Math 1151 Midterm 2
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Math 1151 Midterm 2
February 15, 2021
1) The graph of a function f with domain (一6, 6) is given in the figure below.
a) (1 point) f (一2) = c) (2 points) lim f (x) + 2 =
b) (1 point) f\ (一1) =
d) (2 points) Sketch the secant line through the points corresponding to x = 1 and x = 4. Label it as S .
e) (2 points) Sketch the line tangent to f at the point corresponding to x = 一3. Label it as T .
f) (2 points) Which one of these values is greatest? A, B, or C :
(A) f\ (一5.5) (B) f\ (一2.25) (C) f\ (4.5)
g) (2 points) Which one of these values is least? A, B, or C:
(A) f\ (一5.5) (B) f\ (一2.25) (C) f\ (4.5)
h) (3 points) Find the x-values in (一6, 6) at which f is not differentiable?
x 一 VALUES :
2) We are given that the line y = 3x 一 7 is tangent to the graph of y = f (x) at the point (2, f (2)) (and only at that point) . Set
g (x) = 2x f (^x).
a) (2 points) What is the value of f (2)?
f (2) =
b) (2 points) What is the value of f\ (2)?
f\ (2) =
c) (2 points) What is the value of g (4)?
g (4) =
d) (5 points) What is the value of g\ (4)?
g\ (4) =
e) (4 points) Find an equation for the line tangent to the graph of y = g (x) at x = 4.
3) A function g , with domain (一&, &), has values and derivative values as given in the table below.
|
x |
g (x) |
g\ (x) |
|
1 |
5 |
一1 |
|
2 |
2 |
3 |
|
3 |
4 |
一6 |
|
4 |
一6 |
一5 |
|
5 |
2 |
7 |
|
6 |
一4 |
一3 |
|
7 |
一3 |
2 |
|
8 |
5 |
4 |
Evaluate the following. Don’t forget to JUSTIFY your work.
a) (5 points) ┌ 
╱ 
、┐ (|1
VALUE :
b) (5 points) ┌ 
╱g (2x + 1) sin ╱ 
、、┐(|3
VALUE :
c) (5 points) lim
4) An object traveling along a horizontal line has displacement function given by
s(t) = 4t(t + 1)
with s measured in meters and t measured in minutes.
a) (4 points) Find the instantaneous velocity at time t = 1, v(1).
v(1) =
b) (4 points) Find a formula for the average velocity, va) (t), on the time interval [t, 1] for 0 < t < 1, and on [1, t] for 1 < t < 2.
va) (t) =
c) (4 points) Using your result from b), compute the limit: lim va) (t).
VALUE :
d) (3 points) Explain what the limit from part c) represents.
2022-09-28