University Calculus: Early Transcendentals (3rd Edition)
3rd Edition
ISBN: 9780321999580
Author: Joel R. Hass, Maurice D. Weir, George B. Thomas Jr.
Publisher: PEARSON
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1. Evaluate the integral
f(x, y)dxdy,
of function f R² →R over the domain DC R2, where:
f(x, y) = 2x + y
and D is the is the triangle with vertices (0, -1), (1,0) and (0,2).
Hint. Represent D in the form D = {(x, y) Є R² : x Є (a,b), g(x) < y < h(x)} for
some ab and some functions h(x) and g(x). Then apply Cavalieri principle.
[30 Marks]
Use Green's Theorem to evaluate
Jc (3y-
) dx + ( 7 x + √y 4 + 1 ) dy
(3y-esinx) dx + (7x
2=9
where C is the circle x²+y² = 9.
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- Find all second partial derivatives for f(x, y) = 3xy2 - 2y + 5x2y2 and evaluate fxy(-1, 2).arrow_forwardFor f(x, y) = xex^2y find fx(1, ln 2) and fy(1, ln 2).arrow_forwardFind lim(x, y) as it approaches xy/(x2 +y2) if it exists. If the limit does not exist, say so and justify your answer.arrow_forward
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