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f(x){{:(2x "," if x lt 0 ),(0"," if 0 le...

`f(x){{:(2x "," if x lt 0 ),(0"," if 0 le x le 1),(4x "," if x gt 1 ):}`

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To determine the continuity of the piecewise function \( f(x) \) defined as follows: \[ f(x) = \begin{cases} 2x & \text{if } x < 0 \\ 0 & \text{if } 0 \leq x \leq 1 \\ 4x & \text{if } x > 1 ...
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NAGEEN PRAKASHAN-Continuity and Differentiability-Exercies 5.1
  1. Is the function defined by f(x)={x+5, ifxlt=1x-5, ifx >1 a continuous...

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  2. Discuss the continuity of the function f, where f is defined by f(x){{...

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  3. f(x){{:(2x "," if x lt 0 ),(0"," if 0 le x le 1),(4x "," if x gt 1 ):}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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