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For what value of lamda the function def...

For what value of `lamda` the function defined by `f(x)={{:(lamda(x^(2)+2)", if "xle0),(4x+6", if "xgt0):}` is continuous `x=0` ? Hence check the differentiablity of f(x) at x=0.

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The correct Answer is:
`lamda=3`, f(x) is not differentiable at x=0
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ARIHANT PUBLICATION-CONTINUITY AND DIFFERENTIABILITY -CHAPTER PRACTICE (4 MARK)
  1. Find the derivative of (x+sinx)/(x+cosx) w.r.t. x.

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  2. Differentiate w.r.t. x, sin^(-1)[(2^(x+1)*3^(x))/(1+(36)^(x))].

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  3. If y=(sin(ax+b))/(cos(cx+d)), the find (dy)/(dx).

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

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  5. If y=tan^(-1)((a)/(x))+logsqrt((x-a)/(x+a)), then prove that (dy)/(dx)...

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  6. If x=a((1-t^(2))/(1+t^(2))) and y=(2t)/(1-t^(2)), then find (dy)/(dx).

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  7. If x=a(costheta+log"tan"(theta)/(2)) and y=asin theta, then find the v...

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  8. Differentiate x^(xcosx)+(x^(2)+1)/(x^(2)-1) w.r.t. x.

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  9. If y=(sin x - cos x)^((sinx-cosx)),(pi)/(4)ltxlt(3pi)/(4), then find (...

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  10. If log(sqrt(1+x^(2))-x)=ysqrt(1+x^(2)), then show that (1+x^(2))(dy)/(...

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  11. Discuss the continuity of secant.

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  12. Find the set of points, where the function f given by f(x)=|2x-1|sin x...

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  13. If y=e^(x)sinx, then prove that (d^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0,

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  14. Find (dy)/(dx), where y=x^(cotx)+(2x^(2)-3)/(x^(2)+x+2).

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  15. Find the derivative of (sinx)^(x)+sinsqrt(x) w.r.t. x.

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  16. For what value of lamda the function defined by f(x)={{:(lamda(x^(2)+2...

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  17. Find the value of k, the function, f(x)={:{((1-sinx)/((pi-2x)^(2))",...

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  18. If y=(sin^(-1)x)/(sqrt(1-x^(2))), the prove that (1-x^(2))(d^(2)y)/(dx...

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  19. Differentiate tan^(-1)((x)/(1+sqrt(1-x^(2)))) w.r.t. sin(2cot^(-1)sqrt...

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  20. If y=(x+(1)/(x+(1)/(x+ . . .oo))) find (dy)/(dx), the rhs being a vali...

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