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So far we have considered differentiation of functions of one independent variable. In many situations, we come across functions with more than one independent variable. Since the value of the function is influenced by each independent variable, the rate of change in the value of the function relative to the change in one independent variable can be studied by holding the other independent variable constant. Let z = f(x,y). The change in z for changes in x can be obtained by holding y constant. This is the basic idea behind partial differentiation. The rules for partial differentiation and ordinary differentiation are exactly the same except that when the partial derivative of one independent variable is taken, the other independent variables are treated as constant. The partial derivatives of a function f(x,y) are symbolically represented by to indicate the partial derivative with respect to x and the partial derivative with respect to y respectively.
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a) Let n = (abc) 7 . Prove that n ≡ a + b + c (mod 6). b) Use congruences to show that 4|3 2n - 1 for all integers n ≥ 0.
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a man in rested rupee 800 is buying rupee 5 shares and then are selling at premium of rupee 1.15. He sells all the shares.find profit
Find the center and radius of the circle whose equation is 3 x^2 - 8 x+ 3 y^2+ 4 y+ 2 = 0
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Properties of Dot Product - proof Proof of: If v → • v → = 0 then v → = 0 → This is a pretty simple proof. Let us start with v → = (v1 , v2 ,.... , vn) a
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Partial Derivatives Partial derivatives are used while we want to investigate the effect of one independent variable on dependent variable. For illustration, the revenues of a
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