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Chapter 8: Problem 67
Evaluate the determinant, in which the entries are functions. Determinants of this type occur when changes of variables are made in calculus. $$\left|\begin{array}{ll} x & \ln x \\ 1 & 1 / x \end{array}\right|$$
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Find the domain of the function and identify any horizontal or vertical asymptotes. $$f(x)=3-\frac{2}{x^{2}}$$
Consider a company that specializes in potting soil. Each bag of potting soil for seedlings requires 2 units of sand, 1 unit of loam, and 1 unit of peat moss. Each bag of potting soil for general potting requires 1 unit of sand, 2 units of loam, and 1 unit of peat moss. Each bag of potting soil for hardwood plants requires 2 units of sand, 2 units of loam, and 2 units of peat moss. Find the numbers of bags of the three types of potting soil that the company can produce with the given amounts of raw materials. 500 units of sand 500 units of loam 400 units of peat moss
Find the point of equilibrium of the demand and supply equations. The point of equilibrium is the price \(p\) and the number of units \(x\) that satisfy both the demand and supply equations. Demand \(\quad\) Supply \(p=400-0.0002 x \quad p=225+0.0005 x\)
Solve for \(x\) $$\left|\begin{array}{rr} x & 4 \\ -1 & x \end{array}\right|=20$$
Write the matrix in row-echelon form. Remember that the row-echelon form of a matrix is not unique. $$\left[\begin{array}{rrr} 1 & -4 & 5 \\ -2 & 6 & -6 \end{array}\right]$$
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