2) Sketch the curve with the vector equation r(t) = costi- costj+ sin tk. Show the direction of increasing t with an arrow drawn on your curve.

Q: n 2 (4k – 2) = k=1

A: Recall:  1+2+3+...+n=n(n+1)2

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Q: The population of a city is 125,000. If the population is declining by 3% per year, what will the…

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Q: 2. Let f(x)=x-3x² a. Determine all x-values where f(x)=0 b. Fill in the table below with the…

A: This question can be solved using the concept of points of inflection.

Q: The graph of a function f is given. Use the graph to estimate the following. y 5 (a) All the local…

A:

Q: Let the graph below represent f(x). For which values of x is f(x) increasing? 20 16- 12- -5-3-2 8+…

A: The graph of the function f'x is To evaluate: The values of x for which fx is increasing.

Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

A: We have to find the maximum profit.

Q: Consider the vectors. (-6, 2), (8, 1) (a) Find the dot product of the two vectors. -46 (b) Find the…

A:

Q: Find and classify the critical points of f(z) = 82°(8 - z)7 as local maxima and minima. %3D Critical…

A: Critical points are the points of a function where the derivative does not exist. local maxima: the…

Q: y= v-2² +2²-2x+ 8 (a) Find y'= f'(x). f'(x)=x²+x-2 (b) Find the critical values. (Enter your answers…

A: Solve it

Q: r(t) = cos(nt)i – In(t)j+ vt – 16k; to = 17 | -

A: Given :

Q: 1 x + ex 2 g dx

A:

Q: Find the point of diminishing returns for the function, where R is the revenue (in thousands of…

A: Given the query is to find the point of diminishing returns.

Q: Sketch the region bounded by the graph of the equations and find the area of the region. 1 y = , y =…

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Q: Find the Taylor series generated by fat x = a. f(x) = exa=3 Ο Α.Σ Ο Β. Β. €3(x-3) n! €3(x-3) (n+1)!…

A: Find Taylor series.

Q: Calculate the work expended when a particle is moved from 0 = (0,0) to Q = (4,4) along the segments…

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Q: 30 30 90 12 150 180 210 40 270 30 330 360 20 450

A:

Q: Determine the maximum value of f(x)=-x²+2x²+2 on -2 ≤x≤ 3. a) 3.185 b) -7 Od 2 d) 18 2

A: To find the maximum value of the function.

Q: Find the area (in square units) of the region under the graph of the function f on the interval [0,…

A: Given fx=10 ex on the interval 0,3 The formula to calculate the area under the graph y=g(x) on the…

Q: If sint = 4/5 and t is in the first quadrant, find cos(2 t) -7/25 -9/25 7/25 24/25 None of these

A: There is more than 1 question, as per the Q&A guidelines I am answering the 1st question. If you…

Q: nd the maximum profit and the number of units that must be produced and sold in order to yield the…

A: Given the query is to find the maximum profit.

Q: 3. An airplane with an airspeed of 80 meters per second is due east, gaining altitude, and has a…

A:

Q: The velocity of a particle in space at time t is given by(t) = 2t² i + 2t k Find the distance…

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Q: 10. If 3(a, 3, 2)-2(3, b, b) = (-3, 1, -2), determine a and b. Describe the set spanned by the…

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Q: Select the conic section represented by the equation. 13x 2 + 5y 2 - 6x + 3y - 5 = 0 circle point…

A: We can select the conic section as below.

Q: The u(x) that converts the equation below into an exact equation x\dy + (2x?e" + 1) = 0 ey + y) dx…

A: Let's find.

Q: -3x+1) -3х 2-3* dx

A: According to our company policy we are supposed to answer only first question and rest can be…

Q: 4. Find the volume of the solid that lies under the paraboloid z = x? + y² and above the region R in…

A: We want to find the volume.

Q: 2000, the population of a city was 71,000. The population had grown to 100,000 by 2011. If the…

A: Given query is to find the population in 2026.

Q: n of Calculus to find the derivative of the

A:

Q: 4. (- FIND the center of mass of the lamina of density p if the lamina is shaped like the region…

A: A detailed solution is given below.

Q: ef. F. F. dr. F(x, y) = 9xi + 4yj C: r(t) = ti + √4-t²4j, -2 ≤ t ≤ 2 Evaluate

A:

Q: c) Period d) f(990°)

A: Follow the procedure given below.

Q: 109. f(x)=x* tan x³ -x In (1+x2), then the value of (b) 1 dª f(x) dx 4 at x = 0, is: (d) 15

A:

Q: Use one of the following three formulas for the area of the region enclosed by C 1 fxdy = f - ydx =…

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Q: x-2 lim 3x+5+2x' +2*

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Q: Find the sum of the first 125 positive even whole numbers.

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Q: Find T(t) and N(t) at the given point. r(t) = 8 cos(t)i + 8 sin(t)j; t = 1|3

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Q: Determine the indefinite integral 4 √√x + 3 6x 1/0² - 1717 dx 4 X

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Q: Find two positive numbers satisfying the given requirements. The sum of the first and twice the…

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Q: Consider the vectors. (5, -8), (-4,1) (a) Find the dot product of the two vectors. -28 (b) Find the…

A: Given problem:- Consider the vectors.   <5, -8>, <-4,1>   (a) Find the dot product of…

Q: Find the value of z in the solution of the following system: - 1x – - 4y - 4z = 99 4x + 2y + 2z = 88…

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Q: For u =(5,-5) and v = (-3, 2) find u. v. u v = 2.9 u•v=

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Q: 2. Write down the name of the conic given by the polar curve r = 6/ (3 - 2 cose). Determine the…

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Q: For what values of x does the series converge conditionally? 5x Σ n! n=1 1 O A. x= -7 5 OB. X=0 1…

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Q: Suppose that she applied a force of 20N to push the object for 50m as shown below. If e = 45°, then…

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Q: TOPIC: OPTIMIZATION IN DERIVATIVES Directions: Read and analyze each problem carefully and solve for…

A: Volume

Q: Solve the system using Cramer's Rule. - x + 2y = - 5 4x + 5y = 32 Find the determinant D…

A: D=-1245D=-1(5)-2(4)=-5-8D=-13Dx=-52-325Dx=-5(5)-2(-32)Dx=-25+64Dx=39Dy=-1-54-32Dy=(-1)(-32)-(-5)(4)D…

Q: 1 lim (x² –1)sin x+1

A: To find out the limit.

Q: Solve the given initial-value problem. y'' + 4y' + 5y = 35e−4x,  y(0) = −2,  y'(0) = 1 y(x)=

A: