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x' = tx^2 x(1) = 1
I have missed the lecture to explain this and the lecturer is not available to explain this to me, so any help would be greatly appreciated.
Define q(x) = 1 if x ε Q and g(x) = 0 otherwise. Prove that q is not Riemann integrable on {0,1) by showing that for all partitions P
U (q, P) L(q,P) > 1
I am really lost on this question, any help would be greatly appreciated!
I am not sure how to put this equation into partial fractions. Any help would be appreciated.
10x + 1/(x(x + 1)(x + 2)).
A particle P moves a long a straight line so that its distance x from the origin is given by the formula
x = 2t^3 - 9t/62 + 12t'
Find the velocity v and acceleration a of P at anty time t. Show that v = 0 when t = 1 and t =2.
I have to write the quadratic taylor series for the expression e^(-x^2). This topic was skimmed over during the lectures and now I have no idea what I am doing. Any help would be greatly appreciated!!
Express the area A defined by the upper quadrant of the ellipse x^2/a^2 + y^2/b^2 = 1
as a double integral in the x,y plane. Hence show that A = πab/4
Use Greens theorem in the plane to evaluate the work inegral:
W = ∫ F. dr = ∫ (3x - y) dx + (x + 2y) dy
where C is the boundary of the ellipse x^2 + 4y^2 = 9
Use polar coordinates in the plane to show that the area of a disc of radius a is ∏a^2.
Using this result, determine the volume of a cone of height h and radius a. Find the position of its centre of mass.
Express the area A defined by the upper quadrant of the ellipse
x^2/ a^2 + y^2/ b^2 = 1
as a double integral in the x, y plane. Hence show that A = ∏ab/4
I have a question about using the quotient rule to parial differentiate. I seem to be confusing myself on how to get the answer and I can't get it. Normally quotient rule is really easy for me, now I am going nuts. If anyone could please show me how to work out this example so I can use the technique to work out other problems I would greatly appreciate it!
f(x,y) = (x + y)/(xy - 1)
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