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If f : R to R is defind by f (x) = x...

If f : R `to ` R is defind by f (x) = x - [x], where [x] , is the greatest integer not exceding x , then the set of discontinuous of f is

A

the empty set

B

R

C

Z

D

N

Text Solution

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The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-LIMITS AND CONTINUITY-Exercise 1C(Continuity)
  1. A discontinuous function y=f(x) satisfying x^(2)+y^(2)=4" is given by ...

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  2. The discontinuous points of f(x)=(1)/(log |x|)" are "

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  3. If f : R to R is defind by f (x) = x - [x], where [x] , is the gr...

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  4. If f : R to R is a continuous defined by f(x)=[x]cos ((2x-1)/(2))pi, w...

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  5. f(x)=sqrt(x-[x]) is discontinuous at

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  6. The value of f(0) so that f(x)=(1+x)^(5//x) is continuous at x=0 is

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  7. The value of f(0) so that f(x)=(sin x)/(x) is continuous at x=0 is

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  8. The value of f(0) so that f(x)=(3x+4 tan x)/(x) is continuous at x=3 i...

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  9. The value of f(0) so that f(x)=(3x+4 tan x)/(x) is continuous at x=0 i...

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  10. The value of f(0) so that f(x)=(sqrt(1+x)-1)/(x) is continuous at x=0 ...

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  11. If f(x)=x^(1/(x-1))" for "x ne 1 and if f is continuous at x=1 then f(...

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  12. The value of f(0) so that the function f(x)=((27-2x)^(1//3)-3)/(9-3(24...

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  13. In order that the function f(x)=(x+1)^(cot x) is continous at x=0, f(0...

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  14. The value of f(00) so that the function f(x)=(2x-Sin^(-1)x)/(2x+Tan^(-...

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  15. The value of f(0) so that the function f(x)=(sqrt(1+x)-root3(1+x))/(x)...

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  16. The value of f(0) so that f(x)=(cos^(2)x-sin^(2)x-1)/(sqrt(x^(2)+1)-1 ...

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  17. Extend the definition of the following by continuity f(x)=(1−cos7(x−π)...

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  18. Let f(x)=(1-tan x)/(4x-pi), x ne pi/4, x in [0,pi/2]." If f(x) is cont...

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  19. f(x) ={{:((1-sqrt(2)sin x)/(pi -4x),"if "x ne (pi)/(4)),("k","if "x=(p...

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  20. If f: R to R is defined by f(x)={{:(,(1+3x^(2)-cos2x)/x^(2),"for "x ne...

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