Show the complete solutions, kindly include all the necessary drawings, graphs and illustrations. Find the orthogonal trajectories of the family of curves b. Circles through the origin with centers on the x – axis.

Q: . (x + 2y) dx + (2x + y) dy = 0. ANS. x² + 4xy + y² = c.

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Q: If the sequence { 2 9 - An An - 3 converges to 6, then the sequence {an} converges to 9.

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Q: Let r(t) = t²i + t cos(πt)j + sin(ät) k, find ſª r(t) dt.

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Q: Evaluate the following integral using integration by parts. 4x sin 4x sin x cos x dx Let u=4x sin x.…

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Q: Find the exact value of the indicated trigonometric functio 2 =, , tan 8 <0 Find sin 8. cos 0 =

A: answer is in next step. please give a like !

Q: 8. Consider the differential equation e* (y - x) dx + (1 + e*) dy = 0. (a) Show that this is an…

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Q: [sin¹ 3x cos² 3xdx

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Q: A botanist is studying the development of a bamboo plant. She started keeping a log of its growth 25…

A: Total time= 25 weeks Given that the plant has grown an average of 35 inch each week.  So the plant…

Q: Question Find the linear approximation L(x) of the function f(x) = -5x³ - 5x²-3x - 1 at a = -4.…

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Q: Σ η +1=2 In(n), π

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Q: Question Find the change in volume dV if a circular cylinder with radius r = 8 changes height from 7…

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Q: Proof Prove that if A is an orthogonal matrix, then so are AT and A-1.

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Q: 1).  Apply the ratio test to the series. ∞ n! 6n3 n=1 Find the limit    lim  n→∞  an+1 an .…

A: Concept: Ratio Test: (1):  If limn→∞an+1an=L&lt;1 , then ∑n=1∞an is convergent (2): If…

Q: Let C be the boundary of the portion of the plane x+y+z=2 that lies in the first octant, oriented…

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Q: Please help need asap..answer both please and i will rate high

A: We have to choose the correct option from the given options according to the given infinite series

Q: Evaluate 02 3√2 0 1 3√2 0 1 |- √2 1|2 sino 4cos0 LLL rdzdrd0.

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Q: Consider the following function. f(x)=√x-9, x> 9 What is the domain of f? (Enter your answer using…

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Q: Evaluate the interated integral: LS-² x² sin(y) dy dx

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Q: Evaluate the line integral [21r²yzds with respect to s along the 2 curve C : x = t₁ y = t², z =…

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Q: Let Ln denote the left endpoint sum using n subintervals and let Rn denote the corresponding right…

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Q: Given the equation below, find dy dx - y = 63x² + 140x69y 2x70+ 5y⁹ dy dx 5,9 ZY Now, find the…

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Q: 6. Use an integrating factor to solve the following first order differential equation (x² + 1) + xy…

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Q: Set up a triple integral using cylindrical coordinates that finds the volume of the solid bounded…

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Q: Find an equation of the tangent line to the graph of the function at the given point. y = 8x…

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Q: 2 The current domestic demand for steel is P = 150 - 2Q and the current supply is given by P = 30 +…

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Q: 9.   The nth term of the series has a factor  xn.  Find the range of x-values for which the ratio…

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Q: xydx + (x^2+y2)dy = 0 Prove that it is a Homogenous DE using homegeneity test (degree n)and solve…

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Q: Find the definite integral that will compute for the volume of the solid when the region bounded by…

A: To find the definite integral that will compute the volume of the solid. Given information: The…

Q: Q 14) Does the sequence converge or diverge. If it​ converges, find the limit.

A: Concept: Infinite series converges and diverges: Let ∑k=1∞ak be an infinite series, and let an be…

Q: The traffic flow rate (cars per hour) across an intersection is r(t) = 400+600t - 180t2, where t is…

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Q: 1. Let S be the triangular region in R3³ with vertices at (2,0,0), (0,6,0), and (0,0,3) with upward…

A: we know that triangular  region is part of plane since all the vertices  ( 2, 0,0)  , ( 0, 6, 0)…

Q: Question Find dy and evaluate when a (Enter an exact answer.) Provide your answer below: dy = = -5…

A: The given function is; y=(2x4-4)/(5x+1), x=-5, dx=0.4

Q: QUESTION 15 Use a graphing utility to graph the function over the indicated interval and approximate…

A: The answer as follows:

Q: Evaluate O O In 9 3 2 - In 2 In 2 x² 2 O tan¹ (2) tan¹(1) O ln 2 0 1 3 9 dx. x³ + 1 -

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Q: Answer the following questions for the function f(x)=x√√x² +9 defined on the interval -7 ≤ x ≤ 4.…

A: Concept: Concavity: Assume that f(x) is differentiable on interval I. If f′(x) is growing, the f(x)…

Q: For which of the following infinite series does the Ratio Test fail? IM8 IM8 k=0 k 5k そそ n=1 (n +…

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Q: Find the gradient of the function f(x, y) = sin(x + 2y) O cos(x + 2y) [2î+î] cos(x + 2y) [i+1] O…

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Q: n=1 n²2n-1 (-5)n

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Q: Find an equation of the sphere with points P such that the distance from P to A(-2, 5, 2) is twice…

A: Let    P(x,y,z)  be the general point  A( -2, 5, 2)  and  B(6, 3, -3)PA=2PB Recall

Q: Iƒ F(t) =î+tj+t²k and G(t) = tî+e¹+3k, then find (F × G)(t) at t = 0. 0 Ok O î+ ĵ + k o î+î

A: Topic- Cross Product of vectors

Q: at a price of $55

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Q: f(x) = n=1 (7-2x)" 6n

A: The objective of the question is determine the derivative of the given power series.

Q: [In(cosw)tanwdw

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Q: S= 1 dx xinx

A: This is a problem related to integration. Please follow the procedure given below.

Q: 1 3 The x value(s) of the points where the tangent lines to the curve ³-4x that have a slope equal…

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Q: Express the equation in logarithmic form: (a) 45 = 1024 is equivalent to log4 A = B. A = and B = (b)…

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Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 16x2 +…

A: Solution of given question is written in below steps.

Q: 4. x³+2x+2 2 x²-1 dx

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Q: The formula for the volume of a cone is given below. Find the rate of change of the volume for each…

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Q: Find the divergence of the vector field F(x, y, z) = ln(x² + y²)i + xyj+ln(y² + z²)k. 0 21 2z x² +…

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