[tex]\small \begin{aligned} \lim_{x\to-3} x^3(2x-7) &= (-3)^3(2(-3)-7) \\ &= -27(-6-7) \\ &= -27(-13) \\ &= 351 \end{aligned} [/tex]
[tex] \small\begin{aligned} \lim_{x\to-2} \frac{ x^2-x-2}{ x^2+2x-3} &= \frac{ (-2)^2-(-2)-2}{(-2)^2+2(-2)-3 } \\ &= \frac{ 4+2-2}{ 4-4-3} \\ &= -\frac{4 }{ 3}\end{aligned} [/tex]
[tex] \small\begin{aligned} \lim_{x\to2} \frac{ x-2}{ 3- \sqrt {x+7} } &= \lim_{x\to2} \frac{ x-2}{3- \sqrt {x+7} }\cdot \frac{3+ \sqrt {x+7}}{3+ \sqrt {x+7}}\\ &= \lim_{x\to2} \frac{(x-2)(3+ \sqrt {x+7})}{9-(x+7) }\\ &= \lim_{x\to2} \frac{\cancel{\red{ (x-2)}}(3+ \sqrt {x+7})}{ -\cancel{\red{(x-2)}}}\\ &= \lim_{x\to2} -(3+ \sqrt {x+7} )\\ &= -(3+ \sqrt {2+7} )\\ &= -(3+\sqrt9 ) \\ &= -(3+3) \\ &= -6\end{aligned} [/tex]
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Verified answer
Soal 7
[tex]\small \begin{aligned} \lim_{x\to-3} x^3(2x-7) &= (-3)^3(2(-3)-7) \\ &= -27(-6-7) \\ &= -27(-13) \\ &= 351 \end{aligned} [/tex]
Soal 8
[tex] \small\begin{aligned} \lim_{x\to-2} \frac{ x^2-x-2}{ x^2+2x-3} &= \frac{ (-2)^2-(-2)-2}{(-2)^2+2(-2)-3 } \\ &= \frac{ 4+2-2}{ 4-4-3} \\ &= -\frac{4 }{ 3}\end{aligned} [/tex]
Soal 9
[tex] \small\begin{aligned} \lim_{x\to2} \frac{ x-2}{ 3- \sqrt {x+7} } &= \lim_{x\to2} \frac{ x-2}{3- \sqrt {x+7} }\cdot \frac{3+ \sqrt {x+7}}{3+ \sqrt {x+7}}\\ &= \lim_{x\to2} \frac{(x-2)(3+ \sqrt {x+7})}{9-(x+7) }\\ &= \lim_{x\to2} \frac{\cancel{\red{ (x-2)}}(3+ \sqrt {x+7})}{ -\cancel{\red{(x-2)}}}\\ &= \lim_{x\to2} -(3+ \sqrt {x+7} )\\ &= -(3+ \sqrt {2+7} )\\ &= -(3+\sqrt9 ) \\ &= -(3+3) \\ &= -6\end{aligned} [/tex]