1) Soit la fonction \( f \) définie sur \( \mathbb{R}^{+} \)par : \( f(x)=x^{2}+2 x \) a. Déterminer la monotonie de la fonction \( f \) sur \( \mathbb{R}^{+} \) b. Montrer que \( \forall x \in \mathbb{R}^{+} ; f(x) \geq 0 \) 2) Soit \( g \) la fonction définie sur \( \mathbb{R}^{+} \)par : \( g(x)=-1+\sqrt{1+x} \) a. Déterminer la monotonie de la fonction \( g \) sur \( \mathbb{R}^{+} \) b. Montrer que \( \forall x \in \mathbb{R}^{+} ; g(x) \geq 0 \). 3) Calculer \( (f \circ g)(x) \) et \( (g \circ f)(x) ; \forall x \in \mathbb{R}^{+} \). 4) Représenter dans la même repère orthonormé \( \left(C_{f}\right) \) et \( \left(C_{g}\right) \) Et la droite d'équation \( y=x \).

1. Using tables of values, detern (a) \( \lim _{x \rightarrow 0}(x) \) (b) \( \left.\left.\lim _{x \rightarrow 1}\right) 2 x\right) \) (c) \( \lim _{x \rightarrow 2}(-x+1) \) (d) \( \lim _{x \rightarrow-1}(1-x) \) (e) \( \lim _{x \rightarrow 0}(2 x-1) \) (f) \( \lim _{x \rightarrow 3}(x-3) \) (a) \( \lim _{n}\left(3 x^{2}-2\right) \)

limits of the following. (i) \( \lim _{x \rightarrow 1}\left(x^{3}+1\right) \) (j) \( \lim _{x \rightarrow 0}\left(1-x^{2}-x^{3}\right) \) (k) \( \lim _{x \rightarrow 1} \sqrt{x^{3}-1} \) (l) \( \lim _{x \rightarrow 0} \sqrt{x^{2}-x^{3}} \)

Determine the following limits. (a) \( \lim _{x \rightarrow-4} f(x) \) (b) \( \lim _{x \rightarrow-1} f(x) \) (c) \( \lim _{x \rightarrow 1} f(x) \) (d) \( \lim _{x \rightarrow 3} f(x) \) (e) \( \lim _{x \rightarrow 5} f(x) \)

The total revenue from the sale of a popular book is approximated by the rational function \( R(x)=\frac{1300 x^{2}}{x^{2}+4} \), where \( x \) is the number of years since publication and \( R(x) \) is the total revenue in millions of dollars. Use this function to complete parts a through \( d \). (a) Find the total revenue at the end of the first year. \( \$ 260 \) million (b) Find the total revenue at the end of the second year. \( \$ 650 \) million (c) Find the revenue during the second year only. \( \$ \square \) million

\( \int _ { - 2 } ^ { 2 } \int _ { - \sqrt { 4 - x ^ { 2 } } } ^ { \sqrt { 4 - x ^ { 2 } } } \int _ { \sqrt { x ^ { 2 } + y ^ { 2 } } } ^ { \sqrt { 8 - x ^ { 2 } - y ^ { 2 } } } ( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } ) d z d y d x \)