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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

a. `(1)/(2)`

B

b. `-(1)/(2)`

C

c. 0

D

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 PUBLICATION-LIMITS-Exercises (Single Correct Answer Type)
  1. lim(xto0) [min(y^(2)-4y+11)(sinx)/(x)] (where [.] denotes the greatest...

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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(x->1)(1-sqrt(x))/((cos^(-1)x)^2) is (a)4 (b) ...

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  5. lim(x to pi/2)sin(xcosx)/("cos"(xsinx)) is equal to (a) 0 (b) pi/2 ...

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  6. lim(xto0) [(1-e^(x))(sinx)/(|x|)] is (where [.] represents the greates...

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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(ntooo) n(x^(1//n)-1)," then for "xgt0, ygt0,f(xy) is equal...

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  9. lim(x->0) {(1+x)^(2/x)} (where {.} denotes the fractional part of x ...

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

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  11. ("lim")(x->0)(sin(x^2))/(1n(cos(2x^2-x))) is equal to (a) 2 (b) -2 ...

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  12. lim(xtooo) (e^(1//x^(2))-1)/(2tan^(-1)(x^(2))-pi) is equal to

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  13. lim(xto0) ((2^(m)+x)^(1//m)-(2^(n)+x)^(1//n))/(x) is equal to

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

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  15. ("lim")(xto1)(n x^(n+1)-(n+1)x^n+1)/((e^x-e)sinpix),\ where \n=100 , ...

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  16. lim(x->0)(log(1+x+x^2)+"log"(1-x+x^2))/(secx-cosx)=

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  17. The value of lim(xtooo) (root(3)(x^(3)+2x^(2))-sqrt(x^(2)+x)) is

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  18. The value of lim(x->0)(1+sinx-cosx+"log"(1-x))/(x^3) is (a)1/2 ...

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  19. If lim(xtoa)f(x)=1 and lim(xtoa)g(x)=oo then lim(xtoa){f(x)}^(g(x))=e^...

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  20. If lim xto0(x^(-3)sin3x+a x^(-2)+b) exists and is equal to 0, then

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