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lim(xtooo) (1)/(x+1)tan((pix+1)/(2x+2)) ...

`lim_(xtooo) (1)/(x+1)tan((pix+1)/(2x+2))` is equal to

A

`(1)/(2)`

B

`-(1)/(2)`

C

0

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`underset(xtooo)lim(1)/(x+1)tan((pix+1)/(2x+2))=underset(xtooo)lim(1)/(x+1)cot((pi)/(2)-(pix+1)/(2x+2))`
`=underset(xtooo)lim(1)/(x+1)cot((2pi-2)/(4(x+1)))`
`=(2)/(pi-1).underset(xtooo)lim((pi-1)/(2(x+1)))/("tan"(pi-1)/(2(x+1)))`
`=(2)/(pi-1)`
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CENGAGE-LIMITS-Exercise (Single)
  1. ("lim")(xvec0)[min(y^2-4y+11)(sinx)/x](w h e r e[dot]d e not e st h e ...

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  2. The value of lim(xto0) (1-(cosx)sqrt(cos2x))/(x^(2)) is

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  3. lim(xtooo) (1)/(x+1)tan((pix+1)/(2x+2)) is equal to

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  4. The value of ("lim")(xvec1^-)(1-sqrt(x))/((ccos^(-1)x)^2) is 4 (b) ...

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  5. ("lim")(xvecpi/2)(sin(xcosx)/("cos"(xsinx)i se q u a lto 0 (b) p/2 (...

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  6. ("lim")(xvec0)[(1-e^x)(sinx)/(|x|)]i s(w h e r e[dot] represents the ...

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  7. Evaluate lim(xto0) (x(e^(x)-1))/(1-cosx) is equal to

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  8. If f(x)=lim(n->oo)n(x^(1/n)-1),t h e nforx >0,y >0,f(x y) is equal to ...

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  9. lim(x to 0) {(1+x)^((2)/(x))} (where {.} denotes the fractional part o...

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  10. The value of ("lim")(xvecoo)((2^x^n)^1//e^x-(3^x^n)^1//e^x)/(x^n) (whe...

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  11. ("lim")(xvec0)(sin(x^2))/(1n(cos(2x^2-x)))is equal to 2 (b) -2 (c)...

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  12. ("lim")(xvecoo)(e^1//x^2-1)/(2tan^(-1)(x^2)-pi)i se q u a lto 1 (b) -...

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  13. ("lim")(xto0)((2^m+x)^(1/m)-(2^n+x)^(1/n))/x is equal t o (a) 2(1/(m2...

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

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

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  16. ("lim")(xvec0)(log(1+x+x^2)+"log"(1-x+x^2))/(secx-cosx)= -1 (b) 1 ...

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  17. The value of lim(xto0) (2^(3x)-3^(2x))/x is

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  18. The value of lim(xto0) (1+sinx-cosx+log(1-x))/(x^(3)) is

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

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  20. If ("lim")(xvec0)(x^(-3)sin3x+a x^(-2)+b) exists and is equal to 0, th...

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