3. Residential power consumption has shown certain trends over recent years. Based on date reflecting average usage, engineers at the power company have modeled a town's rate of energy consumption by the function r(t) = 4 + sin(0.263t+4.7) + cos(0.526t+ 9.4) Here, t measures time in hours after midnight on a typical weekday, and r is the rate of consumption in megawatts at time t. a) Using a graphing calculator (or equivalent), sketch a carefully labelled graph of r(t) on the interval [0,24]. b) Without calculating its value, explain the meaning of f*r(t) dt.

2. Use logarithmic differentiation to find for the curve defined by (r+1)" y.

Find the derivative and don't simplify the answer. y=tan-1(5x4)+(cos-1(x))6

1. (#11 Exam 1 Review) Find the equation of the line tangent to the graph of the function: f (x) = x-2x² at x = 1. You must use the Definition of the Derivative to obtain the derivative. 2. (#9 Exam 1 Review) Sketch the graph of the function g for which: g(0) = g(2) = g(4) = 0, g' (1) = g(3) = 0,g' (2) = -1, lim g(x) = ∞, and lim g(x) = -∞ x 5 x-1+ 3. State the three-part Definition of Continuity. 4. (#13 Exam 1 Review) The graph of f is given. State, with mathematically correct reasons, the values for which f is not differentiable. -2 VA 0 2 4 X (Description: Graph with three components. First component is horizontal line in the 2nd quadrant to x = -2. Sharp turn upwards in downward arc into the 1st quadrant and ends with open dot where x = 1. Second component is solid dot at x = 1 vertically below the open dot. Third component begins with open dot at x = 1 below the solid dot. The graph falls in downward arc shape into the 4th quadrant, takes a sharp turn at x = 3 and continues as…