Find the limits: (i) lim[x→1] [(x²+1)/(x+100)] (ii) lim[x→2] [(x³-4x²+4x)/(x²-4)] (iii) lim[x→2] [(x²-4)/(x³-4x²+4x)] (iv) lim[x→2] [(x³-2x²)/(x²-5x+6)] (v) lim[x→1] [(x-2)/(x²-x) - 1/(x³-3x²+2x)]

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CASE_STUDIESLimits of Rational Functions5 sub-questions

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Evaluate: (i) lim[x→1] (x¹⁵-1)/(x¹⁰-1) (ii) lim[x→0] (√(1+x)-1)/x

lim[x→4] (4x+3)/(x-2)

lim[x→-1] (x¹⁰ + x⁵ + 1)/(x - 1)

TextLimits of Rational Functions

lim[x→0] ((1+x)⁵-1)/x

lim[x→2] (3x²-x-10)/(x²-4)

lim[x→3] (x⁴-81)/(2x²-5x-3)