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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.
Vertical asymptote Definition : The function f(x) will contain a vertical asymptote at x = a if we contain any of the following limits at x = a . x→a- Note as well that it
The sum of the series 1+1/2+1/4,..is
Question 1. Use cylindrical coordinates to nd the mass of the solid of density e z which lies in the closed region Question 2. The density of a hemisphere of radius a (y
(1) Prove that Zorn's lemma is equivalent to axiom of choice. (2) Use Zorn's Lemma to prove the existence of E.
Convert or Reduce Reduce 4,500 micrograms to grams
solutions
If z=re i ? ,find the value of |e iz | Solution) z=r(cos1+isin1) |e iz |=|e ir(cos1+isin1) |=|e -rsin1 |=e -rsin1
t=2x/s-7
Example Write down the equation of a circle alongwith radius 8 & center ( -4, 7 ) . Solution Okay, in this case we have r =8 , h = -4 and k = 7 thus all we have to do i
Reasons why we start division : The reason we start division by considering the digit in the leftmost place is efficiency and ease . For instance, suppose we divide 417 by 3, we
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