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{{:((|x|)/(x)","if x ne 0 ),(0"," if x =...

`{{:((|x|)/(x)","if x ne 0 ),(0"," if x = 0 ):}`
Check continuity of f(x) at x = 0

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To check the continuity of the function \( f(x) \) defined as: \[ f(x) = \begin{cases} \frac{|x|}{x} & \text{if } x \neq 0 \\ 0 & \text{if } x = 0 \end{cases} ...
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NAGEEN PRAKASHAN ENGLISH-Continuity and Differentiability-Exercies 5.1
  1. f(x)=2x+3 if x<= 2 and f(x)=2x-3 if x > 2 check continuity of f(x) at ...

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  2. Find all points of discontinuity of f, where f is defined byf(x)={|x|...

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  3. {{:((|x|)/(x)","if x ne 0 ),(0"," if x = 0 ):} Check continuity of f...

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  4. {{:((x)/(|x|)","if x lt 0 ),(-1"," if x ge 0 ):} Check continuity of f...

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  5. f(x)= {{:(x + 1"," if x ge 1 ),(x^(2)+ 1"," if x lt 1):} Check continu...

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  6. f(x){{:(x^(3) - 3"," if x le 2 ),(x^(2) + 1"," if x gt 2 ):} Check co...

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  7. f(x){{:(x^(3) - 1"," if x le 1 ),(x^(2) "," if x gt 1 ):}

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  8. Is the function defined by f(x)={x+5, ifxlt=1x-5, ifx >1 a continuous...

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  9. Discuss the continuity of the function f, where f is defined byf(x)={...

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

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

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

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

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  14. Show that the function g(x)=x-|x| is discontinuous at all integral ...

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

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

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

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

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  19. Determine if f defined byf(x)={x^2sin(1/x) , ifx!=0, 0 ifx=0 is a con...

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

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