Calculate the work done by the vector field F(x,y)=4xy,
2x2
along a smooth, simple curve from point (3, −1) to point (4, 2)
Calculate the work done by the vector field F(x,y)=4xy, 2x2 along a smooth, simple curve from...
Calculate the work done by the vector field F?(x, y?)= ?(4xy, 2x^2) ? along a smooth and simple curve from point (?3, −1)? to point (?4,2)?.
Let f(x)=
if
,
if
if
a) What is the fomain of f(x)? Write in interval notation.
b) Determine the y-intercept of the function, if any. Make sure
to justify your answer.
c) Determine the x-intercepts of the function, if any. Justify
your answer.
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Question
If
a) Find the angle between
b) Find a scalar projection and a vector projection of
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Prove, or give a counter example to disprove the following
statements.
a)
b)
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Solve the harmonic oscillator motion for initial conditions x(0)
= 0, V(0) = V0 in the case of (a) underdamped
(b) overdamped
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Let X be a banach space such that X= C([a,b]) where - ab+ with the sup
norm. Let x and f X. Show
that the non linear integral equation
u(x) = (sin
u(y) dy + f(x) ) has a solution u X. (the integral is
from a to b).
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Evaluate the flux F across the positively oriented surface
S
where
and S is the boundary of
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Suppose that the vector field,
, is continuously differentiable and satisfies
in the interior of the domain
, open and bounded, whose boundary
is a smooth surface (at least
class) , steerable. Show that
cannot be tangent to
in every point of the surface
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Vector Fields problems.
Question 6 Let f (x, y) = x3 + 4xy + 2y2 and of =<P,Q >. P (2, 1) = ? Question 7 vf same as in Question 6 Q (2, 1) =?
sin 0, cos 0
Name the quadrant in which the angle lies
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