\( \operatorname{Rim}\left(x^{2}-\sqrt{2 x^{2}+3}\right) \) \( x \rightarrow+2 \) catuler Ra limite de eelte fonction

(a) \( \sum_{n=1}^{\infty} 2\left(\frac{4}{3}\right)^{n-1} \)

Suppose \( \int_{2}^{4} f(x) d x=-8 \int_{2}^{7} f(x) d x=6 \), and \( \int_{2}^{7} g(x) d x=5 \). Evaluate the following integrals. \( \int_{2}^{7} 6 g(x) d x=30 \) \( \int_{2}^{7}[g(x)-f(x)] d x=-1 \) (Simplify your answer) (Simplify your answer) \( \int_{2}^{7}[5 g(x)-f(x)] d x=\square \) (Simplify your answer.)

\( \int _ { 1 } ^ { 2 } \int _ { - 1 } ^ { 2 } ( 12 x y ^ { 2 } - 8 y ^ { 3 } ) d y d \)

\( \int_{0}^{5} f(x) d x \), where \( f(x)=\left\{\begin{array}{ll}5 & \text { if } x \leq 3 \\ 3 x-4 & \text { if } x>3\end{array}\right. \)

\( \int _ { 0 } ^ { 3 \pi / 2 } x \sin x d x = \square \)