Find a set of parametric equations of the line with the given characteristics. (Enter your answers as a comma-separated list.) The line passes through the point (-1, 4, -2) and is parallel to v = 5i – j.

Q: Determine whether the infinite geometric series is convergent or divergent. If it is convergent,…

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Q: ! Consider the nonhomogeneous DE: y" + y' – 6y = (12 – 16x)e*. - A) Verify that y, = 4xe* is a…

A: The given differential equation is y''+y'-6y =12-16xex. At first we have to verify yp=4xex is a…

Q: Consider the surface defined by the equation z2 = 2x² + 4x - 6y? - 2y+ 1. %3D Find a set of…

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Q: A rock is thrown upward from a bridge that is 53 feet above a road. The rock reaches its maximum…

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Q: Speedometer readings for a motorcycle at 12-second intervals are given in the table. t (s) 12 24 36…

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Q: a) ) Sketch and find the area of the surface obtained by rotating the curve y=/3x+4 for x E [3,5).…

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Q: MY NUTES A projectile is shot upward from the surface of Earth with an initial velocity of 110…

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Q: y = 4e" Vx et y = x2 – 1 x2 – 1

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Q: Consider the following. (The graph Is called a serpentine.) 36x +36 Find the derivative of the…

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Q: 13x y = 241 • Y = 0, 0<x < 5 y = 0 , 0 < x < 5

A: Area bounded by curve

Q: Given the differential equation y' = 8y2 and y (0) = - 1 and its next few implicit derivatives y" =…

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Q: Determine whether the (-1) "3" 00 geometric series * is convergent or n=1 6" divergent, and if it is…

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Q: The graph of f is shown. State the signs of f'and f" on the interval (0, 2).

A: A function f(x) is increasing if              f '(x) &gt;0 The graph of the function f(x) is…

Q: r(t) 12t i + 813/2 j + 3t² k, 0 < t<1

A: Here We have to find the length of the given curve.

Q: Determine the magnitude of the complex number, X. X = 5 + -9j ---------------------       x=5+…

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Q: T 11x + 29 dx The integral is equal to

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Q: 2. y = x+2 sin r, 0<x <T

A: To determine the area of the region bounded.

Q: Suppose you know F(11) = 71, F(3) = 16, where F'(x) = f(x). Find the following. (You may assume f(x)…

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Q: Find the derivative of the function. g(x) = vx2 - 14x + 49 %3! g (x) = %3D

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Q: 1.92 Referring to the definition in Exercise 1.91, answer the following questions. a) Prove that…

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Q: Use the Ratio Test to determine the convergence or divergence of the series. (If you need to use co…

A: This question can be solved using the concept of ratio test.

Q: If a, > 0 and -0 an is convergente then E(an)"2 is also convergente Select one: O True O False

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Q: Find the gradient vector field of f. f(x, y, z) = x cos(8y/ z)

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Q: Write the equation of the line tangent to the graph of the function at the indicated point. As a…

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Q: A company produces x units of a product per month, where C(x) represents the total cost and R(x)…

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Q: Find an equation of the Ellipse that has Foci (-1,-2) & (7, -2) and vertex (8, -2). (a-3)2 (y+2)? 1…

A: We need to find equation of ellipse.

Q: Consider the following. (If an answer does not exist, enter DNE.) F(6) = 2 cos(6) + cos?(e), oses 27…

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Q: Solve the problem. From a thin piece of cardboard 20 in. by 20 in., square corners are cut out so…

A: We have to find the maximum volume and dimensions of the box.

Q: Use Properties of Tangents 1. Draw two circles that have no common tangents. | 2. Draw two circles…

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Q: Integration by Partial E 8. S 4x3—х dx х2—х-30

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Q: The two parameter family of solutions of the DE: y" + 25y = 0 is y = c1 sin 5x + c2 cos 5x. Then,…

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Q: 6.) r(t) = (cos t, sin t, In cos t), (1, 0, 0)

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Q: 2t 3t – 1 Verify the product law for differentiation, (AB)' = A'B + AB' where A(t) = 13 1 and 1-t…

A: To verify the product law for differentiation, AB'=A'B+AB' where, At=2t3t-1t31t and Bt=1-t1+t2t25t3.

Q: 8. According to the following table, what is the limit of this function as x approaches 0? -.001…

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Q: 8 x2 + 16 dx x2 The integral is equal to ...

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Q: Fit a second-order polynomial to the data in the kollowing daha- 0|12/31415 yi 2.17.713.6|272 40.9…

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Q: 1) Find the exact length of the polar curve r = 2+2 cos 0. Show All Your Work!

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Q: The average rate of change of fx) = ax' Over the interval osxs1 IS a

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Q: Find the derivative of the function. 6x3 f(x) = + 8x2 Step 1 The function (x) can be simplified to…

A: The differentiation is given below.

Q: y" – y" – 6y = 0 = () A) Verify that yı = 5, y2 = e-2x and y3 = e* are solutions of the DE. %3D B)…

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Q: (2+In x)' 7.

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Q: Find an equation of the Hyperbola that has Foci (-1,–3) & (-1, 7) with asymptotes y = x+ & y = -a+…

A: Standerd equation of hyperboal is (x-h)2a2-(y-k)2b2=1where (h,k ) be the center

Q: Find the derivative of the function at P, in the direction of A. 0. fxy,2) 3D ху + yz +zx, Pо(3, -…

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Q: Solve for x. Record solution using boxes below. Then answer graph questions. (Given solution in…

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Q: The function 3 y = -e 5 is a particular solution for the nonhomogeneous differential equation y" + y…

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Q: Use the Ratio Test to determine the convergence or divergence of the series. n5 3n n = 1 an+ 'n+ 1…

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Q: 2.34 Let f(x) = cos x – x – sin x. Prove: There exists a solution to the equation f(x) continuous on…

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Q: Use the simple interest formula to determine the missing value. p= $1475, r=?, t 2 years, i= $41.30…

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Q: JA di is concave downward. Find the interval on which the curve x) - 6+ 8t

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Q: The marginal cost of manufacturing æ yards of a certain fabric is C'(x) = 3 – 0.01x + 0.000006x² (in…

A: This is a problem related to changes in cost per yards of production. Based on the general formula…