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If f:[-5,5]vecR is differentiable functi...

If `f:[-5,5]vecR` is differentiable function and if`f^(prime)(x)` does not vanish anywhere, then prove that `f(-5)!=f(5)dot`

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CBSE COMPLEMENTARY MATERIAL-CONTINUITY AND DIFFERENTIABILTY-4 Marks Questions
  1. If x^m y^n=(x+y)^(m+n) , prove that (dy)/(dx)=y/x .

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  2. If (x-y)dot(x-y)/x=a , Prove that y(dy)/(dx)+x=2ydot

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

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

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  5. Differentiate sin^(-1){(2^(x+1). 3^x)/(1+(36)^x)}"w i t hr e s p e...

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  6. If sqrt(1-x^6)+sqrt(1-x^6)=a(x^3-y^3), then prove that (dy)/(dx)=(x^2)...

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  7. If f(x)=sqrt(x^2+1),\ \ g(x)=(x+1)/(x^2+1) and h(x)=2x-3 , then find f...

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  8. If x=s e ctheta-costhetaa n dy=sec^ntheta-cos^ntheta,p rov et h a t ...

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  9. If x^(y)+y^(x)+x^(x)=m^(n)." then find the value of "(dy)/(dx).

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

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  11. If y=tan^(-1) [(sqrt(1+sinx)-sqrt(1-sin x))/(sqrt(1+sin x)+sqrt(1-sin ...

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  12. If x^(2)/a^(2)+y^(2)/b^(2)=1" then show that "(d^(2)y)/(dx^(2))=-b^(4)...

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  13. Verify Rolle's theorem for the function f(x)=e^(x) sin 2x [0, pi/2]

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  14. Verify Lagranges mean value theorem for function f(x)=sqrt(x^2-4) o...

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  15. If Rolle's theorem holds for the function f(x) = x^(3) + bx^(2) + ax +...

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  16. If y={x+sqrt(x^2+1)}^m , show that (x^2+1)y2+x y1-m^2\ y=0

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  17. Differentiate sin^(-1) [(3x+(4sqrt(1-x^(2))))/(5)] w.r.t.x.

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

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  19. If f:[-5,5]vecR is differentiable function and iff^(prime)(x) does not...

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  20. If y^(1/n)+y^(-1/n) = 2x then (x^2-1)y2+xy1 is equal to

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