Reference no: EM131012490
1. Limits and Continuity:
a. Sketch the contour plot for the following functions, and then show that the limit as (x, y) → (0,0) does not exist by determining at least two paths of approach which have different limits as (0. 0):
i. f(x,y) = y/(1-ex)
ii. f(x,y) = 2x2y / (x4+y2)
iii. f(x,y) = x2+y2 / y
2. Partial Dervatives:
a. Consider the following multivariate function:
f(x, y) = 2xy + √(x+4y).
i. Determine the following quantities: fx(x, y), fy{x. y). and fxy(x, y), fxy(x, y) and fyy(x, y).
ii. Determine the equation of the tangent plane at the point (-2. 1). Use it to approximate the value of f(-1. 99, 1. 01).
b. Consider the following multivariate function:
f(x,y) = (x2 - y2) / (x+y)
i. Determine the following quantities: fx(x, y), fy{x. y). and fxy(x, y), fxy(x, y) and fyy(x, y).
ii. Determine the equation of the tangent plane at the point (0, 1). Use it to approximate the value of f(0. 1, 0. 9).
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