Find limits: 1.) lim x-->∞ (5+sqrt(x^2+5))/(x-6) 2.) lim x-->∞ (10x^3-4)/(x^2+2x-6) 3.) lim x-->∞ (sqrt^3(x^3-4x^2-7x-5))/(sqrt(x^2-7x)+9)
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Luca B.
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1) You need to force factor `x^2` to numerator and `x` to denominator such that:
`lim_(x-gtoo) (5+sqrt(x^2(1+5/x^2)))/(x(1-6/x))`
You need to remember that `sqrt(x^2) = +-x` but you need to keep the positive value since x approaches to `+oo` .
`lim_(x-gtoo) (5+xsqrt(1+5/x^2))/(x(1-6/x))`
You need to force factor x to numerator such that:
`lim_(x-gtoo) x(5/x+sqrt(1+5/x^2))/(x(1-6/x))`
Reducing by x yields:
`lim_(x-gtoo) (5/x+sqrt(1+5/x^2))/(1-6/x)`
You...
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