1. Solve the following equations for x: 10ª+5 − 8 = 60, 3(2ª + 4) = a, and e²ª − 5eª + 6 = 0 (Hint: use log wisely for t

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1 Solve The Following Equations For X 10a 5 8 60 3 2a 4 A And E A 5ea 6 0 Hint Use Log Wisely For T 1 (188.25 KiB) Viewed 32 times

1. Solve the following equations for x: 10ª+5 − 8 = 60, 3(2ª + 4) = a, and e²ª − 5eª + 6 = 0 (Hint: use log wisely for the first two; for the last one, let u = eº and solve for u first). 2. Graph each of the following functions and then either obtain its inverse and graph it or explain why the function is not invertible. (a) f(x) = 20x +7 (b) g(x) = 5x² + 6x + 20 (c) h(x) = 40(x8)² + 10, for all x < 8 (d) k(x) = 15 log(x) + 4 for all x > 0 3. Obtain the derivative of the function f(x) = (x+5)³ using only the formal definition f'(x)= lim Ax→0 2x+5 7x-9 4. Take the derivative of the following functions. In parts (d) and (e), compute the partial derivatives. (a) f(x) = ax²-1 I (b) f(x) = (xe)" + b, where is a constant. (c) f(x) = (d) f(x, y) = a ye-* (e) f(x, y) = f(x+Ax)-f(x) Ax y x+y 5. Solve the unconstrained maximization problem max f(x, y), I,y where f(x, y) = 50 - (2x+10)4 - (y - 6)². 6. Use the Lagrange method to solve the following constrained maximization problems. (a) Objective function f(x, y) = xy, constraint 2 = x + 2y (b) Objective function g(x, y) = log(x) + log(y), constraint 2 = x + 2y (c) Objective function h(x, y) = ay + bx, constraint y² + xy - 1 = 0 7. The highway department is planning to build a picnic area for motorists along a major highway. It is rectangular with an area of 4,000 square yards. It is to be fenced off on the three sides not adjacent to the highway. What is the least amount of fencing needed to complete the job?