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lim(xrarr(pi)/(2)) [1+(cosx)^(cosx)]^(2)...

`lim_(xrarr(pi)/(2)) [1+(cosx)^(cosx)]^(2)=`

A

Does not exist

B

`1`

C

`e`

D

`4`

Text Solution

Verified by Experts

The correct Answer is:
D
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CENGAGE PUBLICATION-LIMITS-Single Correct Answer Type
  1. If lim(xrarroo) ((x+c)/(x-c))^(x)=4 then the value of e^(c) is

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  2. If lim(xrarr0) [1+x+(f(x))/(x)]^(1//x)=e^(3)", then "lim(xrarr0) [1+(f...

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  3. lim(xrarr(pi)/(2)) [1+(cosx)^(cosx)]^(2)=

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  4. If agt0, b gt0 than lim(nrarroo) ((a-1+b^((1)/(n)))/(a))^(n)=

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  5. If f(x)=lim(nrarroo) (cos(x)/(sqrtn))^(n), then the value of lim(xrarr...

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  6. lim(xrarr0) (log(e^(x^(2))+2sqrtx))/(tansqrtx) is equal to

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  7. Let f:RrarrR be such that f(a)=1, f(a)=2. Then lim(x to 0)((f^(2)(a+x)...

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  8. L=underset(nrarroo)(lim)((sqrt(n^(2)+n)-1)/(n))^(2sqrt(n^(2)+n)-1)

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  9. If f(n)=underset(xto0)lim{(1+"sin"(x)/(2))(1+"sin"(x)/(2^(2)))...(1+"s...

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  10. lim(nrarroo) (1-x+x.root n e)^(n) is equal to

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  11. The value of lim(xrarr1) (root(13)x-root7x)/(root5x-root3x) is

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  12. The value of underset(xrarr1)(lim)(root(2)x-root4x)/(root3x-root2x) is

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  13. The value of lim(x rarr 0) (1-cos2x)/(e^(x^(2))-e^(x)+x) is

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  14. If f^(prime)(a)=1/4, t h e n(lim)(hvec0)(f(a+2h^2)-f(a-2h^2))/(f(a+h^3...

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  15. underset(xrarr0^(+))(lim)(1)/(xsqrtx)(atan^(-1).(sqrtx)/(a)-b tan^(-1)...

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  16. The value of lim(x->0)((1+2x)/(1+3x))^(1/x^2)e^(1/x) is e^(5/2) b. e^2...

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  17. Let f : R rarr R be a differentiable function at x = 0 satisfying f(0)...

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  18. The value of lim(xrarr(3pi)/(4)) (1+root3(tanx))/(1-2cos^(2)x) is

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  19. lim(x->4)(x-2)/(x-8)

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  20. lim(x->0)(3^x-1)/x

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