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If f(x)={x^2+3x+a ,xlt=1b x+2,forx >1 i...

If `f(x)={x^2+3x+a ,xlt=1b x+2,forx >1` is everywhere differentiable, find the values of `aa n dbdot`

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The correct Answer is:
`a=3,b=5`
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CBSE COMPLEMENTARY MATERIAL-CONTINUITY AND DIFFERENTIABILTY-4 Marks Questions
  1. f(x)={{:(,[x]+[-x], x ne 0),(,lambda,x=0):} Find the value of lambda...

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

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

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

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

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

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

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

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

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

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

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

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  13. 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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  14. 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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  15. If x=s e ctheta-costhetaa n dy=sec^ntheta-cos^ntheta,p rov et h a t ...

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

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

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

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

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

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