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If f(x)=x cos""1/x^(2)" for "x ne 0, f(...

If `f(x)=x cos""1/x^(2)" for "x ne 0, f(0)=1" then at x=0, f(x) is"`

A

continuous

B

discontinuous

C

not determined

D

none

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The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-LIMITS AND CONTINUITY-Exercise 1C(Continuity)
  1. f(x) = (x - [x]) sin ((1)/(X)) , at x = 0 , f is

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  2. If f(x)=x sin ""1/x"for "x ne 0, f(0)=0" then at x"=0, f(x) is

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  3. If f(x)=x cos""1/x^(2)" for "x ne 0, f(0)=1" then at x=0, f(x) is"

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  4. If f(x)=(x)/(1+e^(1//x))"for "x ne 0, f(0)=0" then at x=0, f(x) is"

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  5. The function f(x) =(xe^(1//x))/(1+e^(1//x))+sin""1/x" for "x ne 0, f(0...

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  6. If f(x)=(e^(1//x)-1)/(e^(1//x)+1)" for "x ne 0, f(0)=0" then at x=0, f...

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  7. If f(x)=(sin^(2)ax)/(x^(2))" for "x ne 0, f(0)=1 is continuous at x=0 ...

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  8. if f(x)=(1-cos ax)/(x sin x)" for "x ne 0, f(0)=1//2 is continuous at ...

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  9. A function f is defined by f(x)= {{:((sin (a + 1) x + sinx)/(x)" if...

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  10. f(x)= |x| is

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  11. If f(x)=x^(2)," for x rational" =-x^(2), "for x irrational, then "

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  12. If f(x)=(Tan^(-1)(x+2))/(|x+2|), x ne -2 and f(-2)=2"then "

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  13. f(x)=1 for x is rational f(x)=-1 for x irrational, f is continuous on

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  14. If a lt b then f(x) =sqrt ((x-a)/(b-x)) is continuous on

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  15. The function f(x)={{:(,3x-1,"if "x lt 1),(,x^(2),"if "x gt 2):}} is co...

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  16. If f: RR to RR is defined by f(x)={{:(,(x+2)/(x^(2)+3x+2),"if "x in R-...

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  17. Let 'f' be a non-zero real valued continuous function satisfying f(x ...

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  18. If f(x+y)=f(x) f(y) and f(x)=1+g(x), h(x)" where "underset(x to 0)"Lt"...

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  19. Let f(x)=f(x) f(y) for all x and y. If f(x) is continuous at x=1. then...

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  20. A discontinuous function y=f(x) satisfying x^(2)+y^(2)=4" is given by ...

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