z* cos(Tw) 27. lim (z,w)(-2,1) (2²w – 92) 28. lim eitu (z,w)-(-1,2) y - 2 x² + y? 29. lim 30. lim (1.y)(4,2) Vx2 – 4 (x,y)(0,0) 1+y2 ху lim 31. (1.y)(3,4) /x2 + v? 32. lim (x,y)-(0,0) x2 +y? cos x cos x sin y 33. lim 34. lim (x,y)(0,0) (x.y)(0) sin y |x| 35. lim e- * In(x – y) 36. lim (xy)-(I,-3) (x,y)(0,0) |x|+ lyl 37. lim (xy)(-3,-2) (x²y³ + 4xy) lim e- 38. (x,v)-(2,1) 39. (x.y)(0,0) lim tan(x? + y?) tan x² + y2 x' + y³ 43. Let f(x, y) = x² + y2' " (a) Show that x'I s lx|(x? + y°), Iy°l < \y[(x? + y?) (b) Show that |f(x, y)| s |x| + \yl. (c) Use the Squceze Theorem to prove that lim (x,y)-(0,0) f(x, y) = 0.

z* cos(Tw) 27. lim (z,w)(-2,1) (2²w – 92) 28. lim eitu (z,w)-(-1,2) y - 2 x² + y? 29. lim 30. lim (1.y)(4,2) Vx2 – 4 (x,y)(0,0) 1+y2 ху lim 31. (1.y)(3,4) /x2 + v? 32. lim (x,y)-(0,0) x2 +y? cos x cos x sin y 33. lim 34. lim (x,y)(0,0) (x.y)(0) sin y |x| 35. lim e- * In(x – y) 36. lim (xy)-(I,-3) (x,y)(0,0) |x|+ lyl 37. lim (xy)(-3,-2) (x²y³ + 4xy) lim e- 38. (x,v)-(2,1) 39. (x.y)(0,0) lim tan(x? + y?) tan x² + y2 x' + y³ 43. Let f(x, y) = x² + y2' " (a) Show that x'I s lx|(x? + y°), Iy°l < \y[(x? + y?) (b) Show that |f(x, y)| s |x| + \yl. (c) Use the Squceze Theorem to prove that lim (x,y)-(0,0) f(x, y) = 0.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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