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What is the domain and range of the func...

What is the domain and range of the function `f(x)=(x^(2)-3x+2)/(x^(2)+x-6)`. Find the limit of f(x) as x approaches 2.

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The correct Answer is:
Domain of definition is `{x:x""inRR-(-3,2)};` range is `{f(x):f(x)inRRandf(x)ne1,(1)/(5)};` limit `=(1)/(5)`
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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-CALCULUS
  1. Without using graph paper, draw the graph of the function f(x)=sin""(1...

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  2. What is the domain and range of the function f(x)=(x^(2)-3x+2)/(x^(2)+...

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  3. Show that : lim(xto""pi)(1+cos^(3)x)/(tan^(2)x)=(3)/(2)

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  4. Evaluate : lim(xto(pi)/(2))(cos3x+3cosx)/(((pi)/(2)-x)^(3))

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  5. Show that : lim(xtoa)(sinx-sina)/(sqrtx-sqrta)=2sqrtacosa

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  6. Show that : lim(xtoa)(sinx-sina)/(sqrtx-sqrta)=2sqrtacosa

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  7. Show that : lim(xto0)(sinlog(1+x))/(log(1+sinx))=1

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  8. Show that : lim(xto0)(5xcosx-2sinx)/(3x+tanx)=(3)/(4)

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  9. Show that : lim(xto0)(10^(x)-2^(x)-5^(x)+1)/(x^(2))=log(e)2.log(e)5

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  10. Show that : lim(xto4)((cosalpha)^(x)-(sinalpha)^(x)-cos2alpha)/(x-4)...

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  11. Show that : lim(xto2)(sin(e^(x-2)-1))/(log(x-1))=1

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  12. Show that : lim(xto""pi)(sqrt(2+cosx)-1)/((pi-x)^(2))=(1)/(4)

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  13. Show that : lim(xto0)[(1)/(x)-(log(1+x))/(x^(2))]=(1)/(2)

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  14. Show that : lim(xto(pi)/(4))(sqrt2-(sinx+cosx))/((4x-pi)^(2))=(1)/(1...

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  15. If f(x)=lim(ntooo)(x^(n)g(x)+h(x))/(x^(n)+1) show that f(x) =h(x), wh...

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  16. If lim(xto0)(sin2x+asinx)/(x^(3)) is finite, find a and the limit.

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  17. Evaluate the following limits: lim(xto0)(sqrt(x^2-1)+sqrt(x-1))/(sqr...

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  18. Evaluate the following limits: lim(xto2a)(sqrt(x-2a)+sqrtx-sqrt2a)/(...

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  19. Evaluate the following limits: lim(xto0)(sinx^(2)(1-cosx^(2)))/(x^(6...

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  20. Evaluate the following limits: lim(xto0)(xe^(x)-log(1+x))/(x^(2))

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