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How many roots of the equation (x-1)(x-2...

How many roots of the equation `(x-1)(x-2)(x-3)+(x-1)(x-2)+(x-4)(x-2)(x-3)(x-4)+(x-1)(x-3)(x-4)=0` are positive?

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CENGAGE-APPLICATION OF DERIVATIVES-Solved Examples And Exercises
  1. How many roots of the equation (x-1)(x-2)(x-3)+(x-1)(x-2)+(x-4)(x-2)(x...

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  2. The two curves x^3-3xy^2+2=0 and 3x^2y-y^3-2=0

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  3. Find the angle of intersection of y=a^xa n dy=b^x

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  4. If the sub-normal at any point on y=a^(1-n)x^n is of constant length,...

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  5. Find the cosine of the angle of intersection of curves f(x)=2^x(log)e ...

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  6. Find the value of a if the curves (x^2)/(a^2)+(y^2)/4=1a n dy^3=16 x c...

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  7. The acute angle between the curves y= |x^2 -1| and y=|x^2- 3| at their...

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  8. In the curve x^(m+n)=a^(m-n)y^(2n) , prove that the m t h power of the...

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  9. Find the length of the tangent for the curve y=x^3+3x^2+4x-1 at point ...

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  10. For the curve y=a1n(x^2-a^2) , show that the sum of length of tangent ...

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  11. For the curve y=f(x) prove that (lenght n or mal)^2/(lenght or tanght...

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  12. Find the condition if the equation 3x^2+4a x+b=0 has at least one root...

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  13. Find c of Lagranges mean value theorem for the function f(x)=3x^2+5x+7...

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  14. Let 0<a<b<pi/2dotIff(x)=|tanxtanatanbsinxsinasinbcosxcosacosb|,t h e n...

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  15. Let f(x)a n dg(x) be differentiable for 0lt=xlt=2 such that f(0)=2,g(0...

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  16. Prove that if 2a0 2<15 a , all roots of x^5-a0x^4+3a x^3+b x^2+c x+d=0...

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  17. If f(x) is continuous in [a , b] and differentiable in (a,b), then pro...

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  18. Prove that |tan^(-1)x-tan^(-1)y|lt=|x-y|AAx , y in Rdot

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  19. Using Lagranges mean value theorem, prove that (b-a)/bltlog(b/a)lt(b-a...

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  20. If a &gt; b &gt;0, with the aid of Lagranges mean value theorem, prov...

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  21. Let f(x)a n dg(x) be two functions which are defined and differentiabl...

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