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If lim(xrarroo) ((x+c)/(x-c))^(x)=4 then...

If `lim_(xrarroo) ((x+c)/(x-c))^(x)=4` then the value of `e^(c)` is

A

`1//4`

B

`1//2`

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
D
`underset(xrarroo)(lim)((x+c)/(x-c))^(x)=4`
`rArr" "e^(underset(xrarroo)(lim)[((x+c)/(x-c)-1).x])=4`
`rArr" "e^(underset(xrarroo)(lim)[((x+c-x+c)/(x-c)).x])=4`
`rArr" "e^(2c)=4`
`rArr" "2c=log4rArrc=log2`
`rArr" "e^(c)=2`
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CENGAGE-LIMITS-Single Correct Answer Type
  1. Let f(x) be defined for all x in R such that lim(xrarr0) [f(x)+log(1-(...

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  2. lim(xrarroo) x^(2)sin(log(e)sqrt(cos(pi)/(x)))

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  3. If lim(xrarroo) ((x+c)/(x-c))^(x)=4 then the value of e^(c) is

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

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

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

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

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

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  9. 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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  10. The value of lim(nrarroo) ((sqrtn^(2)+n-1)/(n))^(2sqrt(n^(2)+n-1)) is

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  11. If f(n)=lim(xrarr0) ((1+sin.(x))/(2))(1+sin.(x)/(2^(2)))...(1+sin.(x)/...

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

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

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  14. lim(xrarr1) (root(13)x-root7x)/(root5x-root3x) is

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

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  16. If f(a)=(1)/(4), then lim(hrarr0) (f(a+2h^(2))-f(a-2h^(2)))/(f(a+h^(3)...

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  17. lim(xrarr0^(+)) (1)/(xsqrtx)(a tan^(-1).(sqrtx)/(a)-btan^(-1).(sqrtx)/...

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  18. The value of lim(xrarr0) ((1+2x)/(1+3x))^((1)/(x^(2))).e^((1)/(e^(x)))...

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  19. If F:R rarr R be a differentiable function at x = 0 satisfying f(0)=0 ...

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

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