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Q: 1 x + ex 2 g dx

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Q: Find the center of mass of a thin wire lying along the curve r(t) = 2ti + 4tj+ (x,y,z) = ( (Type…

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Q: Determine whether the series converges or diverges. 4n³ n²-4 n=2

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Q: Find the linear approximation of the function f (x,y) = ln (x - 3y) at point (7,2).

A: To find the linear approximation of the function fx, y=lnx-3y at the point 7, 2.

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A: We have to find X intercept, relative minimum, relative maximum, point of infection and the equation…

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

A: Volume

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Q: Begin with the Maclaurin (Taylor) series: cos r = 1 - 2! 4! 6! (a) Evaluate cos 0. (b) List the…

A: According to the guidelines, we are instructed to answer 1 question or 3 sub question,the others can…

Q: the curve x=l-5¢, y=4€²-1 (0=ts) lengin find the arcC kngth of the curve x=1-. (ux calculator to…

A: This question is based on length of a parametric curve calculated using definite integral.

Q: Find f. f(t) f"(t) = 2e + 3 sin t, f(0) = 0, f(π) = 0

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

A: Given :

Q: g expressions a. lim (2z - 1)(2-1)

A: Given : apply chain rule    find limit of about separately

Q: 2 Evaluate thefallowing cartesian integrats by - changing theminteequivalent Palar integralse 4- to…

A: Solving

Q: Find the arc length L of the graph of r(t). r(t) = 9 cos(t)i +9 sin(t)j + tk, 0≤t≤ 2π

A: This is a problem of vectors and integration. Based on concepts and formula of arc length we will…

Q: Figure (a) shows a vacant lot with an 80 ft frontage in a development. To estimate its area, we…

A: It is midpoint Riemann sum      here length of interval  △x=20

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Q: d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: Solve the differential equation 2xy + y²) dx + (x² + 2xy-y²) dy = 0

A: A homogeneous differential equation is one in which the degree of the function f(x,y) is the same as…

Q: x³+2x-1 (x²+9)² The partial fraction decomposition of has the form None of these Ax+B (x²+9)² A x²+9…

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Q: Determine whether the series converges absolutely, converges conditionally, ges. 4n Σ(-1)", n³+1 n=2

A: Use alternating series test for checking the convergence .

Q: 10 Find the radius of x 2 + y 2 - 10x - 8y + 1 = 0. √41 2√10

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Q: 1 dx x+1 1

A: Evaluate improper integral

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

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Q: Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0),…

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Q: The temperature T at a point (x,y,z) of a solid is given by the function T(x,y,z) = 2x² - y² + 2z +…

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Q: Let f (x, y, z) be a function such that : (i) the function f (x, y, z) decreases most rapidly at the…

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Q: Find the area of the shaded region. 2+ 1 -1- |-3+ 2 3 square units y=x-2 y=√x

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

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Q: Let f(x) = 3x² - 9x + 11 The slope of the tangent line to the graph of f(x) at the point (2,5) is…

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Q: Find the Laplace transform of sint 0<t<27 f() =

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Q: For a person at rest, the velocity v (in liters per second) of air flow into and out of the lungs…

A: Explained below

Q: Dividing the polynomial P(x) by x-1 yields a quotient Q(x) and a remainder of 4.  If Q(-1)=3, Find…

A: P(x) =Q(x) (x-c) + R(x)when the factor is (x-1)R(x)=4P(x)=Q(x) (x-1)+4P(1) =0 +4P(1) =4

Q: Find the limit. NOTE: Enter the answer using round brackets. t² + 8 1 = lim t+x6t²+7'2t (?, ?)

A: Explanation of the answer is as follows

Q: Do not use a calculator for this problem. Find the x-value where the relative maximum of y closest…

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Q: 6 Select the conic section represented by the equation. 5x 2 + 5y 2 = 0 point hyperbola  line…

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Q: Given that the vectors X1 = () e- -2t ,X1 = (C)e-6t are solutions of a system x' = AX, do they form…

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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: A rectangle is bounded by the x- and y-axes and the graph of y = (6 - x)/2 (see figure). What length…

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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.   &lt;5, -8&gt;, &lt;-4,1&gt;   (a) Find the dot product of…

Q: 3 -18 )x are repeated real, 11 = -3 = dz and the Given the eigenvalues for X' = (C eigenvector is K…

A: Solve the following

Q: Consider the space curve r(t) = (cost cos 2t, cost sin 2t, sin t). (a) Find r(t).

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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: 3) Find a vector equation and parametric equations for the line segment that joins (-2, 4, 0) to…

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Q: . Write both an absolute-value and a piecewise function to represent the graph.

A: 5. Absolute function  take graph of f(x)=|x|shift graph 3 units to right and 2 units…

Q: Determine the position function if the acceleration function is a(t) = 6sin t+5, the initial…

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Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

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