Determine R(t) if R' (t) = (2e²t-4,) and R(2) = (3, −5,0).

Q: f"(x) = 24x2 + 2x + 8, f(1) = 2, f'(1) = -2 f(x) =

A: given that f"x=24x2+2x+8, f(1)=2 and f'1=-2 find f(x)

Q: find (a) r'(1), (b) r"(1), and (c) r'(f) • r"(f).

A: The derivative of a position vector gives the rate of change of position of the body or the velocity…

Q: Given f(r, y) = 4a* + 3a*y" - 3y, find 2.6 f:(z, y) = f,(z, y) - fz(2, y) fay(x, y) =

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Q: AB1: Find g(2), g'(2), and g"(2).

A: Given that gx=∫-2x2ftdt Now we have to find g2, g'2 and g''2 In the interval -2,2, fx=4-x2In the…

Q: Find y as a function of x if x²y" +5xy - 12y = x², y(1) = −9, y(1) = 9. y=

A: We have to find as a function of .

Q: Find f, (2,0) if f(x,y) = 18x e Y. 1,(2.0) = %3D

A:

Q: 1-2 h(r) = 1=7²³²₁ 2-3 . Find h' (1).

A:

Q: Let f(x)= x' and g(x)=x² +7. Find (g1f)(2)

A:

Q: flx)=x =X-5 (x)= Find .f)

A: Here, the given function is: f(x)=x-5, g(x)=x2

Q: For f(x) = x? – 3x + 5, find f(2), f'(2), and f(3) – f(2). a. f(2) b. f'(2) = c. f(3) – f(2) =

A: Given that, f(x)=x2-3x+5

Q: Find y'when ye2x = 3y+ x and y(0)=3 (A) -5 B B -6 (© -4 D) -7

A: We need to find y'.

Q: Differentiate the function. r(t) = (3²- + 8)i + r'(t) = (6t)i + ( 132 r'(t) = i + (6t)j r'(t) =…

A:

Q: Find f, (x.y) if f(x.y)=x - 5xy- 4y2.

A:

Q: Find y'

A: given

Q: The windchill index announced during the winter by the weather bureau measures how cold it "feels"…

A:

Q: A company determines that monthly sales S(t), in thousands of dollars, after t months of marketing a…

A: Find S'(t)?

Q: ompany determines that monthly sales S(t), in thousands of dollars, after t months of marketing a…

A: Given:  s(t)=3t^3 - 50 t^2 +230t+180(a). Find; s'(t),s'(2),s'(3),s'(5)And…

Q: g(x,y) = sq root of (5xy - 3x) find gx and g

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Q: Q3 Find f-(x) for the following : 1- y = Jx-3 2- y = (2x³ + 1)'/5

A: For finding the inverse, we will replace x with y and y with x

Q: For the function z = - 8x³ - 2y² - 2xy, find a z(1,-2), andz(1,-2). dz dz a ax' dy ax

A:

Q: SOLVE THE ODE y''+9y=xexp(3x) + 6

A: Step 1: Step 2:Step 3:Step 4:

Q: For f(x) = x² + 2x + 2, find f(2), f'(2), and f(3) – f(2). a. f(2) = b. f'(2) = c. f(3) – f(2) =

A:

Q: If f(x) =x* + 3x² – x – 15, then f" (-2) would be A. -48 В. -24 С. 24 D. 48

A:

Q: For f(x) = x² + 6x + 6, find f(2), f'(2), and f(3) – f(2). a. f(2) = |3| b. f'(2) c. f(3) – f(2) :

A:

Q: Let x + y = 28. Find y"(x) at the point (3, 1). "(3) =

A: The solution of the problem is given in the next steps.