<s>[INST] Calculus limits please demonstrate question? I have been trouble doing some more difficult limits 
I have these two examples from a teacher and think if i can just be shown the working and answer i should be fine from there out. Thanks for your help.
$(a)\; \lim\limits_{x\to-2}\dfrac{3x^2+8x+4}{2x^2+x-6} \\ \; \\ (b)\;\lim\limits_{x\to\infty}\dfrac{3x^4-11x^3+42x}{-15x^4+3x^2 +101}$
 [/INST] $$\lim\limits_{x\to-2}\dfrac{3x^2+8x+4}{2x^2+x-6} = \lim_{x\to -2} \dfrac{(3x+2)(x+2)}{(2x -3)(x+2)} = \lim_{x\to -2}\frac{3x+2}{2x-3} = \frac{-4}{-7}= \frac 47 $$
For the second limit, divide numerator and denominator by $x^4$, and evaluate.
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