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Find all the points of discontinuity of f defined by `f(x)" "=" "|" "x" "|" "" "|" "x" "+" "1" "|` .

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Let `g(x) =|x| - |x +1|`
We know that the modulus function `g(x) = |x|` and
`h(x) = |x +1|` are continuous for all x`ne` R.
`rArr f(x) ` is not discontinuous at any point.
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NAGEEN PRAKASHAN-Continuity and Differentiability-Exercies 5.1
  1. f(x){{:(2x "," if x lt 0 ),(0"," if 0 le x le 1),(4x "," if x gt 1 ):}

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

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

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

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

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

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  7. Discuss the continuity of the following functions:(a) f(x) = s in x + ...

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

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

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  10. Determine if f defined byf(x)={x^2sin1/x , ifx!=0 0, ifx=0

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

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  12. f(x) = {{:((k cosx )/((pi - 2x)"," if x ne (pi)/(2))),(3"," if x = (p...

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  13. f(x) = {{:(kx^(2)"," if x le 2),(3", " if x gt 2):} at x = 2

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  14. Find the value of k for which f(x)={k x+1 when xlt=picosx when x gtpi

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

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

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

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

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

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  20. Find all the points of discontinuity of f defined by f(x)" "=" "|" ...

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