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The value of lim(x->pi)(1+cos^3x)/(sin^2...

The value of `lim_(x->pi)(1+cos^3x)/(sin^2x) is`

(a)`1/3`

(b) `2/3`

(c) `-1/4`

(d) `3/2`

A

[2, 5)

B

(1, 5)

C

(-1, 5)

D

`(-oo, oo)`

Text Solution

Verified by Experts

The correct Answer is:
D
We have `underset(xto pi)lim(1+cos^(3)x)/(sin^(2)x)=underset(xto pi)lim((1+cosx)(1-cosx+cos^(2)x))/((1-cosx)(1+cosx))`
`=underset(xto pi)lim(1-cosx+cos^(2)x)/(1-cosx)=(1+1+1)/(1+1)=3/2`
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CENGAGE PUBLICATION-LIMITS-Exercises (Single Correct Answer Type)
  1. lim(x->oo)(sin^4x-sin^2x+1)/(cos^4x-cos^2x+1) is equal to (a) 0 ...

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  2. If f(x)=2/(x-3),g(x)=(x-3)/(x+4) , and h(x)=-(2(2x+1))/(x^2+x-12) then...

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  3. The value of lim(x->pi)(1+cos^3x)/(sin^2x) is (a)1/3 (b) 2/3 ...

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  4. The value of lim(xto2) (sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)" is "

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  5. The value of ("lim")(xvec2)(2^x+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))i s ...

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  6. lim(x->2)(((x^3-4x)/(x^3-8))^(-1)-((x+sqrt(2x))/(x-2)-(sqrt(2))/(sqrt(...

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  7. If lim(xto-2^(-)) (ae^(1//|x+2|)-1)/(2-e^(1//|x+2|))=lim(xto-2^(+)) si...

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  8. lim(xto1) ((1-x)(1-x^(2))...(1-x^(2n)))/({(1-x)(1-x^(2))...(1-x^(n))}^...

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  9. The value of lim(x->1/(sqrt(2))) ((x-"cos" (sin^(-1)x))/ (1-tan(sin^(-...

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  10. Among (i) lim(xtooo) sec^(-1)((x)/(sinx))" and "(ii) lim(xtooo) sec^(-...

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  11. lim(xtooo) ((x^(3))/(3x^(2)-4)-(x^(2))/(3x+2))" is equal to "

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  12. lim(n->oo)(n(2n+1)^2)/((n+2)(n^2+3n-1)) is equal to (a)0 (b) ...

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  13. lim(x->oo)((2x+1)^(40)(4x-1)^5)/((2x+3)^(45)) is equal to (a)16 ...

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  14. lim(x->oo)[sqrt(x+sqrt(x+sqrt(x)))-sqrt(x)] is equal to (a)0 (...

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  15. lim(xtooo) (2+2x+sin2x)/((2x+sin2x)e^(sinx)) is equal to

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  16. lim(xrarroo)((x+1)^(10)+(x+2)^(10)+...+(x+100)^(10))/(x^(10)+10^(10)) ...

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  17. lim(x->oo)(2sqrt(x)+3x3+4x4++n x n)/(sqrt((2x-3))+(2x-3)3++(2x-3)n) ...

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  18. If lim(ntooo) (n.3^(n))/(n(x-2)^(n)+n.3^(n+1)-3^(n))=1/3, then the ran...

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  19. lim(n->oo)n^2(x^(1/n)-x^(1/((n+1)))),x >0 , is equal to (a)0 (b) e^x ...

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  20. Let f(x)=lim(ntooo) (1)/(((3)/(pi)tan^(-1)2x)^(2n)+5). Then the set of...

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