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Is the function defined by f(x)= {(x+5",...

Is the function defined by `f(x)= {(x+5",","if" x le 1),(x-5",","if" x gt 1):}` a continuous function?

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The correct Answer is:
x=1
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KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-Exercise-5.1
  1. f(x) = {(x^(3)-3",","if" x le 2),(x^(2)+1 ",","if " x gt 2):}

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  2. f(x)= {(x^(10)-1",","if" x le 1),(x^(2)",","if" x gt 1):}

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  3. Is the function defined by f(x)= {(x+5",","if" x le 1),(x-5",","if" x ...

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  4. f(x) = {(3",","if" 0 le x le 1),(4",","if" 1 lt x lt 3),(5",","if" 3 l...

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  5. f(x)= {(2x",","if" x lt 0),(0",","if" 0 le x le 1),(4x",","if" x gt 1)...

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  6. f(x)= {(-2",","if" x le -1),(2x",","if" -1 lt x le 1),(2",","if " x gt...

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

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  8. For what value of lamda is the function defined by f(x)= {(lamda(x^(2)...

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

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

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

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

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

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  14. Discuss the continuity of f(x)= cosx, x in R

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  15. Discuss the continuity of the cosine, cosecant, secant and cotangent f...

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  16. Discuss the continuity of the cosine, cosecant, secant and cotangent f...

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  17. Discuss the continuity of the cosine, cosecant, secant and cotangent f...

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  18. Find all points of discontinuity of f, where f(x)= {((sin x)/(x)",","i...

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

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  20. Examine the continuity of f, where f is defined by f(x)= {(sin x- cos ...

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