Answer Happy

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-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.
a Part (1). Get a lower and upper estimate for the area from x = 0 to 1 = 2 between y=-* and the r-aris using our left-endpoint approrimation and our right-endpoint approrimation. Use an n = 42 Part (2). Calculate the linear approrimation near I = 1 for y = e-* and use the linear approrimation to estimate the area under y = e- and above the -aris 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 approrimation near x = 1 for y=-* and use the quadratic approrimation to estimate the area under y = 1-2 and above the s-aris 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 : l. e-dr Part (5). Use the second part of the FTOC to get the exact answer for the following definite integral : €dx Sathed2-ledz Part (6). Show that the following is equal to e-*: limn–0 Part (7). Discuss the differences in the approximations from Parts 1-3 in one to three paragraphs. Discuss why they are approrimations and whether or not they are over estimates or under estimates. Discuss the accuracy with which they estimate the requested area. h