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If y=A e^(m x)+B e^(n x) , show that (d^...

If `y=A e^(m x)+B e^(n x)` , show that `(d^2y)/(dx^2)-(m+n)(dy)/(dx)+m n y=0` .

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OSWAAL PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-DIFFERENTIABILITY ( LONG ANSWER TYPE QUESTIONS-I)
  1. If x=asin2t(1+cos2t) and y=bcos2t(1-cos2t), show that at pi/4,(dy)/...

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  2. If x=cost(3-2\ cos^2t) and y=sint(3-2s in^2t) find the value of (dy)/(...

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  3. If y=A e^(m x)+B e^(n x) , show that (d^2y)/(dx^2)-(m+n)(dy)/(dx)+m n ...

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  4. If x = a cos theta + b sin theta and y =asin theta-b cos theta, then p...

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  5. If x^my^n=(x+y)^(m+n) prove that (dy)/(dx)=y/x

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  6. Differentiate log (x^(sin x)+cot^(2) x) w.r.tx.

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  7. If x=2costheta-cos2theta and y=2sintheta-sin2theta then prove that (dy...

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  8. If y=(sinx)^x+sin^(-1)sqrt(x) then find dy/dx.

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  9. If y=xlog"{"x/((a+b x))"]" , then show that x^3(d^2y)/(dx^2)=(x(dy)/(d...

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  10. If y=log{x+sqrt(x^2+a^2)} , prove that: (x^2+a^2)(d^2y)/(dx^2)+x(dy)/(...

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  11. If y={x +sqrt(x^(2)+1)}^(m), then show that (x^(2)+1)(d^(2)y)/(dx^(2))...

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  12. If x=tan(1/alogy) , show that (1+x^2)(d^2y)/(dx^2)+(2x-a)(dy)/(dx)=0 .

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  13. If x=costheta,ysin^3theta,"p r o v et h a t" y(d^2y)/(dx^2)+((dy)/(...

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  14. Differentiate the following function with respect to x : (log"\ x...

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  15. If x=asint\ and y=a(cost+logtant/2) , find (d^2\ y)/(dx^2)

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  16. If y^x=e^(y-x) , prove that (dy)/(dx)=((1+logy)^2)/(logy)

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  17. If siny=xsin(a+y), prove that (dy)/(dx)=(sin^2(a+y))/(sina)

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  18. If xsin(a+y)+sinacos(a+y)=0,p rov et h a t (dy)/(dx)=(sin^2(a+y))/(si...

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  19. Differentiate the following with respect to x : sin^(-1)((2^(x+1). 3^x...

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  20. If x=acos^3theta and y=asin^3theta, then find the value of (d^2y)/(...

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