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Show that the function f(x)=(x-a)^2(x-b)...

Show that the function `f(x)=(x-a)^2(x-b)^2+x` takes the value `(a+b)/2` for some value of `x in [a , b]dot`

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CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Discuss the continuity of f(x)={(x{x}+1 ,, 0lt=x<1),(2-{x} ,, 1lt=x<2)...

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

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

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

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

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

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

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

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

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

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

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

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  13. f(x)={([sinpix] ,, 0lt=x<1),(sgn(x-5/4)x{x-2/3} ,, 1lt=xlt=2):} where...

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  14. Find the value of a for which f(x)={x^2,x in Q x+a ,x !in Q is not ...

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  15. Discuss the continuity of f(x)=(log|x|)sgn(x^2-1),x!=0.

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  16. If f(x) is continuous function AAx in R and the range of f(x) = (2, sq...

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  17. Discuss the continuity of f(x) where f(x)=lim(nrarrinfty)("sin" (pix)/...

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  18. Discuss the continuity of f(x)=[tan^(-1)x]

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  19. If y=1/(t^2+t-2),where \ t=1/(x-1), then find the number of points w...

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  20. Let f be a continuous function defined onto [0,1] with range [0,1]. S...

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