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Evaluate: lim(x to2)(sqrt(x^(3)-x-3)-sq...

Evaluate: `lim_(x to2)(sqrt(x^(3)-x-3)-sqrt(x+1))/(x-2)`

A

`1/(sqrt(3))`

B

`sqrt(3)`

C

`5/(sqrt(3))`

D

`2sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
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VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-LEVEL -1
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  2. Evaluate: lim(x to2)(sqrt(x^(3)-x-3)-sqrt(x+1))/(x-2)

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  3. Evaluate underset(xtooo)limsqrt(x^(2)+1)-root(3)(x+1)/(root(4)(x^(4)+1...

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  4. Evaluate Lim(x to a ) (x^(3/5) -a^(3/5))/(x^(1/3)-a^(1/3))

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  5. Evaluate: lim(xto oo)(2x^(2)-2x-sin^(2)x)/(3x^(2)-4x+cos^(2)x)

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  6. Evaluate underset(xto1)lim("cos"(pi)/(2)x)/(1-sqrt(x))

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  7. The value of lim(theta to pi//4)((sqrt(2)-cos theta-sin theta))/((4 th...

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  8. Evaluate underset(xto0)lim(5sinx-7sin2x+3sin3x)/(x^(2)sinx).

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  9. lim(x->1)(x^2-x*lnx+lnx-1)/(x-1)

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  10. Evaluate: lim(xto1)(sin|||x|-2|-3|) is

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  11. The value of underset(xrarr0)(lim)(sqrt(1-cosx^(2)))/(1-cos x) is

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  12. Evaluate : ("lim")(xvec2a^+)(sqrt(x-2a)+sqrt(x)-sqrt(2a))/sqrt(x^2-4a^...

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  13. lim(x rarr -pi) |x+pi|/sinx is

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  14. Let f(x) = x(-1)^([1//x]); x != 0 where [.] denotes greatest integer f...

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  15. Evaluate underset(xto-1^(+))lim(sqrt(pi)-sqrt(cos^(-1)x))/(sqrt(1+x)).

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  16. Evaluate lim(xto oo)sqrt((x-sinx)/(x+cos^(2)x))

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  17. Evaluate underset(xto1)lim(1-x)"tan"(pix)/(2).

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  18. Statement 1: lim(xto0)[(sinx)/x]=0 Statement 2: lim(xto0)[(sinx)/x]=...

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  19. Statement 1: If f(x)=2/(pi) cot^(-1)((3x^(2)+1)/((x-1)(x-2))), then li...

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  20. Statement 1: lim(xto oo)(1/(x^(2))+2/(x^(2))+3/(x^(2))+…………..+x/(x^(2)...

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