Find a non-zero value of the constant \( k \), if possible, at which \[ f(x)=\left\{\begin{array}{ll}\frac{\sin (k x)}{x} & x<0 \\ -7 x+6 k^{2} & x \geq 0\end{array}\right. \] is continuous at \( x=0 \) \( k= \)

\( e = \frac { 2 } { \theta + 1 } . \quad \frac { d e } { d \theta } = - \frac { 2 } { ( \theta + 1 ) ^ { 2 } } \)

1) Evaluate \( \int_{0}^{2}\left(x^{3}+3 x^{2}\right) d x \)

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.

Determina la derivada de las siguientes funciones. 1.- Encuentra la derivada de la función \( f(x)=3 x+x^{2} \) 2.- Encuentra la derivada de la función \( f(x)=-2 x^{2}+5 \) 3.- Encuentra la derivada de la función \( f(x)=3 x \) 4.- Encuentra la derivada de la función \( f(x)=2 x-6 \) 5.- Encuentra la derivada de la función \( f(x)=x^{3} \)

choose the correct answer: \( f(x)=x^{3}-3 x^{2}+4 x+8 \) A) FAlls to the left and rises to the right B) Rises to the left and falls to the right C) Rises to the left and rises to the right D) falls to the left and falls to the right