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2~i + (3x − 6y) ~j and C is the line segment from (3, 7) to (0, 12).
If the temperature on metal sheet is defined by f (x, y,z) = e2x
cos(y − 2z) then find the maximum
rate of change of the function at the (4, −2, 0) and the direction in which this maximum rate of change
of temperature occurs.
If the temperature on metal sheet is defined by f (x, y,z) = e ^2xcos(y − 2z) then find the maximum
rate of change of the function at the (4, −2, 0) and the direction in which this maximum rate of change
of temperature occurs.
Let R be the region bounded by the lines y=2x-1,y=2x-2,y=0 and y=4. By making the substitutions u=(2x-y)/2 ,v=y/2 and integrating over a suitable region evaluate the integral
"\\intop"04 "\\intop"x=y/2+1 x=y/2. (2x-y)/2 dxdy
Use a triple integral to determine the volume of the region bounded by
z
=
√
x
2
+
y
2
and
z
=
x
2
+
y
2
in 1st octant.
Find the critical numbers of the function
ƒ(x) = 2x³ +8x +x²
Find the absolute maximum and minimum values of f on the given interval
ƒ(x) = x^4 + 4x³ - 9
Verify the MVT and find the value of c in the given interval
y = x³ - 9x² + 24x − 18; [2, 4]
evaluate
"\\int_{y=1}^2\\int_{x=0}^3(1+8xy)dxdy"
Evaluate integral integral integral yz dv where E is the region bounded by x = 2y^2 + 2z^2 - 5 and the plane x = 1
