If an converge to zero then the series , an is convergente Select one: True False Question 5 If the series 1(an)? convergente then we must have limn-o an # 0 m%3D1 Select one: True O False

Q: Find the directional derivative of the function at P in the direction of f(x, y, z) = xy + yz + xz,…

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Q: 4. S V4x –1 dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Consider the following optimization problem. Maximize P = xyz with x + y = 36 and y + z = 36, and x,…

A: We have to find P(y), P'(y) and maximize P.

Q: Find dy/dx for  a.) y=xx+3

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Q: Find the curvature K of the plane curve at the given value of the parameter. r(t) = 6ti – 8tj, t = 1…

A: The formula for the curvature is κ(t) = r't×r''tr't3

Q: 3. In the differential equation (2x+ y)dx- 3(2x+ y+4)dy=0, we let the substitution dy =,

A: According to our company's guidelines I can only answer first question since you have asked multiple…

Q: Let f be a continuous function. Show that 2022 f(1/a) dx f(x) dz. %3D 1/2022

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Q: Find the curvature K of the plane curve at the given value of the parameter. = ti +tj, t = 3 36 r(t)…

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Q: Find r'(t), r"(t), and r'(t) · r"(t). r(t) = 5 cos(t)i + 4 sin(t)j (a) r'(t) (b) r"(t) (c) r'(t) ·…

A: Here is the solution

Q: A balloon leaves the ground 50 ft from an observer, rises at the rate of 8 ft/sec. How fast is the…

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

A: Given equation passing through the points (5 , -3, -2)  and  -23 , 23 ,1

Q: Find u · v, u· u, ||v||2, (u · v)v, and u · (3v). u = (3, 11), v = (-4, 3) (a) u: V (b) u. u (c)…

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Q: 1. (2x+ y)dx-3(2x+ y+4)dy =0

A: Let's find.

Q: 1. Let f(x) be a function of period 2n such that 1, -7 <x < 0 0 <x <7. 5(<) = { 0, a) Sketch a graph…

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Q: at Given that £{cos bt}(s) = use the translation property to compute £{e cos bt}. Click here to view…

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Q: man holds a rope that leads a horse. The horse walks in a circular path as shown by the dashed line,…

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Q: 85 2 1 r³)(1 x2 O A. (3x? – 2+ 3 - O B. 85 2 1 (3x2 – 2+ -x3)(x+ 3 · (1 – →)(x³ – 2æ + 17x3) 85 2 1…

A: Given query is to find the derivative using product rule.

Q: 7. Evaluate the definite integrals. a) S TVr - Idx b) Si evE dx

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Q: Determine whether the following series is convergent or divergente: (-1) " n7 +5 n= 1

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Q: (a) Find the area of the region bounded below by the curve y = r² and above by the line y = 4 (b)…

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Q: 5. St? V1- t dt (2x+3) dx 6. S (x2+3x-6)

A: Please see the answer below.

Q: Set up and evaluate the integral for finding the area and moments about the x- and y-axes for the…

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Q: Item # 5. 15 pts The following figure shows the graphs of y = f(x) and y = g(x), together with the…

A: A=2.5∫-3-1 f(x) dx = 2.5B=3.3∫-11f(x)dx=-3.3C=2∫13f(x)dx=2D=3∫-3-1g(x) dx =-3E=4.3∫-11g(x)dx…

Q: 4. In the differential equation (6x–3y+2)dx-(2x- y-1)dy=0, we let the substitution dx=

A: Given differential equation, 6x-3y+2dx-2x-y-1dy=0              6x-3y+2dx=2x-y-1dy…

Q: Determine the values of x that causing the following series to converge. (3x- 1)n 2n n=1

A: This is a problem related to convergance of the series. Based on the general formula we will answer…

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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Q: Rojana is 8 years older than AJ, and the sum of their ages is less than 24. Find their possible…

A: Let Age of Rojana is x , and age of AJ is y. Given, Rojana is 8 year older than AJ. Therefore, x=y+8…

Q: Let f(x) = Va and g(x) = x² – 1. Find go f and determine its domain. |3D %3D

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Q: Prove the following function T : R3 → R³ defined by T(x, y, z) = (2x – y, y – 2, x + 2) is a linear…

A: Explanation of the answer is as follows

Q: t sin(t² + 4) dt cos(t² + 4)

A: To evaluate: ∫tsint2+4cost2+4dt Let I = ∫tsint2+4cost2+4dt

Q: The following figure shows the graphs of y - f(x) and y = g(x). together with the indicated areas.…

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Q: A sales representative for a company that produces electric mixers can sell x units of their deluxe…

A: Given

Q: 10. If G(x) is an antiderivative of g(x) then y = G(x) is a solution to the differential dy equation…

A: If G(x) is the antiderivative of g(x), an integrable function. Then ∫g(x)dx=G(x)+C, C is a constant.…

Q: Find the directional derivative of the function at P in the direction of v. f(x, y) %3D х3 — уз,…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Find the equilibrium point for the supply and demand functions below. Enter your answer as an…

A: Given,            The supply and demand function are            Sx=4x2+19x+8            Dx=116-5xTo…

Q: Find an equation for the ellipse whose graph is shown. y 5 4

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Q: 5. x3 + 2x – 6 dx x4 + 2x2

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Q: Item # 6. 15 pts Suppose that a population of bacteria for an experiment increases according to the…

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Q: Sketch flx) = 2 cos x-Sin 2x , osx<2o

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A: This is a question related to vector. Based on the general formula of plane we will solve.

Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

A: Using she'll method, volume is evaluated.

Q: ||r'(t) × r"(t)|| Use the formula k(t) = to find k(t). 13 r(t) = el2"i +e-j 12ts K(t)

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Q: Find parametric equations for the lines The line through (2, 4, 5) perpendicular to the plane 3x +…

A: 1) To find the parametric equations for the lines. The required line is perpendicular to the plane…

Q: Find the area of the triangle with vertices P(1,5, –4), Q(0,0, 0) and R(4, 5, 1). NOTE: Enter the…

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Q: dy 2. x2 dx xy = (x² + y²) tan-() %3D -

A: Here, the given differential equation is: x2dydx-xy=(x2+y2)tan-1yx...(1)

Q: Determine the maximum and minimum values ​

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Q: Q1/ a) Sketch the graph of y = sin2x for 0 <x SI %3D b) find the total area bounded by the curve and…

A: This is a problem related to calculating area under curve of the polar equation. Based on the…

Q: n2+5 n First four terms of the sequence are: 1+9n O None of them 14 3 19 36 19 5 1437 19 36 19 14 37…

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Q: on

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Q: 4 n+ 2 is divergent. n=1 1+6n Select one: O True O False

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