In each part, evaluate the integral ∫ C ( 3 x + 2 y ) d x + ( 2 x − y ) d y along the stated curve. (a) The line segment from (0,0) to (1,1). (b) The parabolic are y = x 2 from (0,0) to (1, 1). (c) The curve y = sin ( π x / 2 ) from (0,0) to (1, 1). (d) The curve x = y 3 from (0,0) to (1, 1).
In each part, evaluate the integral ∫ C ( 3 x + 2 y ) d x + ( 2 x − y ) d y along the stated curve. (a) The line segment from (0,0) to (1,1). (b) The parabolic are y = x 2 from (0,0) to (1, 1). (c) The curve y = sin ( π x / 2 ) from (0,0) to (1, 1). (d) The curve x = y 3 from (0,0) to (1, 1).
In each part, evaluate the integral
∫
C
(
3
x
+
2
y
)
d
x
+
(
2
x
−
y
)
d
y
along the stated curve.
(a) The line segment from (0,0) to (1,1).
(b) The parabolic are
y
=
x
2
from (0,0) to (1, 1).
(c) The curve
y
=
sin
(
π
x
/
2
)
from (0,0) to (1, 1).
(d) The curve
x
=
y
3
from (0,0) to (1, 1).
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
5) Determine the slope of the tangent line to the function with the given information:
a. f(x, y) = sin(xy) in the direction 2î - 3ĵ, at the point (, -1).
b. f(x, y) =
3+x²
y²
going directly away from the origin, at the point (4,−1).
c. f(x, y) = -6x + 2y + 3 in the direction 30° counter-clockwise from the
negative y-axis, at the point (-2,2).
d. f(x, y) = x³y² + √3x − y in the direction toward (0,5), at the point (3, 1).
The equation of the tangent to the curve y = x' – 3x – 2x + 2 at the point where the curve cuts the y-
axis is
Select one:
O y = x - 1
O y = -2x + 4
O y = x + 2
O y = 2x + 2
O y = -2x + 2
1 of 17 >
Find the equation of the tangent plane to the graph of
f(x, y) = In (14x² – 11y²)
at the point (1, 1).
(Use symbolic notation and fractions where needed. Enter your answer using x-, y-, z-coordinates.)
the equation:
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