The supply and demand for the sale of television sets by an electronics company are given by \( S(p)=\ln p \) and \( D(p)=\ln \frac{193000}{p} \), where \( S(p)= \) the number of television sets that the company is willing to sell at \( \$ p \) and \( D(p)= \) the quantity that the public is willing to buy at \( \$ p \). Find the equilibrium point.

Solve the following inequality. \[ x^{4}>256 \]

3. Verificar gráficamente que las siguientes funciones no son derivables en el punto dado: \( \begin{array}{ll}\text { (i) } f(x)=5-|x-1|, x_{0}=1 & \text { (ii) } f(x)=|2 x-4|, x_{0}=2\end{array} \)

Question 1 A die is rolled. Find the probability of the given event. Write your answers as whole numbers or reduced fractions. (a) The number showing is a 6 \( P(6)= \) (b) The number showing is an even number \( P( \) even \( )=\square \) (c) The number showing is greater than 2

Simplify the expressions. Enter your answer in exponential form. a. \( \left(t^{2}\right)^{6}=\square \) b. \( \left(s^{9}\right)^{3}=\square \) c. \( \left((-2)^{11}\right)^{3}=\square \)

Divide the polynomials. Your answer should be in the form \( p(x)+\frac{k}{x} \) where \( p \) is a polynomial and \( k \) is an integer. \( \frac{4 x^{3}-3 x+1}{x}=\square \)