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Let f(x)=lim(ntooo) (1)/(((3)/(pi)tan^(-...

`Let f(x)=lim_(ntooo) (1)/(((3)/(pi)tan^(-1)2x)^(2n)+5)`. Then the set of values of x for which `f(x)=0` is

A

199

B

198

C

0

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Given `g(x)=underset(ntooo)lim(1)/(((3)/(pi)tan^(-1)2x)^(2n)+5)=0`
or`underset(ntooo)lim[((3)/(pi)tan^(-1)2x)^(2)]^(n)rarroo`
or`((3)/(pi)tan^(-1)2x)^(2)gt1`
or `|tan^(-1)2x|gt(pi)/(3)`
i.e., i.e.,`tan^(-1)2xlt-(pi)/(3)" or "tan^(-1)2xgt(pi)/(3)`
`2xlt1sqrt(3)" or "2xgtsqrt(3),i.e.,|2x|gtsqrt(3)`
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CENGAGE ENGLISH-LIMITS-Exercises (Single Correct Answer Type)
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  3. Let f(x)=lim(ntooo) (1)/(((3)/(pi)tan^(-1)2x)^(2n)+5). Then the set of...

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  6. If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f((pi)/...

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  7. lim(xto1) (xsin(x-[x]))/(x-1), where [.] denotes the greatest integer ...

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  8. lim(xtooo) (x^(2)"tan"(1)/(x))/(sqrt(8x^(2)+7x+1)) is equal to

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  9. lim(xto0) (x^(a)sin^(b)x)/(sin(x^(c))), where a,b,c inR~{0}, exists an...

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

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

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

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

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

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

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

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

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

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

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