Use the properties of the derivative to find r(t) = 3/i+6f³j+31³k u(t)=2i+2r²j-3t³k [r(t) - u(t)] given the following vector-valued functions.

Q: Q5A) Find volume of body from above Z = Triple integration. 4-x2 - y2 and below Z = 1 using

A: To find the volume of body bounded by given curves.

Q: if a = 7 and b=4, whats the value of f'(7)? 8|77|80 IN TA O a) Ob) Oc) =/ a) 1/2

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Q: dy Given y³ In x + x¹e³y = sin-¹(xy), compute da

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Q: Using the definition of the derivative, find f'(x). Then find f'(1), f'(2), and f'(3) when the…

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Q: Question 7 Find the partial derivative of z with respect to x 8: da = -2x (3x²+1) sin(x²) + 6xcos…

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Q: Find the interval of convergence of the power series: ∞ n [²(+1²] (x + 1)n 1)"] 2n n=0

A: To find the interval of convergence.

Q: Give the domain and range of the graph shown to the right. Then, use the graph answer parts (a)…

A: Domain is the value of x for which curve is defined.  Range is the value of y for the different…

Q: a) y || (т. 3x 5x-x2 3

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Q: Find both first partial derivatives. z = 8y2 sqaureroot x

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Q: Find an equation of the tangent line to the graph of y = x³ – 3x – 1 at the point (2, 1). 09x - 2y -…

A: 1.y=x3-3x-1 at the point (2,1)2.y=logx2e

Q: (7) ² Fi²+ Fi²+ ² Fi Fz Cos/20 49=F₁²+ F²-FiFe- tan 8= 48- = 4√3 4√3= F₂S in 190 Fit F₂ Golze $7…

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Q: Find fx, fy, and fz, and evaluate each at the given point. f(x, y, z) = x2y3 + 2xyz − 7yz, (−3,…

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Q: If [ f(x) dx O 10 0 2 O O -2 = 4 and 4 [*g(x)dx = 6, what is 5 2 [ f(x)dx + ² g(x)dx? 4

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Q: 23 In the graph below, determine whether the given walk is a trail, a path, or a circuit. VI V5 V2…

A: We have to determine the path of given walk.

Q: Evaluate x/12 0 14√/1- cos 12x dx.

A: Given, ∫0π4141-cos12xdx

Q: (1) f(x) = sin (5x + 6) (3) f(x) = sin(x-³) (2) f(x) = sin (3x4 + 2) (4) f(x) = cos (4+ 3x)

A: To find f'(x)

Q: Find the volume of the region that lies below the parabola y2 = x and above the x-axis the interval…

A: Given curves is y2=x

Q: Suppose the revenue from producing (and selling) x units of a product is given by R(x) = 15x-.06x²…

A: To find marginal revenue at production level of 35.

Q: 1. Find each of the following derivatives. d a. dx (4 sinx) b. [ln (2x4 - 3x)]

A: We have to find derivative of given function.

Q: 18 What is the total degree G? 3 6 5 VI e₁ V2 ez VA

A: From the given graph G, we have to find its total degree

Q: There are $448 available to fence in a rectangular garden. The fencing for the side of the garden…

A: Given that , Total available cost = $448 Road side cost = $12 per foot and other side cost = $4 per…

Q: f 2³x dx = O 0 23x In 2 + C ○ 23x+1 + C 3x+1 23x In 8 0 23x ln 2 O + C + C

A: To evaluate: I=∫23xdx

Q: For the next three exercises, use power series operations to determine the Maclaurin series for the…

A: We need to determine Maclaurin series for xarctan(x2).

Q: At which value of x is the function whose graph is shown below differentiable? 8 -8 -6 8 0=7 O=14…

A: To determine the value of x at which the function whose graph is shown below is differentiable.

Q: Home Work: Solve the following system of equations. 1 -1 2 0 2 -3 1 -4 3 X₂ 14 1 -4 5 -1 X3 -1 4-2…

A: We can solve the given system of equations.

Q: Find y': y=V5+2 — 2 O y = 7-2x 2√5+2x-x² Oy = √2-2x 1 Oy = 2√5+2x-x² 1-x O y = √5+2x-x2

A: We have to find derivative of given function.

Q: Using the Inverse Function Theorem, what is (-¹) (8) given that f(x)=√6x-2? Note that (11) = 8. (Do…

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Q: B)Prove (cose + i sine)" = cosne + i sin no

A: Solution is given below:

Q: Evaluate x/10 Than S 11√1+ cos 10x dx. 0

A: We know that integration of cosx is sinx +C . And trigonometry relation is - Cos2x = cos2x - sin2x =…

Q: Evaluate: S (5 — 2 sec 0 tan 0) de - O 0.79 0.68 O 0.95 0.84

A: ∫π6π4(5-2secθtanθ)dθ

Q: Evaluate the integral. 2 [ 11t sec-'t dt 2/√√3 2 S 11t sect dt = [ 2/√√3 (Type an exact answer,…

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Q: Given f(x) = -7x - 2, find f' (5) using the definition of a derivative. Provide your answer below:…

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Q: 1(3). If f(x) = 2 cos x + x³, find 06 2 4 8

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Q: dy -(x²+y) B)Solve differential equation = dx x+siny

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Q: 3 X and f'(-2) if f(x) = 6x. 8 (-2)=(Simplify your answer. Type

A: Given: f(x)=x38-6xTo find:f'(-2)

Q: Find the general solution of the following differential equation. 25y" - 25y' - 6y = 0 NOTE: Use c₁…

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Q: really need help with drawing this graph I already got the area of the region i just need help with…

A: Follow the procedure given below.

Q: Draw a graph to match the description given. f(x) has a positive derivative over (-∞, -1) and…

A: Here, given that the function f(x) has a positive derivative over -∞,-1 & (-1,7) and a negative…

Q: Identify any extrema of the function by recognizing its given form or its form after completing the…

A: To find out the extrema of the function.

Q: Classroom activity 9.1 the monthly income earned by each of the following workers paid by the hour…

A: We have to determine the monthly income.

Q: 2. Which of the following sets of ordered pairs could be part of a linear function? F II (0, 1), (3,…

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Q: Sketch the graph off and use your sketch to find the absolute and local maximum and minimum values…

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Q: Q1A)The vectors A = 3i+j+ 4k, B = 2i-3j-k, find vector normal to A and In plane of A and, B.

A: See the details solution in below

Q: 2. A line passes through the points P(4, -3) and Q(6,2). Write the following equations of the line:…

A: A line passes throughvthe points P(4,-3) and Q(6,2). Write the following equations of line. A) a…

Q: Which point is the vertex of the parabola y = 6(x+3)^2 - 5?

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Q: You are driving a car away from home. Your velocity (miles per hour) t hours after noon is given by…

A: you are driving a car away from home.your velocity t hours after noon is given by,…

Q: 2. If w = f(x + ct) + g(x- ct) show that c²wxx = Wtt C= constant.

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Q: Which of the following interval is f(x) = O (2, +∞0) O [2, +∞0) 0 (-∞0, +∞0) ○ (0, +∞) 1 Vx…

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Q: Evaluate f(2x² + 3x + 1)5 (8x + 6) dx

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Q: S 2³x dx = 0 23x+1 3x+1 23x In 2 O O O + C + C 23x + C In 8 2³x In 2 + C

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