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("lim")(xvecoo)(2sqrt(x)+3sqrt(x)+4sqrt(...

`("lim")_(xvecoo)(2sqrt(x)+3sqrt(x)+4sqrt(x)+...+nsqrt(n))/(sqrt((2x-3))+(sqrt(2x-3))+....+(sqrt(2x-3))`i se q u al to 1 (b) `oo` (c) `sqrt(2)` (d) none of these

A

0

B

1

C

`sqrt(2)`.

D

`2sqrt(2)`.

Text Solution

Verified by Experts

The correct Answer is:
C
Since the highest degree of x is `1//2,` divide numerator and denominator by `sqrt(x).` Then we have limit `(2)/(sqrt(2))` or `sqrt(2)`.
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CENGAGE-LIMITS-Exercise (Single)
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  2. lim(xtooo) ((x+1)^(10)+(x+2)^(10)+...+(x+100)^(10))/(x^(10)+10^(10)) i...

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  3. ("lim")(xvecoo)(2sqrt(x)+3sqrt(x)+4sqrt(x)+...+nsqrt(n))/(sqrt((2x-3))...

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  4. If("lim")(xvecoo)(n .3^n)/(n(x-2)^n+n .3^(n+1)-3^n)=1/3, t h e nt h e ...

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  5. lim(ntooo) n^(2)(x^(1//n)-x^(1//(n+1))),xgt0, is equal to

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  6. Let f(x)=("lim")(xvecoo)1/((3/pitan^(-1)2x)^(2n)+5)dot Then the set of...

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

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  8. The value of ("lim")(xvecoo)[(2n)/(2n^2)cos(n+1)/(2n-1)-n/(1-2n)dot(n(...

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  9. If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f(pi/2)...

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  10. ("lim")(xvec1)(xsin(x-[x]))/(x-1),w h e r e[dot] denotes the greatest ...

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

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  12. ("lim")(xvec0)(x^asin^b x)/(sin(x^c)), where a , b , c in R ~{0},exis...

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  13. lim(xto0) (x^(4)(cot^(4)x-cot^(2)x+1))/((tan^(4)x-tan^(2)x+1)) is equa...

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  14. ("lim")(xvec1)(1-x^2)/(s in2pix)i se q u a lto 1/(2pi) (b) -1/pi (c...

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

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  16. ("lim")(xvec0)((x+y)sec(x+y)-xsecx)/yi se q u a lto (a)secx(xtanx+1)...

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  17. lim(xto0)(1+x)^(1/(3x))

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  18. ("lim")(n->oo)sum(x=1)^(20)cos^(2n)(x-10) is equal to (a) 0 (b) 1 (...

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  19. lim(xto-1) ((x^(4)+x^(2)+x+1)/(x^(2)-x+1))^((1-cos(x+1))/(x+1)^(2)) is...

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  20. ("lim")(xvecoo)"{"x+5")"tan^(-1)(x+5)-(x+1)tan^(-1)(x+1)} is equal to ...

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