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For what value of lambda is the function...

For what value of `lambda` is the function defined by
`f(x)={{:(lambda(x^(2)-2x)," if "x le 0),(4x+1," if "x gt 0):}`
continuous at x= 0? What about continuity at x =1?

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Verified by Experts

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 BANGLISH-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5.1
  1. Discuss the continuity of the function f, where f is defined by f(x)...

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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 lambda is the function defined by f(x)={{:(lambda(...

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

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

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  6. Discuss the continuity of the following functions : f(x)= sin x +cos...

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  7. Discuss the continuity of the following functions : f(x)= sin x - co...

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  8. Discuss the continuity of the following functions : f(x) = sin x. co...

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  9. Discuss the continuity of the cosine functions.

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  10. Find all points of dicontinuity of f, where f(x)={{:((sinx)/(x)," if...

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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 by f(x)={{:(sin x-co...

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

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

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

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

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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 func...

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

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

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