# Find an equation of the tangent line to the following curve at point (0,4). xe^y+ye^x = 4.?

• Find an equation of the tangent line to the following curve at point (0,4). xe^y+ye^x = 4.?

Answer #1 | 08/02 2014 12:51
tangent equation of f(x) at (a , f(a)) is y - f(a) = f '(a) (x - a)
Positive: 53 %
Answer #2 | 08/02 2014 12:59
Differentiate implicitly. e^y + xe^y dy/dx + dy/dx e^x + ye^x = 0 ==> dy/dx = -(e^y + ye^x)/(xe^y + e^x). The slope m of the tangent line is dy/dx evaluated at (0, 4). m = -(e^4 + 4)/(1) = -(e^4 + 4). y - 4 = m(x- 0) ==> y = -(e^4 + 4)x + 4
Positive: 47 %

1. First-order ODE’s 1A. ... 1 yex a) y = y2 ln x, y(2 ... For each tangent line to the curve, ...
Positive: 53 %
( A ) z = e- x 2- y 2 , (0 , , 1) ( B ) z = x 3- 2 xy (1 ,- 1 , 3) 18. Let C be the intersection of from ... Find Flashcards; Create Flashcards; About ...
Positive: 48 %
12.Find the parametric equation for the tangent line to the curve x= 2sin ... (0;4): 17.A particle moves ... at the point (1; 2;1): 30.Find the equation of ...