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Deine F(x) as the product of two real fu...

Deine `F(x)` as the product of two real functions `f_1(x) = x, x in R`, and `f_2(x) ={ sin (1/x)`, if `x !=0, 0` if `x=0` follows : `F(x) = { f_1(x).f_2(x)` if `x !=0, 0`, if x = 0. Statement-1 : F(x) is continuous on R. Statement-2 : `f_1(x)` and `f_2(x)` are continuous on R.

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MCGROW HILL PUBLICATION-LIMITS AND CONTINUITY-Questions for Previous Years AIEEE/JEE Main Papers
  1. The value of p and q for which the function f(x) = {((sin(p+1)x+sinx...

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  2. Let f : R to [0,oo)" be such that "underset(x to 5)lim f(x)" exists an...

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  3. Deine F(x) as the product of two real functions f1(x) = x, x in R, and...

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  4. The value of lim(xto2)sqrt(1-cos 2(x-2))/(x-2) , is

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  5. If f:""RvecR is a function defined by f(x)""=""[x]cos((2x-1)/2)pi wher...

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  6. lim(x to 0) ((1-cos 2x)(3+cosx))/(x tan 4x) is equal to

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  7. If the function f(x)={((sqrt(2+cosx)-1)/(pi-x)^2 ,; x != pi), (k, ; x ...

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  8. underset(xto0)lim(sin(picos^(2)x))/(x^(2)) is equal to

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  9. If f(x) is continuous and f(9/2)=2/9 , then : lim(x to 0) f((1-cos 3x...

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  10. If Lt(x->2) (tan(x-2)[x^2+(k-2)x-2k])/(x^2-4x+4)=5. then K is equal ...

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  11. if lim(x->oo) (e^(x^2)-cosx)/sin^2x is

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  12. lim(x to 0) ((1-cos 2x)(3+cosx))/(x tan 4x) is equal to

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  13. Let k be a non-zero real number . If f(x)={{:((e^x-1)^2/(sin(xpi/k)log...

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  14. Let p=lim(x->0^+)(1+tan^2 sqrt(x))^(1/(2x)) then log p is equal to

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  15. If lim(xto oo) (1+(a)/(x)-(4)/(x^2))^(2x)=e^3 , the a is equal to

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  16. Let a , b in R,(a in 0). If the funtion f defined as f(x)={{:(,(2x^(...

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  17. Lim( x -> 0) (1 -cos2x)^2 / (2xtanx - x tan2x) is

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  18. Let p=lim(x->0^+)(1+tan^2 sqrt(x))^(1/(2x)) then log p is equal to

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  19. If lim(xto oo) (1+(a)/(x)-(4)/(x^2))^(2x)=e^3 , the a is equal to

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  20. lim(x->3) (sqrt(3x)-3)/(sqrt(2x-4)-sqrt2) is equal to

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