Find the linear approximation to g(x) x at x = 2. Use the linear approximation to...

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Find the linear approximation to g(x) x at x = 2. Use the linear approximation to approximate the value of 3 and 10. Compare the approximated values to the exact values. Write the linear approximation in exact form; then use your calculator to determine the approximated values and exact values to the nearest thousandth place. What is the percent error of each? Which linear approximation value is much closer to the exact value than the other? Why? = Graphing calculator allowed. The position function of a particle in rectilinear motion is given by the equation t s(t) = +2+5 for t 0. (15 points) t a. Sketch graphs of the position, velocity, and acceleration graphs for the interval 0 t 16. Label and mark the axes. b. Determine, to the thousandths place, the value of t at which the particle reverses direction. Explain. C. Find the position, velocity, and acceleration at the t value found in part b. d. Determine the time intervals on which the particle is speeding up and when it is slowing down. Explain. Determine when particle has its maximum and minimum velocities. e. Determine the limit, showing and explaining your work: lim x1 In x x4 - 1 Find the linear approximation to g(x) x at x = 2. Use the linear approximation to approximate the value of 3 and 10. Compare the approximated values to the exact values. Write the linear approximation in exact form; then use your calculator to determine the approximated values and exact values to the nearest thousandth place. What is the percent error of each? Which linear approximation value is much closer to the exact value than the other? Why? = Graphing calculator allowed. The position function of a particle in rectilinear motion is given by the equation t s(t) = +2+5 for t 0. (15 points) t a. Sketch graphs of the position, velocity, and acceleration graphs for the interval 0 t 16. Label and mark the axes. b. Determine, to the thousandths place, the value of t at which the particle reverses direction. Explain. C. Find the position, velocity, and acceleration at the t value found in part b. d. Determine the time intervals on which the particle is speeding up and when it is slowing down. Explain. Determine when particle has its maximum and minimum velocities. e. Determine the limit, showing and explaining your work: lim x1 In x x4 - 1