**QUESTION**

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Graph of $f$ The graph of the function $f$ on the closed interval $-3 \leq x \leq 8$ consists of six line segments and the point $(5,2)$, as shown in the figure above. The function $g$ is given by $g(x)=\frac{1}{10}\left(4 x^{3}+3 x^{2}-10 x-17\right)$. It is known that $\int_{-3}^{-1} g(x) \mathbb{d} x=-4.8$ and $\int_{-3}^{4} g(x) \mathbb{d} x=11.2$. (a) Find the value of $\int_{4}^{8} f(x) d x$, or explain why the integral does not exist.

(b) (i) Find the value of $\int_{-1}^{4} g(x) \mathbb{d} x$. Show the work that leads to your answer. (ii) Find the value of $\int_{-1}^{4}(2 g(x)-4 f(x)) \mathbb{d} x$ Show the work that leads to your answer. 느 친 Upload files (PDF, JPG, GIF, PNG, TXT, Word, Excel, Powerpoint, file formats supported) (c) Let $h(x)=\left\{\begin{array}{ll}g(x) & \text { for } x \leq-1 \\ f(x)+b & \text { for } x>-1\end{array}\right.$. Find the value of $b$ for which $\int_{-3}^{4} h(x) \mathbb{d} x=14.2$ Upload files (PDF, JPG, GIF, PNG, TXT, Word, Excel, Powerpoint, file formats supported) (d) Find $\lim _{x \rightarrow 1} \frac{f(x)}{g(x)+2}$. Show the work that leads to your answer.