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if g(x)=(x-a)/x+x/(x-b)then show that g(...

if `g(x)=(x-a)/x+x/(x-b)`then show that `g((a+b)/2)=(4ab)/(a^2-b^2)`

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UNITED BOOK HOUSE-THE SCOTTISH CHURCH COLLEGIATE SCHOOL-EXERCISE
  1. If y=cos^2(x/2)then dy/dx is

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  2. In the expansion of (1+x)^(m+n)the co-efficient of x^mis

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  3. if g(x)=(x-a)/x+x/(x-b)then show that g((a+b)/2)=(4ab)/(a^2-b^2)

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  4. Find the domain of definition of the function f(x)=1/(sqrt(5x-x^2-6))

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  5. If tan(pi/4-theta)=1/2then find sin2theta

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  6. Prove that 2sin(pi/8)=sqrt(2-sqrt2)

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  7. If Z is a complex number |Z+3|le5.then find the greatest and smallest ...

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  8. Find the value of n so that (a^(n+1)+b^(n+1))/(a^(n)+b^n) may be the ...

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  9. In the expansion of (x^2+K/x)^6the co-efficient of x^3is 160.what is t...

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  10. If (2^(2n)-1)is division by 3,then show that [2^(2(n+1))-1]is also div...

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  11. Find the equation of the st.line which pass through the pt(3,1) and pe...

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  12. Show that the locus of the pt of intersection of the st.lines xcosthe...

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  13. Find the focus of the parabola y=x^2+x+1.

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  14. Prove that the derivative of an odd function an ever function .

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  15. Evaluate :lim(xrarry)(cos^2x-cos^2y)/(x^2-y^2)

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  16. If y = sqrt(x+sqrt(x+sqrt(x+* * * infty))) then (dy)/(dx)=

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  17. Prove that Axx(BcupC)=(AxxB)cup(AxxC)

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  18. If cos theta=(acosphi+b)/(a+bcosphi)(theta,phiacute angle)show that ta...

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  19. If (tan3alpha)/(tanalpha)=lambda,show that (sin3alpha)/(sinalpha)=(2la...

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  20. For all n ge 1 prove that (1)/(1.2)+ (1)/(2.3)+(1)/(3.4)+.....+(1)/...

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