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If y^2=P(x), where P(x) is a polynomial ...

If `y^2=P(x)`, where P(x) is a polynomial of degree 3, then `2d/dx(y^3(d^2y)/(dx^2))`

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Suppose that f(x) is a quadratic expresson positive for all real x If ...

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  2. If y=cos^(-1)x ,find (d^2y)/(dx^2).

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  3. If y^2=P(x), where P(x) is a polynomial of degree 3, then 2d/dx(y^3(d^...

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  4. If g(x)=|(f(x+c),f(x+2c),f(x+3c)),(f(c),f(2c),f(3c)),(f'(c),f'(2c),f'(...

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  5. If f(a)=2,f^(prime)(a)=1,g(a)=-1,g^(prime)(a)=2, then the value of li...

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  6. If x=a(cost+tsint) and y=a(sint-tcost), find (d^2y)/(dx^2)

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  7. Prove that (2^((log)2 1/4x)-3^((log)(27)(x^2+1)^3)-2x) /(7^(4(log)(49...

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  8. (lim)(hvec0)((e+h)^(1n(e+h))-e)/hi s

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  9. If (x-a)^(2)+(y-b)^(2)=c^(2), for some c gt 0, prove that ([1+((dy)/...

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  10. if y=(x^2-1)^m , then the (2m)th differential coefficient of y is

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  11. If function f satisfies the relation f(x)*f^(prime)(-x)=f(-x)*f^(prim...

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  12. If y=(a+b x^(3/2))/(x^(5/4))a n dy^(prime)=0a tx=5, then the value o...

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  13. If y=e^(acos^(-1)x),-1lt=x<1,s how t h a t (1-x^2)(d^2y)/(dx^2)-x(dy)...

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  14. Let f(x)=(x-1)(x-2)(x-3)...(x-n),n in N ,a n d f'(n)=5040. Then the v...

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  15. If y=((a x+b))/((x^2+c)) , then find dy/dx .

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

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  17. y=f(x), where f satisfies the relation f(x+y)=2f(x)+xf(y)+ysqrt(f(x)),...

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  18. If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 ...

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  19. Prove that (d^n)/(dx^n)(e^(2x)+e^(-2x))=2^n[e^(2x)+(-1)^n e^(-2x)]

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  20. If e^y(x+1)=1, prove that (d^2y)/(dx^2)=((dy)/(dx))^2

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