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("lim")(xvec1)(1-x^2)/(s in2pix)i se q u...

`("lim")_(xvec1)(1-x^2)/(s in2pix)i se q u a lto` `1/(2pi)` (b) `-1/pi` (c) `(-2)/pi` (d) none of these

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-LIMITS-Exercise (Single)
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  2. lim(xto0) (x^(4)(cot^(4)x-cot^(2)x+1))/((tan^(4)x-tan^(2)x+1)) is equa...

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  3. ("lim")(xvec1)(1-x^2)/(s in2pix)i se q u a lto 1/(2pi) (b) -1/pi (c...

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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")(xvec0)((x+y)sec(x+y)-xsecx)/yi se q u a lto (a)secx(xtanx+1)...

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  6. lim(xto0)(1+x)^(1/(3x))

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  7. ("lim")(n->oo)sum(x=1)^(20)cos^(2n)(x-10) is equal to (a) 0 (b) 1 (...

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  8. lim(xto-1) ((x^(4)+x^(2)+x+1)/(x^(2)-x+1))^((1-cos(x+1))/(x+1)^(2)) is...

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

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  10. The value of ("lim")(xvec0)([(100 x)/(sinx)]+[(99sinx)/x]) (where [.] ...

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

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

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

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