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The function f(x)={:{((x^2-1)/(x^3+1),...

The function `f(x)={:{((x^2-1)/(x^3+1),x ne -1),(P, x=-1):}` is not defined for x=-1. The value of f(-1) so that the function extended by this value is continuous is……..

A

`2/3`

B

`-2/3`

C

1

D

0

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The correct Answer is:
B
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FULL MARKS-DIFFERENTIAL CALCULUS - LIMITS AND CONTINUITY-EXERCISE 9.6
  1. lim(x to infty)sqrt(x^2+1)/(2x+1)......

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  2. lim(x to infty)(a^x-b^x)/x.......

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  3. lim(x to 0) (8^x-4^x-2^x+1)/x^2.........

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  4. If f(x)=x(-1)[1/x]xle0, then the value of lim(xto0)f(x) is equal to

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  5. lim(x to3)|x|=..........

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  6. Let the function f be defined f(x)={:{(3x,0lexle1),(-3x+5,1ltxle2):} t...

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  7. If f: R to R is defined by f(x)=lfloorx-3rfloor+lfloorx-4rfloor for x ...

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  8. lim(x to 0) (xe^x-sinx)/x is......

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  9. If lim(x to 0) (sinpx)/(tan3x)=4 then the value of p is……….

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  10. lim(ato pi//4)(sina-cosa)/(a-pi//4)is........

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  11. lim(n to infty)(1/n^2+2/n^2+3/n^2+4/n^2+....+n/n^2)........

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  12. lim(x to 0)(e^(sinx)-1)/x=.......

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  13. lim(x to 0) (e^(sinx)-e^x)/(sinx-x)..........

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  14. The value of lim(x to 0) (sinx)/sqrt(x^2) is.......

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  15. The value of lim(x to k^-) x-[x] , where k is an integer is………….

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  16. At x=3/2 the function f(x)=|2x-3|/(2x-3) is……….

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  17. Let f:R to R be defined by f(x)={:{(x, x " is irrational"),(1-x, x ...

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  18. The function f(x)={:{((x^2-1)/(x^3+1),x ne -1),(P, x=-1):} is not de...

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  19. Let f be a continuous function on [2,5].IF f takes only rational value...

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  20. Let a function f be defined by f(x)=(x-|x|)/x for x ne 0 and f(0)=2. T...

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