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If f(x)={(ln x).sgn({x-1/2});1 < x le 3 ...

If `f(x)={(ln x).sgn({x-1/2});1 < x le 3 and {x^2};3 < x le 3.5.` Find the pointswhere the continuity of `f(x),` should be checked, where [.] is greatest integer function and {.} fractional part function.

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CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
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  2. Find the values of a if f(x)=("lim")(n rarr oo)(a x^(2n)+2)/(x^(2n)+a...

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Discuss the differentiability of f(x)={((sinx^2)/x ,x!=0), (0,x=0):} a...

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  17. If f is an even function such that lim(hrarr0)(f(h)-f(0))/h has some f...

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  18. Using intermediate value theorem, prove that there exists a number x s...

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  19. Is the function is non-differential at x=0? f(x)="x"|"x"|

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  20. Is the function is non-differential at x=0? f(x)="cos"|x|

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