to x = 2 between y = e −x and the x-axis using our left-endpoint
approximation and our right-endpoint approximation. Use an n = 42.
Part (2). Calculate the linear approximation near x = 1 for y = e
−x and use the linear approximation to estimate the area under y =
e −x and above the x-axis from a = 0 to b = 2 with a sum of your
choosing and the limit as n goes to infinity. Part (3). Calculate
the quadratic approximation near x = 1 for y = e −x and use the
quadratic approximation to estimate the area under y = e −x and
above the x-axis from a = 0 to b = 2 with a sum of your choosing
and the limit as n goes to infinity. Parts 4-7 can be
completed with the skills we have learned throughout our course up
though section 5.3 Part (4). Use desmos.com to evaluate the
following : R 2 0 e −xdx Part (5). Use the second part of the FTOC
to get the exact answer for the following definite integral : R 2 0
e −xdx Part (6). Show that the following is equal to e −x : limh→0
R x+h 0 e−zdz− R x 0 e−zdz h Part (7). Discuss the differences in
the approximations from Parts 1-3 in one to three paragraphs.
Discuss why they are approximations and whether or not they are
over estimates or under estimates. Discuss the accuracy with which
they estimate the requested area.
- Part 1 Get A Lower And Upper Estimate For The Area From X 0 To X 2 Between Y E X And The X Axis Using Our Left 1 (70.19 KiB) Viewed 36 times