1.(2.2) Find the limit. (1) lim 5x x-0 sin 4x (2) lim 2x3+3y4 (x,y)(0,0) x2 + y² 2.(2.3) Let f(x, y) = xy(ex + e) for (x, y) = R². (1) Find fx and fy. (2) Find an equation of the tangent plane to the graph of ƒ at (1, 1, 2e). 3.(2.4) (1) Let c(t) = (sect, tant), πT 2 πT 2

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 59E
icon
Related questions
Question
1.(2.2) Find the limit.
(1) lim
5x
x->0 sin 4x
2x3 + 3y4
(2) lim
(x,y)(0,0) x2 + y²
2.(2.3) Let f(x, y) = xy(ex + e³) for (x, y) = R².
(1) Find fx and fy.
(2) Find an equation of the tangent plane to the graph of ƒ at (1, 1, 2e).
3.(2.4) (1) Let c(t)
=
(sect, tant),
П
2
πT
<t< be a path. Find an xy-equation of this
2
path.
(2) Let c(t) = (cost, sint, t) be a path. Find an equation of the tangent line of c(t) at t =
2
Transcribed Image Text:1.(2.2) Find the limit. (1) lim 5x x->0 sin 4x 2x3 + 3y4 (2) lim (x,y)(0,0) x2 + y² 2.(2.3) Let f(x, y) = xy(ex + e³) for (x, y) = R². (1) Find fx and fy. (2) Find an equation of the tangent plane to the graph of ƒ at (1, 1, 2e). 3.(2.4) (1) Let c(t) = (sect, tant), П 2 πT <t< be a path. Find an xy-equation of this 2 path. (2) Let c(t) = (cost, sint, t) be a path. Find an equation of the tangent line of c(t) at t = 2
Expert Solution
steps

Step by step

Solved in 4 steps with 2 images

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,