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Evaluate lim(xto0) (x(e^(x)-1))/(1-cosx)...

Evaluate `lim_(xto0) (x(e^(x)-1))/(1-cosx)` is equal to

A

`e`

B

`(1)/(e)`

C

1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
`underset(xto0)lim(x(e^(x)-1))/(1-cosx)=underset(xto0)lim(2x(e^(x)-1))/(4"sin"^(2)(x)/(2))`
`=2underset(xto0)lim[((x//2)^(3))/("sin"^(2)(x)/(2))]((e^(x)-1)/(x))=2`
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CENGAGE-LIMITS-Exercise (Single)
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  2. ("lim")(xvec0)[(1-e^x)(sinx)/(|x|)]i s(w h e r e[dot] represents the ...

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  3. Evaluate lim(xto0) (x(e^(x)-1))/(1-cosx) is equal to

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  4. If f(x)=lim(n->oo)n(x^(1/n)-1),t h e nforx >0,y >0,f(x y) is equal to ...

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  5. lim(x to 0) {(1+x)^((2)/(x))} (where {.} denotes the fractional part o...

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  6. The value of ("lim")(xvecoo)((2^x^n)^1//e^x-(3^x^n)^1//e^x)/(x^n) (whe...

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  7. ("lim")(xvec0)(sin(x^2))/(1n(cos(2x^2-x)))is equal to 2 (b) -2 (c)...

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  8. ("lim")(xvecoo)(e^1//x^2-1)/(2tan^(-1)(x^2)-pi)i se q u a lto 1 (b) -...

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  9. ("lim")(xto0)((2^m+x)^(1/m)-(2^n+x)^(1/n))/x is equal t o (a) 2(1/(m2...

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  10. The value of lim(ntooo) (1)/(n)[e^(1/n)+e^(2/n)+...+e] is

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  11. The value of lim(ntooo) [1/n+2] is

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  12. ("lim")(xvec0)(log(1+x+x^2)+"log"(1-x+x^2))/(secx-cosx)= -1 (b) 1 ...

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  13. The value of lim(xto0) (2^(3x)-3^(2x))/x is

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  14. The value of lim(xto0) (1+sinx-cosx+log(1-x))/(x^(3)) is

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  15. The value of lim(ntooo) [(1+2+3+...+n)/n^2] is

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  16. If ("lim")(xvec0)(x^(-3)sin3x+a x^(-2)+b) exists and is equal to 0, th...

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  17. If lim(x->0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must b...

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  18. ("lim")(xto0)((1+tanx)/(1+sinx))^(cos e cx)i se q u a l t o (a)e (b)...

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  19. The value of lim(xto1) (2-x)^(tan((pix)/(2))) is

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  20. The value of ("lim")(xvecoo)(cos"x"/"m")^("m") is 1 (b) e (c) e^(-1...

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