Find f. (use c for the constant of the first antiderivative, d for the constant of the second antiderivative and e for the constant of the third antiderivative.)
f '''(t) = sqrt(t) − 3 cos(t)
find f. f '''(x) = cos x, f(0) = 7, f '(0) = 6, f ''(0) = 6
a particle is moving with the given data. find the position of the particle.
v(t) = sin(t) − cos(t), s(0) = 3
a particle is moving with the given data. find the position of the particle.
a(t) = t2 − 5t + 3, s(0) = 0, s(1) = 20

(a)

(b)

(c) The position of the particle is

(d) The position of the particle is

Step-by-step explanation:

An anti-derivative of a function f(x) is a function whose derivative is equal to f(x). That is, if F′(x) = f(x), then F(x) is an anti-derivative of f(x).

If F(x) is any anti-derivative of f(x) then the most general anti-derivative of f(x) is called an indefinite integral and denoted,

, c is any constant.

(a) To find f(t) of you must:

1.

2.

3.

(b) To find f(x) of you must:

1.

We use f''(0) = 6 to find the value of C

Thus,

2.

We use f'(0) = 6 to find the value of D

Thus,

3.

We use f(0) = 7 to find the value of E

Thus,

(c) You need to use the relation to find the position of the particle.

We know that , so

We use s(0) = 3 to find the value of C

Therefore, the position of the particle is

(d) You need to use the relation to find the velocity of the particle.

We know that , so

Next, you need to use the relation to find the position of the particle.

We know that , so

We use s(0) = 0, s(1) = 20 to find the value of C and D

Therefore, the position of the particle is

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.