For \( x \quad>\quad 0 \), which answer best describes the curve of the function \( f(x)=x^{\frac{1}{2}} ? \) Positive values of \( f(x) \); steep near 0 , but flattening as \( x \) approaches \( \infty \) Negative values of \( f(x) \); steep near 0, but flattening as \( x \) approaches \( \infty \) Positive values of \( f(x) \); flat near 0, but steepening as \( x \) approaches \( \infty \) Negative values of \( f(x) \); flat near 0, but steepening as \( x \) approaches \( \infty \) None of the above.

Calculate the maximum value of \( S \) if \( S=\frac{6}{x^{2}+2} \)

1) Integrer les equations suivante 1) \( y^{\prime}=\frac{1+y^{2}}{1+x^{2}} \) 2) \( y^{\prime \prime}-3 y^{\prime}+2 y=x^{2}-3 x \)

Consider the differential equation \( \frac{dy}{dx} = 4x^2 \) with the initial condition \( y(1) = 5 \). Determine the specific solution.

(2) Nontrer que la forme implicite de la solution de l'ED \( 9 y y^{\prime}+4 x=0 \) est \( \frac{x^{2}}{9}+\frac{y^{2}}{4}=k \) (cste)

Use the intermediate value theorem to show that the function has a real zero between the two numbers given. Then, use your calculator to approximate the zer \( P(x)=4 x^{2}-2 x-6 ; 1 \) and 2 \( P(1)=\square \)