Sheet1 - Math 21C DHC Kouba Discussion Sheet 1 1 Sketch the...

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Unformatted text preview: Math 21C DHC Kouba Discussion Sheet 1 1.) Sketch the following surfaces in three—dimensional space. a.) x2+y2+z2=4 b.) $2+yzzz2+4 c.) $2=y2+22+4 2.) Sketch the following two surfaces and their intersection in three-dimensional space. Also plot the projection of this intersection in the my-plane : 22x2+y2 and zzi/ZO—x2—y2 3.) a.) Plot the level curves for z = a using the following values of z : cc 0, 11, i2, i3, i1/2, 1:10 b.) Use part a.) to describe in words what the surface z 2 g looks like. 4.) Evaluate the following limits or justify that the limit does not exist. £1323] 3 3 a.) lim 517 + y 3 3 b.) lim c.) lim “7 +3, ($»y)‘*(1»*1) x2 — y2 (aw—40,0) :54 + By2 (aw—mp) :c + y3 5.) Consider the graph of y = :1: in the scy-plane. Form a surface in three dimensional space by rotating the m—axis about this line. Determine a formula for this surface. 6.) Give an 6/5 proof of the fact that a. lim 3:4 — 4 = 0 . ) (riy)—+(0i0)( y ) . my b. 11m m = 0 . ) (unsure) 3:2 + y2 + 3 ...
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