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Discuss the continuity of the following ...

Discuss the continuity of the following function : `f(x)={1,if x` is `rational`,
`0`,if `x` is `irrational`

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CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
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  2. Find the value of x where f(x)={x ,if x is rational 1-x ,if x is ir...

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  3. Discuss the continuity of the following function : f(x)={1,if x is rat...

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  4. If f(x)=(x+1)/(x-1)a n dg(x)=1/(x-2),t h e n discuss the continuity ...

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  5. If p,q,r are any real number, then

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  6. Discuss the continuity of f(x)=("lim")(n->oo)cos^(2n)xdot

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  7. Find the values of a if f(x)=("lim")(n rarr oo)(a x^(2n)+2)/(x^(2n)+a...

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  8. If f(x)={(ln x).sgn({x-1/2});1 < x le 3 and {x^2};3 < x le 3.5. Find t...

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  9. Discuss the continuity of f(x)=(lim)(n->oo)(x^(2n)-1)/(x^(2n)+1)

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  10. If f(x)=sgn(2sinx+a) is continuous for all x , then find the possible ...

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  11. Discuss the continuity of f(x)=|x|sgn(x^3-x)

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  12. Discuss the continuity of f(x)=sgn(2cosx-1)

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  13. Discuss the continuity of f(x)=sgn(x^2-2x+3)

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  14. Discuss the continuity of f(x)={(x{x}+1 ,, 0lt=x<1),(2-{x} ,, 1lt=x<2)...

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  15. Discuss the continuity of f(x)=sgn(x^3-x)

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  16. Show that the function f(x)=(x-a)^2(x-b)^2+x takes the value (a+b)/2 f...

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  17. Prove that f(x)=(x^3)/4-sinpix+3 takes the value of 7/3 for x in [-2,2...

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  18. Suppose f is a continuous map from R to R and f(f(a))=a for some adot ...

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  19. Let f:[0,1] rarr [0,1] be a continuous function. Then prove that f(x)...

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  20. Discuss the differentiability of f(x)={( x sin(ln x^2),x!=0),( 0,x=0):...

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