Software used to program video games often uses an origin at the top left of the display canvas. The positive x -axis is to the right and the positive y -axis is downward. Suppose that a player moves on a direct path from the origin to a point P with pixel location 135 , 200 . Then the player moves directly to point Q at a pixel location of 420 , 150 . a. Find the player's bearing from the origin to point P . Round to one-hundredth of a degree. b. Find the player's bearing from point P to point Q . Round to one-hundredth of a degree.
Software used to program video games often uses an origin at the top left of the display canvas. The positive x -axis is to the right and the positive y -axis is downward. Suppose that a player moves on a direct path from the origin to a point P with pixel location 135 , 200 . Then the player moves directly to point Q at a pixel location of 420 , 150 . a. Find the player's bearing from the origin to point P . Round to one-hundredth of a degree. b. Find the player's bearing from point P to point Q . Round to one-hundredth of a degree.
Solution Summary: The author calculates the bearing of the player at point P if the software that is used to program video game often uses an origin at the top left
Software used to program video games often uses an origin at the top left of the display canvas. The positive
x
-axis
is to the right and the positive
y
-axis
is downward. Suppose that a player moves on a direct path from the origin to a point
P
with pixel location
135
,
200
. Then the player moves directly to point
Q
at a pixel location of
420
,
150
.
a. Find the player's bearing from the origin to point
P
. Round to one-hundredth of a degree.
b. Find the player's bearing from point
P
to point
Q
. Round to one-hundredth of a degree.
Given lim x-4 f (x) = 1,limx-49 (x) = 10, and lim→-4 h (x) = -7 use the limit properties
to find lim→-4
1
[2h (x) — h(x) + 7 f(x)] :
-
h(x)+7f(x)
3
O DNE
17. Suppose we know that the graph below is the graph of a solution to dy/dt = f(t).
(a) How much of the slope field can
you sketch from this information?
[Hint: Note that the differential
equation depends only on t.]
(b) What can you say about the solu-
tion with y(0) = 2? (For example,
can you sketch the graph of this so-
lution?)
y(0) = 1
y
AN
(b) Find the (instantaneous) rate of change of y at x = 5.
In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of
change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the
following limit.
lim
h→0
-
f(x + h) − f(x)
h
The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule
defining f.
f(x + h) = (x + h)² - 5(x+ h)
=
2xh+h2_
x² + 2xh + h² 5✔
-
5
)x - 5h
Step 4
-
The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x).
-
f(x + h) f(x) =
= (x²
x² + 2xh + h² -
])-
=
2x
+ h² - 5h
])x-5h) - (x² - 5x)
=
]) (2x + h - 5)
Macbook Pro
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