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If f: R `rarr` R is a function such that f(x +y) =f(x) +f(y) `forall` x,y `in` R then f is continuous on R if it is continuous at a single point in R.

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x=0
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AAKASH SERIES-CONTINUITY -ADVANCED SUBJECTIVE TYPE QUESTIONS
  1. The value of f(0), so that the function f(x)=(sqrt(a^(2)-ax+x^(2))-sqr...

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  2. 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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  3. Find the value of f(0) so that f(x) = (1)/(x) - (2)/(e^(2x) -1) , ...

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  4. Find the value of AO) so that the function f(x) = ((a+x)^(2)sin(a+x)-a...

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  5. If f(x) =(e^(1)/(x^(2))+1)/(e^(1)/(x^(2))-1) (x ne 0) is continuous a...

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  6. Let f(x) be an even function forall x in R If f(x) is continuous at x...

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  7. Let f (x) be an odd function for continuous at x in R If f(x) is conti...

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  8. If f: R rarr R is a function such that f(x +y) =f(x) +f(y) forall x,y ...

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  9. Show that the function f (x) = I x I + I x -1 1 + I x - 2 I is continu...

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  10. If f(x)={{:((1-sin^(3)x)/(3 cos^(2)x),if x lt (pi)/(2)),(a,if x=(pi)/(...

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  11. The number of points of discontinuity of f(x) = [2x—2011] where x in (...

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  12. Find the points where f(x)={{:(x^(2),x in Q),(2-x^(2),x in Q^(c )):} ...

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  13. Find all points of discontinuity of f, where f is defined by f(x)={...

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  14. Find all points of discontinuity of f, where f is defined by f(x)={...

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  15. Is the function defined by f(x)={{:(x+5," if "x le1),(x-5," if "x gt...

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  16. Determine if f defined by f(x)={{:(x^(2)sin""(1)/(x)," if "x ne 0),(...

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  17. Discuss the continuity of the following functions : f(x)= sin x +cos...

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  18. Discuss the continuity of the following functions : f(x) = sin x. co...

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  19. For what value of lambda is the function defined by f (x) f(x)={{:(la...

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  20. Find all points of dicontinuity of f, where f(x)={{:((sinx)/(x)," if...

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