Midterm Calculus 2019
October 2019
1
Given the line l : x = (1, 3, 2) + λ · (6, 2, −1) and point P = (1, 7, −1), find the
plane V that contains l and P .
Answer: V : y + 2z = 5
2
The plane W is perpendicular to l and goes through P . Find the intersection
of l and W .
3
Calculate lim 2x +
x→−∞
Answer: 32
√
4x2 − 6x + 5
4
Prove by using the − δ criteria that lim
Let δ =
3
x→2
3x2 −4−4
x−2
=8
5
√
d
Show that f (x) = x 1 + 3x4 is invertible and find dx
(f inv )(2)
Answer:
Derivative of f (x) is strictly increasing therefore f is invertible.
d
inv
)(2) = 1/5
dx (f
1