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1. Suppose n ≡ 7 (mod 8). Show that n ≠ x 2 + y 2 + z 2 for any x, y, z ε Z. 2. Prove ∀n ε Z, that n is divisible by 9 if and only if the sum of its digits is divisible by 9.
Determine the domain of each of the following functions. f( x ) = x - 4 / x 2 - 2 x -15 Solution With this problem we have to avoid division by
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Find the value of x if 2x + 1, x 2 + x +1, 3 x 2 - 3 x +3 are consecutive terms of an AP. Ans: a 2 -a 1 = a 3 -a 2 ⇒ x 2 + x + 1-2 x - 1 = 3x 2 - 3x + 3- x
GIVE EXAMPLE OF ROW EQUIVALENT
Calculus with Vector Functions In this part we need to talk concisely on derivatives, limits and integrals of vector functions. Like you will see, these behave in a quite pred
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Solution : We'll require the first and second derivative to do that. y'(x) = -3/2x -5/2 y''(x) = 15/4x -7/2 Plug these and also the funct
Prove: 1/cos2A+sin2A/cos2A=sinA+cosA/cosA-sinA
Explain Identifying Conic Sections The graph of a quadratic equation in the variables x and y, like this one, x 2 + 3y 2 + 6y = -4, is a conic sections. There are three kind
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