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The fuction f(x) is defined as follows: ...

The fuction f(x) is defined as follows:
f(x)`={(2x-3,x lt 2),(x-1, x ge 2):}`
Prove that f(x) is continuous x at =2.

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NAGEEN PRAKASHAN ENGLISH-Continuity and Differentiability-Exercies 5a
  1. Prove that the function f(x)=2x^2-3x+2 is continuous at at x=1.

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  2. The fuction f(x) is defined as follows: f(x)={(2x-3,x lt 2),(x-1, ...

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  3. Discuss the continuity of the function f(x)={(1+x^2,x le 1),(1-x, x ...

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  4. If f(x) f(x)={((x^2-9)/(x-3)","" " xne3),(" 6""," " "x = 3")...

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  5. Discuss the continuity of the function f(x)={(x", " x ge 0),(2", "...

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  6. The fuction f(x) is defined in the interval [0,1] as follows: f(x)={...

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  7. Discuss the continuity of the function f(x)={(3-x", "x le 0),(x", ...

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  8. Show that the function f(x)={(x-4", "x le 5),(5x-24", "xgt5):}...

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  9. The function f(x) ={{:( 5x-4, " for " 0 lt x le 1) ,( 4x^(2) - 3x, ...

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  10. If f(x)={(x^2+1", "x ne 1),(" "3 ", "x=1):} , then check whethe...

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  11. Discuss the continuity of the function f defined by f(x)=1/x , x!=0.

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  12. Discuss the continuity of the function f(x)={((|x|)/x", " xne 0)...

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  13. (i) Dissusse the continuity of the function f(x)={(|x-a|", " xne a...

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  14. Show that f(x) = sinx is continuous for all values of x.

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  15. Prove that f(x) = {sinx/x ; x != 0 and 1 ; x=0. is continuous at x=0...

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  16. If f(x) ={:{((sin 3x)/(sin 5x)", "x ne 0),(0", " x= 0):}, then d...

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  17. Show that the function f(x) ={:{((sin 3x)/(x)", "x ne 0),(1", " ...

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  18. Discuss the continuity of f(x) ={:{((sin^2 2x)/(x^2)", "x ne 0),(1", ...

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  19. Discuss the continuity of f(x) ={:{(cos""(1)/(x)", "x ne 0),(" "1",...

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  20. Discuss the continuity of f(x) ={:{(sin""(1)/(x)", "x ne 0),(" "1", ...

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