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Determine the values of a ,\ b ,\ c f...

Determine the values of `a ,\ b ,\ c` for which the function `f(x)={(sin(a+1)x+sinx)/x ,\ \ \ for\ x<0c ,\ \ \ for\ x=0(sqrt(x+b x^2))/(b x^(3//2)),\ \ \ for\ x >0` is continuous at `x=0`

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The correct Answer is:
`a=(-3)/(2), b=R-{0}, c=1/2`
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CBSE COMPLEMENTARY MATERIAL-CONTINUITY AND DIFFERENTIABILTY-4 Marks Questions
  1. For what values of constant K, the following functions are continuous ...

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  2. For what values a and b f(x)={{:(,(x+2)/(|x+2|)+a,if x lt -2),(,a+b,if...

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  3. Determine the values of a ,\ b ,\ c for which the function f(x)={(s...

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  4. f(x)={{:(,[x]+[-x], x ne 0),(,lambda,x=0):} Find the value of lambda...

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  5. Let f(x)={{:((1-sin^(3)x)/(3cos^(2)x),"if "x lt(pi)/(2)),(a,"if "x=(pi...

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  6. If f(x)={x^2+3x+a ,xlt=1b x+2,forx >1 is everywhere differentiable, f...

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  7. Find the realtionship between a and b so that the function defined by ...

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  8. Differentiate tan^(-1)((sqrt(1-x^(2)))/(x)) w.r.t. cos^(-1)(2xsqrt(1-x...

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  9. If y=x^(x^(x)), "then find "(dy)/(dx).

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  10. Differentiate (x cos x)^(x)+(x sin x)^(1/x) w.r.t.x.

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

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

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

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

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

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  16. 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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  17. 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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  18. If x=s e ctheta-costhetaa n dy=sec^ntheta-cos^ntheta,p rov et h a t ...

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

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

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