Ex. 1. A company manufactures and sales \( X \) units of radio transistor per week. If the weekly cost and demand equations are: \[ C(X)=5,000+2 x \] \[ P(X)=10-\frac{x}{1,000} \quad P \text { is price } \quad[0,8000] \] or each week find:- 1) The production level that leads to maximum revenue and the maximum revenue. 2) The production levels that leads to maximum profit and the maximum profit. 3) The production level that leads to minimum cost and the minimum cost.

Determine the first derivative of the \( 1.1 \quad y=x^{3}-\cot \left(x^{3}+3 x-1\right) \)

кцияның туындысын табыңыз: \( \left\{\begin{array}{l}x=t^{3}+3 t^{2}-5 \\ y=3 t^{2}+6 t-3\end{array}\right. \)

(iv) In integral equation of the form \( \int_{0}^{1} \frac{F(u) d u}{(t-u)^{n}}=G(t) \) is called. (a) Exact equation (b) Convolution type (c) Integro-differential equation (d) Abel's equation

1) Sout \( x>0 \). En appliquant le thécorème des accroissement fines à la fonction \( \ln \) montrer que: \( \exists c \in] x, x+1\left[\frac{1}{c}=\ln \left(1+\frac{1}{x}\right)\right. \) 2) \( M q: \exists c \in] 0, x\left[\right. \) arctan \( (x)=\frac{x}{1+c^{2}} \) 3) En déduire que \( \forall x>0: \) \( \frac{1}{1+x}<\ln \left(1+\frac{1}{x}\right)<\frac{1}{x} \)

\( \int _{0}^{\frac{\pi }{2}}\frac{1}{2+\cos (x)} d x \)