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′P′ is a prime number (P>1000). If P ≡ r (mod 1000). how many value of ′r′. |
Solve the following equation simultaneously and find the stationary points: 2xy^2 c^2 − 4x^3 y^2 − 2xy^4 = 0 -----(1) 2x^2 yc^2 − 2x^4 y − 4x^2 y^3 = 0 -----(2) Please, I need a well detail calculation Thank you |
∫_0 ^( ∞) ((sin^( 3) (x))/x^( 2) ) dx= ? |
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(√(2x−5+3=?)) |
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If A,B,C are finite sets whose elements are from the same universal set U and n(A) denotes the number of element in the set A (a) Show by means of venn diagram that n(A ∪ B) = n(A) + n(B) − n(A ∩ B) (b) Using the fact that (A ∪ B ∪ C) = (A∪B)∪C =A∪(B∪C) deduce an expression for (A∪B∪C) (c) If n(A∪B)= n(A∩B), what can be said about A and B? How did you reach your conclusion. Thank you in advance |
∫_0 ^1_ (dx/((1−x^6 )^(1/6) )) =(π/3) |
Solve for x : 3^(x+2) =15^(x−1) |
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Find the maximum value of the function f(x,y)=x^2 y^2 z^2 subject to the condition that x^2 +y^2 +z^2 =c^2 , where c is the constant. Thank you in advance |
Determine the maximum and minimum of the function: f(x,y)=x^4 +4x^2 y^2 −2x^2 +2y^2 −1 Thank you |
Solve: 4x^3 +8xy^2 −4x=0 -----(1) 8x^2 y−4y =0 -----(2) simultaneosly i.e find the stationary point Thank you |
Find the value of: Π_(n=1) ^∞ ((2^n +1)/(2^n −1)) |
Evaluate the given limit: lim_(n→∞) (((8)^(1/n) −1)/( ((16))^(1/n) −1)) |
ze^z =e Obviously z=1 Now find at least one solution for z∈C |
(d^(3 ) y/dx^3 )=4(x+(1/4))^2 −4y |
x^4 +cx+d=0 then find p from p^6 −4((d^( 3) /c^4 ))^(1/3) p^2 −1=0 x=(c^(1/3) /2)(p±(√(−p^2 −(8/p))) ) |
1×3×5×7×9×...×2005 = ... (mod 1000) |
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Pg 116 Pg 117 Pg 118 Pg 119 Pg 120 Pg 121 Pg 122 Pg 123 Pg 124 Pg 125 |