Determine if the limits lim (x, y)-(0, 0) f(x, y) exist by changing the problem to polar coordinates. Use the fact that r→ 0+ as (x,y) → (0, 0) in your work. There are several different situations that can arise. First, if the limit blows up or depends on 0 as r→ 0+ then the If(r cos(0), r sin(0))| ≤ g(r) for all (r, e) and lim f(x, y) = 0. Evaluate the limit below. (If an answer does not exist, enter DNE.) g(r)= 0, then r-0+ (5x³+4y³) lim (x, y) (0, 0) x² + y² (5x³ + 4y³) lim (x, y) (0, 0) x² + y² = lim (x,y) → (0, 0)
Determine if the limits lim (x, y)-(0, 0) f(x, y) exist by changing the problem to polar coordinates. Use the fact that r→ 0+ as (x,y) → (0, 0) in your work. There are several different situations that can arise. First, if the limit blows up or depends on 0 as r→ 0+ then the If(r cos(0), r sin(0))| ≤ g(r) for all (r, e) and lim f(x, y) = 0. Evaluate the limit below. (If an answer does not exist, enter DNE.) g(r)= 0, then r-0+ (5x³+4y³) lim (x, y) (0, 0) x² + y² (5x³ + 4y³) lim (x, y) (0, 0) x² + y² = lim (x,y) → (0, 0)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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