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Assume that (X, d) is a metric space and let (x1, : : : , xn) be a nite set of pointsof X. Elustrate , using only the de nition of open, that the set X\(x1, : : : , xn) obtained by removing every xi from X is open in X. (Sketch a picture to get some intuition!)
Differentiate following functions. (a) f ( x ) = 15x 100 - 3x 12 + 5x - 46 (b) h ( x ) = x π - x √2 Solution (a) f ( x ) = 15x 100 - 3x 12 + 5x - 46 I
A painting was purchased 11 years ago for $26900. It has just been sold for $78000. Calculate the flat rate of appreciation p.a.
x^2 + 10x +2 4
Find and classify all the equilibrium solutions to the subsequent differential equation. y' = y 2 - y - 6 Solution First, get the equilibrium solutions. It is generally
1. Find the third and fourth derivatives of the function Y=5x 7 +3x-6-17x -3 2. Find the Tangent to the curve Y= 5x 3 +2x-1 At the point where x = 2.
Evaluate the area of the region. a. 478 units 2 b. 578 units 2 c. 528 units 2 d. 428 units 2 b. Refer to the diagram to evaluate the area of the shaded
Two people are 50 feet separately. One of them begin walking north at rate so that the angle illustrated in the diagram below is changing at constant rate of 0.01 rad/min. At what
A round balloon of radius 'a' subtends an angle θ at the eye of the observer while the angle of elevation of its centre is Φ.Prove that the height of the center of the balloon is a
Calucations of gradients find f Graph some level curve f=const. f=9x^2 = 4y^2
It is totally possible that a or b could be zero and thus in 16 i the real part is zero. While the real part is zero we frequently will call the complex numbers a purely imaginar
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