Evaluate- limx-2sinx2-5x-6x2-7x-10

= lim_x→ 2sin(x^2 5x+6)x^2 7x+10 = lim_x→ 2sin(x 2)(x 3)(x 5)(x 2) = lim_x→ 21(x 5)lim_x→ 2sin(x 3)(x 2)(x 2) = (13)( 1) = 13 ...

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Algebra of Limits

Evaluate: l...

Question

Evaluate: ${lim}_{x \to 2} \frac{sin (x^{2} - 5 x + 6)}{x^{2} - 7 x + 10}$

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Solution

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l = lim x \to 2 (\frac{1}{(x^{2} - 5 x + 5)} + \frac{1}{(2 x^{2} - 7 x + 6)})

lim x \to 2 \frac{x^{2} - 5 x + 6}{x^{2} - 7 x + 10}

lim x \to 2 \frac{x (x^{2} - 4)}{x^{2} - 5 x + 6}

lim x \to 0 \frac{2^{x} {.3}^{x} {.5}^{x} - 7^{x} {.11}^{x}}{11^{x} {.5}^{x} - 2^{x} {.3}^{x} {.7}^{x}}

\begin{matrix} l i m x \to 0 \end{matrix}

^{2}

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