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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.
Integration Integration is the reversal of differentiation An integral can either be indefinite while it has no numerical value or may definite while have specific numerical v
Derivatives The rate of change in the value of a function is useful to study the behavior of a function. This change in y for a unit change in x is
Circles - Common Polar Coordinate Graphs Let us come across at the equations of circles in polar coordinates. 1. r = a . This equation is saying that there is no matter
Describe the System with 3 Variables ? This is an example of solving a system of equations using the substitution method. Warning: You will not understand this example if you
Chain Rule : Assume that we have two functions f(x) & g(x) and they both are differentiable. 1. If we define F ( x ) = ( f o g ) ( x ) then the derivative of F(x) is,
In proving relation of trigonometric ratios we became confused that what should we do next, so to complete any question quickly what should we do?
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A comparison of the wearing out quality of two types of tyres was obtained by road testing. Samples of 100 tyres were collected. The miles traveled until wear out were recorded and
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