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What is the condition required for a function to be odd?
f is a function defined by : f(x) = x^2-3.
Find f(0), f(2) and f(4).
graph of the following function .
f(x)=-2^x-2
If "y= \\cos x" then dy/dx is
Use implicit differentiation to find the points where the parabola defined by
x^2−2xy+y^2−4y+16=0
has horizontal and vertical tangent lines.
The parabola has horizontal tangent lines at the point(s)
.
The parabola has vertical tangent lines at the point(s)
.
Assume some planet has a radius of roughly c, meters,
and an object located x meters from the center of this planet 1.
weighs w(x) Newtons, where
2.
W(x) =
(
Ax,
B
+2,
3
x>C
and A and B are positive constants. Assuming that
W(x) is continuous for all x
For what values of x w(x) have
a practical interpretation?
What must be true about A and
B?
Roughly sketch the graph of
w(x).
e
A
O
X
b) F sunny
#
(r. Q)
ENG
Let S be the portion of the cone z = 5 − (x2+y2)1/2 lying on and above the plane z = 1 and the portion of the plane z = 1 that encloses it. calculate
"\\intop\\intop" S(x2+y2+z2)5/2 ds and "\\intop\\intop" S(xi+yj+z2k).ds
Find the maximum and minimum values of f(x, y, z) = xyz subject to the constraint 4x2+9y+z2 = 4 Assume that y ≥ 0. Why is this assumption required?
Let D1 be the region in the XY-plane enclosed by the triangle with vertices (0, 0),(1, 1),(2, 0). Let D2 be the semi-circular region of radius 1 with the center at (1, 0) lying below the x-axis. Let D = D1 ∪ D2.
a) Argue whether D is an elementary region.
b) Compute the area of D.
c) Without using Green’s theorem, evaluate "\\intop"C(xydx + x2dy), where C denotes the boundary of D oriented clockwise.
d) Use Green’s theorem to evaluate the line integral given in part c).
A mathematical biologist created a model to administer medicine reaction (measured in change of blood pressure or temperature) with the model given by
2
R= m^2 (C/2- M/3)
where c is a positive constant and m is the amount of medicine absorbed into the blood. The sensitivity to the medication is defined to be the rate of change of reaction R with respect to the amount of medicine absorbed in the blood.
