A company has determined the demand curve for their product is \( q=\sqrt{5000-p^{2}} \), where \( p \) is the price in dollars, and \( q \) is the quantity in millions. If weather conditions are driving the price up \( \$ 2 \) a week, find the rate at which demand is changing when the price is \( \$ 40 \). (Round your answer to the nearest hundredth.) A. Decreasing by 1.37 million items per week B. Increasing by 1.37 million items per week C. Decreasing by 3.17 million items per week D. Increasing by 3.17 million items per week E. None of the answers

Calculate the Riemann sum for the function \( f(x) = x^2 \) on the interval [1, 3] using 4 subintervals with left endpoints.

\( \int _{}^{}\frac{1}{e^{x^{2}}}e^{\int _{}^{}2 d x} d x \)

77-78 Use l'Hospital's Rule to evaluate the limit. 77. \( \lim _{x \rightarrow 0} \frac{1}{x^{2}} \int_{0}^{x} \frac{2 t}{\sqrt{t^{3}+1}} d t \)

\( \int _{}^{}\frac{e^{x^{2}}}{x^{2}} d x \)

\[ f(x)=\frac{x^{2}+3}{x-1} \] a. El dominio de \( f \). b. El dominio de continuidad de \( f \). c. \( f^{\prime}(x) y f^{\prime \prime}(x) \) d. Los puntos críticos de f. e. Los extremos relativos de f. f. Los puntos de inflexión de \( f \). g. Los intervalos en que \( f \) es creciente \( y \) h. Los intervalos en que \( f \) es cóncava hacia i. Los cortes con los ejes. j. Las asíntotas verticales, horizontales \( u \) k. Con la información recompilada, dibuje la k. Gráfica de f.