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lim(xtooo) (2+2x+sin2x)/((2x+sin2x)e^(si...

`lim_(xtooo) (2+2x+sin2x)/((2x+sin2x)e^(sinx))` is equal to

A

sec `x(xtanx+1)`

B

`xtanx+secx`

C

`xsecx+tanx`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
The ginve limit is
`underset(xtooo)lim((2)/(x)+2+(sin2x)/(x))/((2+(sin2x)/(x))e^(sinx))`
`=(0+2+0)/((2+0)xx("a valule between "1/e" and "e))`
`[becauseunderset(xtooo)limsinx in(-1,1)]`
Hence, limit does not exist.
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CENGAGE ENGLISH-LIMITS-Exercises (Single Correct Answer Type)
  1. lim(xtooo) ((2x+1)^(40)(4x+1)^(5))/((2x+3)^(45)) is equal to

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  2. lim(xtooo) [sqrt(x+sqrt(x+sqrt(x)))-sqrt(x)] is equal to

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  3. lim(xtooo) (2+2x+sin2x)/((2x+sin2x)e^(sinx)) is equal to

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  4. lim(xtooo) ((x+1)^(10)+(x+2)^(10)+...+(x+100)^(10))/(x^(10)+10^(10)) i...

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  5. lim(xtooo) (2sqrt(x)+3root(3)(x)+4root(4)(x)+...+nroot(n)(x))/(sqrt((2...

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  6. If lim(ntooo) (n.3^(n))/(n(x-2)^(n)+n.3^(n+1)-3^(n))=1/3, then the ran...

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  7. ("lim")(xvecoo)n^2(x^(1/n)-x^(1/((n+1)))),x >0,i se q u a lto 0 (b) e...

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  8. Let f(x)=lim(ntooo) (1)/(((3)/(pi)tan^(-1)2x)^(2n)+5). Then the set of...

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  9. f(x)=("ln"(x^(2)+e^(x)))/("ln"(x^(4)+e^(2x))). Then lim(x to oo) f(x) ...

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  10. The value of lim(ntooo) [(2n)/(2n^(2)-1)"cos"(n+1)/(2n-1)-(n)/(1-2n).(...

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  11. If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f((pi)/...

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  12. lim(xto1) (xsin(x-[x]))/(x-1), where [.] denotes the greatest integer ...

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  13. lim(xtooo) (x^(2)"tan"(1)/(x))/(sqrt(8x^(2)+7x+1)) is equal to

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  14. lim(xto0) (x^(a)sin^(b)x)/(sin(x^(c))), where a,b,c inR~{0}, exists an...

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  15. lim(x->0)(x^4(cot^4x-cot^2x+1)/(tan^4x-tan^2x+1)) is equal to (a) 1 (...

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  16. lim(xto1) (1-x^(2))/(sin2pix) is equal to

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  17. lim(xto0) (1)/(x)cos^(1)((1-x^(2))/(1+x^2)) is equal to

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  18. lim(yto0) ((x+y)sec(x+y)-xsecx)/(y) is equal to

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  19. lim(xto1) (1+sinpi((3x)/(1+x^(2))))/(1+cospix) is equal to

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  20. ("lim")(xvecoo)sum(x=1)^(20)cos^(2n)(x-10)i se q u a lto 0 (b) 1 (...

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