz : -3, —2, —1, 0, 1, 2, 3 a.)z=y b.)z=1——$—y c.)22=w2+y2 d.) m2+y2+z2=9 3.) Sketch all three coordinate plane traces (i.e., :r = O, y = O, and z = 0) for each of the following equations (surfaces). a.)x+2y+32=6 b.)z=;r2+y2 c.)z=yz——:c2 d.)22=a:2+y2 4.) Sketch in three—dimensional space each of the following equations (surfaces). Use intercepts, traces, and/ or level curves as necessary. a.)y:3 b.)x=—2 c.)y=w d.)y:3—:1: e.)y=503 f.)y:ex g.)y:ln:r h.)y=\/E i.):r=y2 j.)y=% k.) m2+y2+z2 =4 l.) m+2y+3z=6 m.) z=m2+y2 n.) 22 =:z:2+y2 o.)z2=w2+y2—1 p.) z2=$2+y2+1 q.)z=yz—:1:2 5.) Determine the center and radius of each of the following spheres. a.) m2+y2+22=144 b.) m2+y2+z2=6y c.) $2+2m+y2—4y+22+6z= 11 d.) sphere whose diameter has endpoints (—1,1,3) and (1,4, —3) 6.) Sketch the domain of each function. a.) f(rry) =ln(;I:2 +y: —4) b.) f(a:,y) 1H(1+37+3J) c. SL‘, :_ d. :r, =‘/ 172—4 2—1 7.) Determine the domain and range of each function. a.) #1311) = m 13) fizzy) =3+em2+y2 C')f($’y)=4”$2“92 d-)f(:v,y)=a;+y+1 8.) Let f(ar,y) = ln(9—ar2 —y2). a.) Determine and sketch the domain of f. b.) Determine the range of f. 0.) Sketch the graph of f . 9.) Sketch a surface corresponding to the following level curves. +++++++++++++++++++++++++++++++++ ”I intend to live forever. So far, so good.” - Steven Wright ...
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