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If f: R rarr R is a function such that f...

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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AAKASH SERIES-CONTINUITY -ADVANCED SUBJECTIVE TYPE QUESTIONS
  1. If f: R rarr R is a function such that f(x +y) =f(x) +f(y) forall x,y ...

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  2. Find the value of a so that f(x)={{:(ax+3,if x lt 3),(3-x +2x^(2),if...

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  3. Find the values of a and b if f(x)={{:(ax-b,"for" x le -1),(3x^(2)-...

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  4. The value of f(0) so that f(x)=(log(1+x//a)-log(1-x//b))/(x) is contin...

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  5. Show that the function f(x)=(x)/(1+e^(1//x),x ne 0, f(0)= 0 is continu...

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  6. Show that the function f(x) =x sub (1)/(x) , x ne 0 f(0) =0 is conti...

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  7. Show that the function f(x) = x cos (1//x), x ne 0 f(0) = 1 is discont...

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  8. If the function f(x)=(1-cos^(3)ax)/(x sin x) for x ne 0f(0) =1/2 is co...

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  9. Discuss the continuity of f(x)={{:(2x=-1,if x le1),(x^(2),if 1 lt x ...

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  10. If f(x)={{:((sqrt(1+kx)-sqrt1-kx)/(x),"for" -1 le x0),(2x^(2)+3x-2,"fo...

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  11. Define (i) f(x)=(1+5x)^(1//x) is continuous at x = 0.

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  12. Define (i) f(x)=(1+x)/(1-x)^(1//5x) is continuous at x = 0.

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  13. Define (i) f(x)=(1+2x)^(1//3x) is continuous at x = 0.

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  14. Find the values of a and b so that the function defined by f(x) = f(...

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

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  16. The value of f(0), so that the function f(x)=(sqrt(a^(2)-ax+x^(2))-sqr...

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

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

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

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

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