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For what value of lambdais the function...

For what value of `lambda`is the function defined by `f(x)={lambda(x^2-2x), ifxlt=0 4x+1, ifx >0`continuous at `x = 0`? What about continuity at `x = 1`?

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The correct Answer is:
For no value of `lambda`, f is continuous at x= 0 but f is continuous at x=1 fo any value of `lambda`.
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NCERT GUJARATI-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5.1
  1. f(x) {{:(-2"," if x le -1),(2x"," if -1lt x le 1),(2"," if x gt 1):}

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  2. Find the relationship between a and b so that the function f defined b...

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  3. For what value of lambdais the function defined by f(x)={lambda(x^2-2...

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  4. Show that the function defined by g(x)=x-[x] is discontinuous at all i...

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  5. Is the function defined by f(x)=x^2-sinx+5continuous at x=pi?

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  6. Discuss the continuity of the following functions a) f(x)=sinx+cosx

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  7. Discuss the continuity of the following functions a) f(x)=sinx+cosx

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  8. Discuss the continuity of the following functions a) f(x)=sinx+cosx

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  9. Discuss the continuity of the cosine, cosecant, secant and cotangen...

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  10. Find all points of discontinuity of f, wheref(x)={(sinx)/x , ifx<0x+1,...

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  11. Determine if f defined by f(x)={{:(x^(2)sin""(1)/(x)," if "x ne 0),(...

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  12. Examine the continuity of f, where f is defined byf(x)={sinx-cosx , if...

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  13. Find the values of k so that the function f is continuous at the in...

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  14. Find the values of k so that the function f is continuous at the in...

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  15. Find the values of k so that the function f is continuous at the in...

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  16. Find the values of k so that the function f is continuous at the indi...

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  17. Find the values of a and b such that the function defined by f(x)={...

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  18. Show that the function defined by f(x)=cos(x^2)is a continuous functi...

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  19. Show that the function defined by f(x) = | cos x |is a continuous fun...

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  20. Examine that sin |x| is a continuous function.

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