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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.
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Explanation of Unitary Method Unitary Method keeps of following two steps:- Step 1 involves find the value of one unit. Step 2 involves find the value of requi
Theorem, from Definition of Derivative If f(x) is differentiable at x = a then f(x) is continuous at x =a. Proof : Since f(x) is differentiable at x = a we know, f'(a
Q1: Find three positive numbers whose sum is 54 and whose product is as large as possible.
Equation s(in Tth second)=u+at-a/2 seems to be dimensionally incorrect.why?
1) At a midway game at the state fair, the probability of winning an individual game is advertised to be 30% ( p = . 3). Suppose 50 people played the game (assume all 50 outcomes
If cos?+sin? = √2 cos?, prove that cos? - sin? = √2 sin ?. Ans: Cos? + Sin? = √2 Cos? ⇒ ( Cos? + Sin?) 2 = 2Cos 2 ? ⇒ Cos 2 ? + Sin 2 ?+2Cos? Sin? = 2Cos 2 ? ⇒
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