Question:medium
If \(\alpha, \beta\) are the roots of the equation \(ax^2 + bx + c = 0\), then:
\[ \lim_{x \to \beta} \frac{1 - \cos(ax^2 + bx + c)}{(x - \beta)^2} \]
If \(\alpha, \beta\) are the roots of the equation \(ax^2 + bx + c = 0\), then:
\[ \lim_{x \to \beta} \frac{1 - \cos(ax^2 + bx + c)}{(x - \beta)^2} \]
\[ \lim_{x \to \beta} \frac{1 - \cos(ax^2 + bx + c)}{(x - \beta)^2} \]
Show Hint
When dealing with limits involving trigonometric functions and polynomials, use Taylor series expansions around the point of interest to simplify the expressions and solve the limit.
Updated On: Nov 28, 2025
- \((\alpha - \beta)^2\)
- \(\frac{1}{2}(\alpha - \beta)^2\)
- \(\frac{a^2}{4}(\alpha - \beta)^2\)
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