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Consider the following linear mapping from C[-pi,pi] into itself:
L(f)=integral from -pi to pi of G(x),h(y),f(y)dy for any function f(x) in C[-pi,pi]. Here G(x), H(x) are given continuous functions. Find a function f such that L*f=lambda*f for some lambda and find the value of lambda. This is a generalization of the notion for particular case G(x)=cosx,H(x)=x^2. Hint Look for f(x)=aG(s). Explain why this assumption is reasonable.
Construct an explicit deformation retraction of the torus with one point deleted onto a graph consisting of two circles intersecting in a point, namely, longitude and meridian circles of the torus.
Suppose that you select 2 cards without replacement from an ordinary deck of playing cards. If the first card that you select is a king, what is the probability that the second card that you select is a heart?
Dividing a complex number with another number.
Dividing a complex number with another number
Test for independence of attributes
You are told that a line is tangent to the circle centred at (3,2) with radius 2. If the tangent line and circle intersect at the point (4, 2+ sqrt(3)) find the equation of the tangent.
Estimate rate of changes.
Coffee is draining - Application of calculus
Use linear approximation, the tangent line approximation, to approximate the following: Note: the correct answer are different from the calculator computed values
A bullet is fired vertically upward. Its distance s (in ft) above the ground is given by: s=2250t-16.1t^2 where t is the time (in s).
Find the range of angles that trace out the full graph and determine and graph the equations of the tangent lines at each relative maximum of r
Important information about Probabilty, A single die is rolled once. You lose $12 if a number divisible by 3 turns up. How much should you win if a number not divisible by 3 turns up for the game to be fair?
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