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lim(xto1) (1-x^(2))/(sin2pix) is equal t...

`lim_(xto1) (1-x^(2))/(sin2pix)` is equal to

A

0

B

`oo`

C

-2

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
`underset(xto1)lim(1-x^(2))/(sin2pix)=-underset(xto1)lim(2pi(1-x)(1+x))/(2pisin(2pi-2pix))`
`=underset(xto1)lim((2pi-2pix))/((2pi-2pix))(1+x)/(2pi)=(-1)/(pi)`
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CENGAGE ENGLISH-LIMITS-Exercises (Single Correct Answer Type)
  1. lim(xto0) (x^(a)sin^(b)x)/(sin(x^(c))), where a,b,c inR~{0}, exists an...

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  2. lim(x->0)(x^4(cot^4x-cot^2x+1)/(tan^4x-tan^2x+1)) is equal to (a) 1 (...

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  3. lim(xto1) (1-x^(2))/(sin2pix) is equal to

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  4. lim(xto0) (1)/(x)cos^(1)((1-x^(2))/(1+x^2)) is equal to

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  5. lim(yto0) ((x+y)sec(x+y)-xsecx)/(y) is equal to

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  6. lim(xto1) (1+sinpi((3x)/(1+x^(2))))/(1+cospix) is equal to

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  7. ("lim")(xvecoo)sum(x=1)^(20)cos^(2n)(x-10)i se q u a lto 0 (b) 1 (...

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  8. ("lim")(xvec1)((x^4+x^2+x+1)/(x^2-x+1))^(1-"cos"(x+1))/((x+1)^(2))i se...

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  9. lim(xtooo) {(x+5)tan^(-1)(x+5)-(x+1)tan^(-1)(x+1)} is equal to

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  10. The value of lim(xto0) ([(100x)/(sinx)]+[(99sinx)/(x)]) (where [.] rep...

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  11. The value of lim(xtoa) sqrt(a^(2)-x^(2))"cot"(pi)/(2)sqrt((a-x)/(a+x))...

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  12. lim(xto0) [min(y^(2)-4y+11)(sinx)/(x)] (where [.] denotes the greatest...

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

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

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

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

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

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

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

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

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