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Evaluate the following limit : \(\lim\limits_{\text x \to 1}\cfrac{\text x^4-3\text x^3+2}{\text x^3-5\text x^2+3\text x+1}\)

lim(x→1) (x4 - 3x3 + 2)/(x3 - 5x2 + 3x + 1)

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Best answer

Since the form is indeterminant

\(=\cfrac00\)

Method 1: factorization

Since a3 - b3 = (a - b) (a2 + b2 + ab) & a- b2 = (a + b) (a - b)

Method 2: By L hospital rule:

Differentiating numerator and denominator separately:

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