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The value of lim(x to 0) (e^x+e^-x-2)/(x...

The value of `lim_(x to 0) (e^x+e^-x-2)/(x^2))^(1/x^2)` equals

A

`e^(1//2)`

B

`e^(1//4)`

C

`e^(1//3)`

D

`e^(1//12)`

Text Solution

Verified by Experts

The correct Answer is:
D
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MCGROW HILL PUBLICATION-LIMITS AND CONTINUITY-Solved Examples Level 2 (Single Correct Answer)
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  2. If ("lim")(xveca)(a^x-x^a)/(x^x-a^a)=-1a n da >0, then find the value ...

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  3. The value of lim(x to 0) (e^x+e^-x-2)/(x^2))^(1/x^2) equals

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  4. If underset(xtooo)lim{(x^(2)+1)/(x+1)-(ax+b)}=0, then find the values ...

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  5. Let f(x)=g(x)(e^(1//x) -e^(-1//x))/(e^(1//x) + e^(-1//x)), where g is ...

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  6. The value of f(0) , so that the function f(x) = (sqrt(a^(2)-ax+x^(3)...

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  7. If f(x)=(2-(256-7x)^(1//8))/((5x+32)^(1//5)-2) ( x ne 0) , then for f ...

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  8. Let f(x)=(x(1+acosx)-bsinx)/(x^3), x!=0 and f(0)=1.The value of a and...

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  9. f(x)={{:((3//x^2)sin2x^2,"if" x lt 0),((x^2+2x+c)/(1-3x^2), "if" x ge ...

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  10. The function f(x)=(sin 2x)^(tan^(2)2x) is not defined at x=(pi)/(4). T...

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  11. Let f(x)=(log (1+x+x^2)+log(1-x+x^2))/(sec x-cosx) , x ne 0 .Then the ...

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  12. The value of k(k gt 0) for which the function f(x)=(e^x-1)^4/(sin(x^2/...

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  13. The function f(x) = (log(1+ax)-log(1-bx))/(x) is not defined at x = 0....

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  14. Let f(x)=log(1+x^2)/(x^4-26x^2+25Then 1)f is continuous on ([6,10](2) ...

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  15. Let f(x)=(sin (pi cos^2 x))/x^2 , x ne 0 . The value of f(0) so that f...

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  16. Let f(x)={{:((e^(alphax)-e^x)/x^2, x ne 0),(3//2,x=0):} The value of a...

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  17. Let f be a continuous function on R such that f(1//2^n) =(sin e^n) e^...

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  18. Let f(x)=lim(n to oo) sinx/(1+(2 sin x)^(2n)) then f is discontinuous ...

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  19. Let f be a non-zero continuous function satisfying f(x+y)=f(x)f(y) for...

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  20. Let f be a function on [0,1] defined by f(x)=(1//2)^n , (1//2)^(n+1) ...

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