Question

Could someone please double check these answers quick? Thanks! :)

1. Evaluate lim (as t approaches infinity) sin(1/t)
Answer: 0

2. The motion of an object along a horizontal path is modeled by the equation x(t) = 3 - |t - 3|, where x(t) is the position from the origin in meters and t is the time in seconds. Find the distance traveled by the object on the time interval 0 ≤ t ≤ 10.
Answer: 4

3. Locate the absolute maximum value of the function f (x) = x^3 - 27x + k on the interval [0, 5].
Answer: k-10

Answer 1

1. Looks good

Answer 2

Yay! :)

Answer 3

May I ask how you approached 2? Your answer does look correct

Answer 4

x(10) right?

Answer 5

You also did realize that distance is a scalar quantity

Answer 6

Yep! :)

Answer 7

So 2. Looks good

Answer 8

d = x(10) = (3 - |10 - 3|)m = (3 - |7|)m = -4m

Answer 9

Right but its +4 as distance is a scalar quantity

Answer 10

Yepperz :)

Answer 11

How did you get k-10? What does that mean?

Answer 12

What is the first derivative of f(x)?

Answer 13

f'(x) = 3x² - 27 = 0

Answer 14

Right now solve for x and see what values are within your given interval then we must take the second derivative that will tell us if it's a maximum or minimum

Answer 15

(second derivative at the x value)

Answer 16

3x² = 27
x² = 27/3 = 9
x = ±√9 = ±3
I used x=3
f"(x) = 6x
f"(3) = 6(3) = 18
f(0) = (0)³ - 27(0) + k = k
f(5) = (5)³ - 27(5) + k = -10 + k
Thus, the maximum occurs at x = 0 but my options given are:

k-54
k-10
k
there is no absolute maximum value

so I went with k-10 since that's what I got before reaching 0

Answer 17

I don't agree with your answer to #2

Answer 18

What do you think it is?? :)

Answer 19

no

Answer 20

they are not asking for the distance from the start. They are asking for the distance traveled

Answer 21

My options for #4 are:
3
4
7
10

Answer 22

I know the answer...I don't need a list

Answer 23

Okay sorry... Just thought that might help

Answer 24

How would I find the distance traveled?

Answer 25

Ah gotcha, sorry I was thinking of where it started

Answer 26

@Breee615 What is the distance travelled used Zarkon's image if needed

Answer 27

3?? :)

Answer 28

*10 gosh I can't type today

Answer 29

2. The motion of an object along a horizontal path is modeled by the equation x(t) = 3 - |t - 3|, where x(t) is the position from the origin in meters and t is the time in seconds. Find the distance traveled by the object on the time interval 0 ≤ t ≤ 10.

(Distance is different from displacement)

x'(t)=(t-3)/|3-t|
(from the def. of abs value)
x'(t) is negative for t>3, so if you just go,

x(10)-x(0)? then this is not precise, because you are looking for scalar (not vector) displacement.

Rather, |x(0)-x(3)| + |x(3)-x(10)| is the distance, i think

Answer 30

oh, my bad wrong f

Answer 31

yes...10 is a better answer

Answer 32

Okay that makes a bit more sense, thank you :)

Answer 33

x'(t)=(t-3)/|t-3|
(for the correct f)

but, then x'(t)<0 for x<3,
so you have the same distance,

|x(0)-x(3)| + |x(3)-x(10)|

Answer 34

((just that I misread the function))

Answer 35

Does my answer for 3 make sense? :)

Answer 36

@astrophysics

Answer 37

@fakeee