Question 3 (a) Show that the limit łycosy lim (x.y)→(0,0) 2x4 +y² does not exist.

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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Question
Q3 (a)
Question 3
(a)
Show that the limit
xżycosy
lim
(x,y)→(0,0) 2x4 +y²
does not exist.
(b)
If u = x² cos y+ye", where x= s+2t and y = st, prove that
ди
2
ди
= (s – 21) (x² siny – xye" – e").
dt
Let f(x, y) = (x² +(3))’. Determine the directional derivative of f at the point
(1,0) in the direction of ū =
(c)
(},).
Transcribed Image Text:Question 3 (a) Show that the limit xżycosy lim (x,y)→(0,0) 2x4 +y² does not exist. (b) If u = x² cos y+ye", where x= s+2t and y = st, prove that ди 2 ди = (s – 21) (x² siny – xye" – e"). dt Let f(x, y) = (x² +(3))’. Determine the directional derivative of f at the point (1,0) in the direction of ū = (c) (},).
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