If \( p(x) \) is a polynomial, then \( \lim _{x \rightarrow a} p(x)=p(a) \)

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?

Deduce that \( \left(x_{n}\right) \) is a Cauchy sequence and thus convergent.

to find the principal resistance values for optimizing power flow across the network. 1. In a distributed system, the latency \( L(x, y, z)=x^{2}+2 y^{2}+3 z^{2} \) (in milliseconds) depends on the numbe servers at locations \( x, y \), and \( z \). The total number of servers is constrained by \( x+y+z=20 \). Find the configuration of servers that minimizes latency.

\( ( 4 x + 2 y ) d x + ( 2 x - 4 y ) d y = 0 \)

If time \( t \) be regarded as a function of velocity \( v \), prove that the rate decrease of acceleration \( f \) is given by \( f^{\frac{d}{} f^{\prime}} d v^{2} \) [Bikaner सस्न रेखा में चल रहे किसी कण की मूल बिंद ती दूरी \( x \) पर वेग \( \left.\left(a^{2}-x^{2}\right)^{\frac{1}{2}} \right\rvert\, x^{2} \) सम्यनुपाती है। इसके त्वरण का नियम ज्ञात कीजिए। The velocity of a particle moving along a straight line, when a distance \( x \) from the origin varies as \( \left(a^{2}-x^{2}\right)^{\frac{1}{2}} / x^{2} \). Find the law