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Evaluate lim(x to 0) ((x+4)/(2-x))^((x^(...

Evaluate `lim_(x to 0) ((x+4)/(2-x))^((x^(2)+2x-3)/(x-1))`

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`underset(xto0)lim((x+4)/(2-x))^((x^(2)+2x-3)/(x-1))`
`=(underset(xto0)lim(x+4)/(2-x))^((x^(2)+2x-3)/(x-1))`
`((0+4)/(2-0))^((0+0-3)/(0-1))`
`2^(-3)`
`1//8`
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CENGAGE-LIMITS-Question Bank
  1. Evaluate lim(x to 0) ((x+4)/(2-x))^((x^(2)+2x-3)/(x-1))

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  2. If Lim(x rarr 0) (1-cosx)/(e^(ax)-bx-1) exist and is equal to 1, then ...

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  3. If graph of a function f(x) is shown in the adjacent figure, then Lim(...

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  4. If beta(1)+beta(2)+beta(3)+....+beta(n) = p and Lim(x rarrp)((3-3tan(p...

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  5. Let f(x) be a function continuous for all x except at x =0 such that f...

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  6. Let f(x) =(sec x)^(cosecx) + (cot x)^(sin x). Then the value of Lim(x ...

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  7. Lim(z rarr 0){{max((sin^(-1)x + cos^(-1)x)^(2), min(x^(2)+4x+7))}. (si...

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  8. ((8e^(a))/e)lim(n rarr oo) ((n/(n+1))^(a) + sin (1/n))^(n))where a in ...

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  9. If the value of lim(x rarr oo) (root(3)(x^(3)+x^(2)-root(3)(x^(3)-x^(2...

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  10. Let f(x) be a polynomial satisfying lim(x rarr oo) (x^(2)f(x))/(2x^(5)...

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  11. Let L(1) = Lim(x rarr 0)(cos(pix)(e^(lambda x)-1)/(pi sin x) and L(2) ...

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  12. If Lim(c rarr 0) (asinc+btanc)/c^(3) = 3/2, find the value of |a+2b|.

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  13. Lim(n rarr oo) (1-1/2^(2))(1-1/3^(2))(1-1/4^(2))…(1-1/n^(2)) equals

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  14. The value of Lim(x rarr 0)(sum(k =1)^(2016){(sinx)/x+2015k})/2016 is [...

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  15. Lim(x rarr oo) (30+4sqrtx+7root(3)(x))/(2+sqrt(4x-7)+root(3)(6x-2) )eq...

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  16. If Lim(x rarr0) ((a sin x + b tan x)/x^(3))= 3/2 then |a+2b| is equal ...

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  17. lim(x rarr 0)(1/(1+n^(2))+2/(1+n^(2))+3/(1+n^(2))+....+n/(1+n^(2))) is...

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  18. Find the value of lim(n rarr oo)sum(k=1)^(n)(k^(2)+k-1)/((k+1)!) .

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  19. If Lim(x rarr 0)(1-cos(1-cos(1-cosx)))/x^(a) is finite then teh maximu...

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  20. The value of Lim(x rarr 0)((tanx)^(1/x)+(1+sinx)^(x)) where x gt0 is e...

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  21. Let f(x) be a differentiable function satisfying f(x+y) = f(x)+f(y) A...

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