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If a,b, c, d are positive, then lim(x ra...

If a,b, c, d are positive, then `lim_(x rarr oo) (1 + 1/(a+bx))^(c+dx)=`

A

e

B

`c^(((c+d))/((a+b))`

C

`e^(d/b)`

D

`e^(c/a)`

Text Solution

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The correct Answer is:
C
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HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
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  2. lim(x rarr 0) (a^(x)-1)/(sqrt(1+x) -1) =

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  3. If a,b, c, d are positive, then lim(x rarr oo) (1 + 1/(a+bx))^(c+dx)=

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  4. lim(x rarr 0) ((1+tanx)/(1+sin x))^(cosec x) =

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  5. lim(x rarr 00) ((2+x)^(30)(4+x)^(7))/((2-x)^(37)) =

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  6. lim(x rarr 0) [(10^(x)-2^(x)-5^(x)+1)/(x . tan x)] =

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  7. lim(n rarr oo) (3.2^(n+1) - 4.5^(n+1))/(5.2^(n) + 7.5^(n)) =

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  8. If lim(x rarr 0) (1 + px)^(q/x) = e^(4), where p,q in N, then

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  9. lim(x rarr 0) (sin x + log (1-x))/x^(2) =

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  10. Let f(x) = {(1+x, x gt 0),(x, x le 0):} . Lim(x rarr 0) f(x) =

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  11. lim(h rarr 0) (sqrt(x+h) - sqrtx)/h =

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  12. The values of a and b so that lim(x rarr oo) [(x^(2)+1)/(x+1) - ax-b] ...

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  13. lim(x rarr 2) (sqrt(x-2) + sqrtx - sqrt2)/(sqrt(x^(2)-4)) =

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  14. lim(x rarr pi//3) (2 sin (x-pi//3))/(1-2 cos x) equals :

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  15. Let f(x) = 4x^(9)-3x^(8)+2x^(7)+x^(3)+x^(2)-4, then lim(h rarr 0) (f(1...

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  16. Let f(x) = {{:(x (sin 1//x + sin (1//x^(2))),,x ne 0),(0,,x = 0):} The...

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  17. If lim(x rarr -a) (x^(9)+a^(9))/(x+a) = 9, then a =

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  18. lim(x rarr oo) [sqrt(x+sqrt(x + sqrt (x-)) sqrtx]=

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  19. lim(x rarr 1) (log(e)x)/(x-1) equals :

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  20. If f be a function such that f(9) = 9 and f'(9) = 3, then : lim(x ra...

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