[ Calculus I Archive ]
Review Questions:
Linear approximation, quadratic approximation, Newton's method
Question 1
Question 2
Question 3
Find the linear and quadratic approximations to the tangent function at
the origin. Find intervals throughout which these approximations give errors
of less than 0.1.
Question 4
An object is dropped from rest off a 100 meter cliff. The acceleration
due to gravity is 9.8 meters per second per second. Denote the height of
the object at time t by h(t). Give the linear and quadratic approximations
to the function h at time t=0. Comment on the accuracy of these approximations.
Question 5
Find the linear and quadratic approximations to the square root of 103
and to the cube root of 29. Compare these approximations with the actual
values given by your calculator.
Last update: November 11, 1998.