Calculus

Problem 2: f(x) = x + e

x 2 1) Find the equation of the tangent line to f at the point (0;1) 2) Use the tangent line at the point (0;1) to approximate the value of f(0:1). 3) Is the approximation found previously an over or under estimate of the actual value of f(0:1)? Justify your answer EXPERT ANSWER

5. The figure shows the graphs of the position, velocity, and acceleration of a car. Identify each curve and justify your answers. (12 points) 6. Given the function f(x) = x + 4x a. Find the relative extrema of f. (4 points) i no elsvietni lis bns biswa svono a todas as now no sleva (etnog) niebeb vnosa b. Find the tangent line approximation of fat x = -1.(4 points) nog dobitni lotnico C. Use your tangent line approximation to approximate the value of f(-1.01). d. Is your approximation an underestimate or overestimate of the actual value of f-1.01)? Justify your answer. (1 point)

EXPERT ANSWER

1. (a) Let a closed to region R be revolved about the x-axis. Also let (x,y) be any arbitrary point in the region. Then co-ordinate of the center of gravity of the solid generated region the by revolving the R is given by (T. 9, Z) =( SI Rxy dx dy SSR y dx dy Explain why } and Ē must be zero. Use the formula (1) given in Cartesian co-ordinates to prove that if R is the region bounded by the polas curve 8= f(9), then formula transforms into: 3 ,0,0) SSR 83 sin a do do (5,4,5) = ( SSR usin@ cos do de

EXPERT ANSWER REASON FOR Y AND Z OF CENTER OF GRAVITY BEING ZERO: There are two ways to explain this. One the qualitative way and another quantitative. Here are the both explanations. The solid formed here (by rotation about the x-axis) will definitely be symmetric with the x-axis. The center of gravity of a symmetric …

1. (a) Let a closed to region R be revolved about the x-axis. Also let (x,y) be any arbitrary point in the region. Then co-ordinate of the center of gravity of the solid generated region the by revolving the R is given by (T. 9, Z) =( SI Rxy dx dy SSR y dx dy Explain why } and Ē must be zero. Use the formula (1) given in Cartesian co-ordinates to prove that if R is the region bounded by the polas curve 8= f(9), then formula transforms into: 3 ,0,0) SSR 83 sin a do do (5,4,5) = ( SSR usin@ cos do de Read More »