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("lim")(xtooo)(a n-(1+n^2)/(1+n))=b , wh...

`("lim")_(xtooo)(a n-(1+n^2)/(1+n))=b ,` where `a` is a finite number, then(a) `a=1` (b) `a=0` (c) `b=1` (d) `b=-1`

A

`f(0)=1`

B

`f((pi)/(2))=1`

C

`f(a)=(cosa)^(cos^(2)a).(sina)^(sin^(2)a)" if "ain(0,(pi)/(2))`

D

`f(a)=((sina)^(sin^(2)a))/((cosa)^(cos^(2)a))" if "ain(0,(pi)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
A, C
Limit`=underset(ntooo)lim(an(1+n)-(1+n^(2)))/(1+n)=underset(ntooo)lim((a-1)n^(2)+an-1)/(n+1)`
If `a-1=0," limit "=underset(ntooo)lim(an-1)/(n+1)=a=b`
`:. a=b=1`
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CENGAGE-LIMITS-Exercise (Multiple)
  1. Let f(x)={1+(2x)/a ,0lt=x<1a x ,1lt=x<2dotIf("lim")(xvec1)f(x)e xi s t...

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  2. If f(x)=|x-1|-[x],w h e r e[x] is the greatest integer less then or eq...

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  3. ("lim")(xtooo)(a n-(1+n^2)/(1+n))=b , where a is a finite number, then...

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  4. If m , n in N ,("lim")(xvec0)(sinx^m)/((sinx)^m)i s 1,ifn=m (b) 0,i...

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  5. If f(x)={x^nsin(1/(x^2)),x!=0 0,x=0,(n in I),t h e n ("lim")(xvec0)...

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  6. If L=lim(xto0) (1)/(x^(3))((1)/(sqrt(1+x))-(1+ax)/(1+bx)) exists,then

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  7. Which of the following is true?

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  8. The value of lim(nto0) [(1+2+3+...+n)/n^2] is

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  9. If ("lim")(xto1^-)(2-x+a[x-1]+b[1+x]) exists, then aa n db can take th...

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  10. L=("lim")(xveca)(|2sinx-1|)/(2sinx-1)dotT h e n limit does not exist ...

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  11. Let f(x)=lim(ntooo) (x)/(x^(2n)+1). Then

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  12. lim(ntooo) (-3n+(-1)^(n))/(4n-(-1)^(n)) is equal to (n inN)

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  13. Given a real valued function f such that f(x)={tan^2[x]/(x^2-[x]^2) ,...

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  14. If f(x)=(3x^2+a x+a+1)/(x^2+x-2), then which of the following can be c...

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  15. The value of lim(ntooo) [1/n+2] is

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  16. Let f(x) = (x^2-9x+20)/(x-[x]) where [x] denotes greatest integer less...

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  17. Given ("lim")(xvec0)(f(x))/(x^2)=2,w h e r e[dot] denotes the greatest...

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  18. If f(a)=lim(xto2)(sin^(x)a+cos^(x)a)^((1)/((x-2)))" for "ain[0,(pi)/(2...

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