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Prove that a^p b^ q <((a p+b q)/(p+q))^(...

Prove that `a^p b^ q <((a p+b q)/(p+q))^(p+q)dot`

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CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. Given are positive rational numbers a ,b , c such that a+b+c=1, then p...

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  2. Prove that [(a^2+b^2)/(a+b)]^(a+b)> a^a b^b >{(a+b)/2}^(a+b)dot

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  3. Prove that a^p b^ q <((a p+b q)/(p+q))^(p+q)dot

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  4. Let x1, x2, ,xn be positive real numbers and we define S=x1+x2++xndot...

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  5. If 2x^3 +ax^2+ bx+ 4=0 (a and b are positive real numbers) has 3 real ...

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  6. Find the greatest value of x^2y^3z^4 if x^2+y^2+z^2=1,w h e r ex ,y ,z...

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  7. Prove that nC1(nC2)^2(n C3)^3.......(n Cn)^n le ((2^n)/(n+1))^((n+1)C2...

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  8. If y=(x^4)/(x^8+8x^2) , then find the value of dy/dx

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  9. If a , b ,c are three distinct positive real numbers in G.P., then pro...

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  10. For xgeq0 , the smallest value of the function f(x)=(4x^2+8x+13)/(6(1...

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  11. If first and (2n-1)^th terms of an AP, GP. and HP. are equal and the...

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  12. For positive real numbers a ,bc such that a+b+c=p , which one holds?...

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  13. If x ,y ,z are positive numbers is AdotPdot,t h e n (a)y^2geqx z ...

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  14. int 1/((1-x^2)sqrt(1+x^2))dx

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  15. If a >0, then least value of (a^3+a^2+a+1)^2 is (a)64 a^2 (b)16 a^4 ...

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  16. The minimum value of |2z-1|+|3z-2| is

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  17. If a ,b ,c ,d in R^+ such that a+b+c=18 , then the maximum value of a...

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  18. If x ,y and z are posirive real umbers and x=(12-y z)/(y+z) . The max...

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  19. Let x^2-3x+p=0 has two positive roots aa n db , then minimum value if ...

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  20. If a ,b ,c in R^+ , then the minimum value of a(b^2+c^2)+b(c^2+a^2)+...

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