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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

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
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