The total cost function for a product is \[ C(x)=750 \ln (x+10)+1700 \] where \( x \) is the number of units produced. (a) Find the total cost of producing 300 units. (Round your answer to the nearest cent.) \( \$ \) (b) Producing how many units will give total costs of \( \$ 7500 \) ? (Round your answer to the nearest whole number.) units

Given \( \lim _{x \rightarrow 6} f(x)=8 \) and \( \lim _{x \rightarrow 6} g(x)=5 \), evaluate \[ \lim _{x \rightarrow 6} f(x) \cdot g(x) \] (If the limit does not exist, enter "DNE".) Limit = Submit answer

emplee la integral doble en coordena- das polares para calcular el área de la región acotada por las gráficas de las ecuaciones polares que se indican. \( r=2 \operatorname{sen} \theta, r=1 \)

Given that \( f^{\prime \prime}(x)=\cos (x), f^{\prime}(\pi / 2)=10 \) and \( f(\pi / 2)=4 \) find: \( f^{\prime}(x)=\square \) \( f(x)=\square \)

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 \( x=0 \) \( k= \)

A particle moves along the \( y \)-axis so that its position at time \( t \) is given by \( y(t)=t^{2} \tan \left(\frac{1}{t}\right) \) for \( t>1 \). (b) At time \( t=\frac{4}{\pi} \), is the particle moving toward the origin or away from the origin? Give a reason for your answer.