University:
Seattle Pacific University
Course:
MAT 1236 | Calculus III
Academic year:

2024
Views:

271

Pages:

1
Author:

saireerowboz

Workshop #14 1. Find the limits. Note which functions are continuous at the limit point and which functions have a removable discontinuity. (a) 3x2 − y 2 + 5 x2 + y 2 + 2 (f) x2 − 2xy + y 2 x−y (g) xy − y − 2x + 2 x−1 (h) lim cos y + 1 y − sin x (i) lim ln |1 + x2 y 2 | (j) lim (x,y)→(0,0) (b) lim (x,y)→(1,1) (c) lim (x,y)→(1,1) (d) (e) (x,y)→( π2 ,0) (x,y)→(1,1) x+y−4 √ x+y−2 (x,y)→(2,2) !2 1 1 lim + x y (x,y)→(2,−3) √ √ x− y+1 lim x−y−1 (x,y)→(4,3) y e sin x lim x (x,y)→(0,0) √ 2x − y − 2 lim (x,y)→(2,0) 2x − y − 4 lim 2. Prove that the limit does not exist. (a) lim (x,y)→(0,0) (b) lim (x,y)→(0,0) x4 x4 + y 2 x2 + y y (c) lim (x,y)→(0,0) (d) xy 4 x3 + y 6 lim (x,y,z)→(0,0,0) x2 yz + 4y 2 + 9z 2 3. The wind-chill index W is the perceived temperature when the actual temperature is T and the wind speed is v, so we can write W = f (T, v). The table below represents some values of this function. aa T aa v 30 40 50 60 70 -15 -20 -25 -26 -33 -39 -27 -34 -41 -29 -35 -42 -30 -36 -43 -30 -37 -44 a a (a) What row or column would we use to compute f (−20, v)? f (T, 60)? Explain what f (−20, v) and f (T, 60) would represent. ∂W ∂W (b) If we were to compute and , explain what they would represent. ∂T ∂v 4. Find the first partial derivatives of the function. Write your answer with no negative exponents or complex fractions. (a) f (x, y) = x4 y 3 + 8x2 y − x + 4y (b) f (x, y) = x2 tan(xy) 3st2 5s4 + 2t √ (d) f (u, v) = ln u2 − v (c) f (s, t) = 2x3 (e) f (x, y) = e (y+1) (f) f (x, y) = y x