nilai k jika \( \int_{1}^{2}[10 \mathrm{f}(\mathrm{x})-\mathrm{kx}] \mathrm{d} x=10 \) the value of \( k \) if \( \int_{1}^{2}[10 f(x)-k x] d x=10 \)

A área transversal de um solide varia conforme é exato \( A(x) = 2x + 1 \). Encontre o volume desse sólido sobre o intervalo \([0, 4]\).

\( \int _ { 0 } ^ { t } \sin u e ^ { t - u } d u \)

9. The market research department of a Company recommends that the Company to manufacture and market new TV after suitable test. The marketing department also presents the following demand equation. \( X=28,000-2000 P \) or \( P=14-x / 2000 \), where \( P \) is price and \( X \) is production. Furthermore, the financial department provides the following cost equation: \( C(X)=15 \), \[ 000+7 x \] Conduct a marginal analysis for the company and calculate the amount of the products that maximized total profit?

Find the area of the region bounded by the curves \( y = \frac{1}{x} \) from \( x = 1 \) to \( x = 2 \) and the line \( y = 1 \).

The network latency \( L(x)=-2 x^{2}+12 x-10 \) for data packets is studied for input size ' \( x \) '. If the latency is qual at \( x=1 \) and \( x=5 \), use Rolle's theorem to find a value ' \( c \) ' in the interval \( (1,5) \) where the latency's rate of hange is zero. In a network flow system, the following equations represent the flow through three nodes \( \mathrm{A}, \mathrm{B} \), and \( \mathrm{C}: 2 A+ \) \( +C=100 \) (total inflow); \( A+3 B+2 C=200 \) (flow through node B ); \( 3 A+B+4 C=300 \) (outflow from ode \( C \) )