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Prove that the function defined by f(...

Prove that the function defined by
`f(x)= cosx^2`
is a continuous function

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BODY BOOKS PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. (d(a^x))/dx =... a)a^x b)log(a^x) c)a^xlog a d)xa^(x-1)

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  2. Find dy/dx if x^y = y^x

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  3. Prove that the function defined by f(x)= cosx^2 is a continuous f...

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  4. if y=e^(a cos^-1x),-1lexle1, show that dy/dx= (-ae^(acos^-1x))/(...

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  5. If y=e^(acos^-1x) , then show that (1-x^2)y2-xy1-a^2y=0

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  6. Find dy/dx if (sinx)^(cosy) = (cosy)^(sinx)

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  7. Find all points of discontinuity of f where f is defined by f(x)={(2x+...

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  8. If e^(x-y)=x^y then prove that dy/dx=logx/[logex]^2

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  9. Find dy/dx if x^3+2x^2y+3xy^2+4y^3=5

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  10. Find dy/dx if x=2cos^3theta,y=2sin^3theta.

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  11. Find dy/dx of y=sin^-1 2xsqrt(1-x^2) (-1)/sqrt2<x<1/sqrt2

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  12. Find the value of k if the function f(x) = kx+1 if x<5 ...

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  13. Find dy/dx, If x=a(t-sint) , y=a(1+cost)

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  14. Verify Rolle's theorem for the function f(x)=x^2+2 in the interval [...

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  15. Consider f(x)={(3x-8,xle5),(2k,x>5):} . Find the value of k if f(x) is...

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  16. Find dy/dx , if y=(sinx)^logx , sinx>0

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  17. If y=(sin^-1x)^2 , then show that (1-x^2)(d^2y)/(dx^2)-xdy/dx=2

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  18. Determine the value of k so that the function f(x)={(k(x^2+x+1),x<0)...

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  19. If y=[x+sqrt(x^2+9)]^n , show that dy/dx=(ny)/(sqrt(x^2+9)

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  20. Find dy/dx of x=sqrt(a^(sin^-1t) y=sqrt(a^(cos^-1t)

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