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The division algorithm says that when a is divided by b, a unique quotient and remainder is obtained. For a fixed integer b where b ≥ 2, consider the function f : Z → Z given by f(a) = r where r is the unique remainder obtained when a is divided by b.
(a) What is the range of f? Based on your answer, is f onto?
(b) Determine whether f a 1-1 function.
What is the ratio of the cone''s volume to the cylinder''s volume
solve the in-homogenous problem where A and b are constants on 0 ut=uxx+A exp(-bx) u(x,0)=A/b^2(1-exp(-bx)) u(0,t)=0 u(1,t)=-A/b^2 exp(-b)
Variable stars are ones whose brightness varies periodically. One of the most visible is R Leonis; its brightness is modelled by the function where t is measured in days.
Non Linear Relationships If the correlation coefficient and the scatter diagram do not indicate linear relationship, then the relationship may be nonlinear. Two such relations
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Classifying critical points : Let's classify critical points as relative maximums, relative minimums or neither minimums or maximums. Fermat's Theorem told us that all relative
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Quotient Rule (f/g)' = (f'g - fg')/g 2 Here, we can do this by using the definition of the derivative or along with Logarithmic Definition. Proof Here we do the pr
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A 25 foot ladder just reaches the top of a house and forms an angle of 41.5 degrees with the wall of the house. How tall is the house?
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