Find the orthogonal trajectories of the family of curves c. y²=4Cx

Q: Use the given function and the given interval to complete parts a and b. f(x) = 2x³ - 36x² + 192x on…

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Q: Find the number(s) b such that the average value of on the interval [0, b] is equal to 6. f(x) = 6x²…

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Q: Use Newton's method to approximate a root of the equation 5x7 + 4x + 4 = 0 as follows. Let x1 = 1 be…

A: We have to find out as approximation

Q: Using Trigonometric Substitution a substitution of x = 6 sin(theta) was used to solve an integral.…

A: trignometric substitution

Q: You deposited $50 into a bank that offers 2.5% interest for 30 years. A: What is simple interest…

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Q: If the coordinates of the endpoints of a diameter of the circle are​ known, the equation of a circle…

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Q: The decay equation for a radioactive substance is known to be y = y₀e⁽⁻.⁰⁵⁴⁺), t in days. About how…

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Q: (-9) Σ 5 0 = 1

A: The answer is given below:   Ration Test

Q: Find the limit. lim X→1 lim X→1 √√x² +15-4 2 X-1 2 x + 15 -4 X-1 || = (Type an integer or a…

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Q: Use an iterated integral to find the area of the region bounded by the graphs of y = 6x ² and y = ²…

A: Topic = Area

Q: Determine whether the vector field F(x, y) = 5y² (yi+2xj) is conservative. F is not conservative F…

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Q: (y² - 2xy + 6x) dx − (x² − 2xy + 2) dy = 0. ANS. xy²x²y + 3x² - 2y = c.

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Q: Evaluate the following integral. 12 S 0 4 log 13 (x + X + 1 1) -dx

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Q: Express -2√3 - 2i in the form ree with 0 ≤ 0 < 2π. O 4ei O 4e¹ 4ei 5m 4e 6 11 m 4e 6 2

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Q: 5. Solve the differential equation dy 4t dt y² + t²y² = subject to the initial condition y(0)=2.

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Q: What is the coefficient of the term containing x^2y in the expansion of (4x+y)^3?

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Q: Jxy co R xy cos y dA R: -1≤x≤ 1,0 ≤ y ≤

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Q: Question Find the linear approximation L(x) of the function f(x) = cos(x) at a = - 품. (Enter an…

A: We can find the linear approximation as below.

Q: Let f(x) = 14x + 6 - 17e. Then the equation of the tangent line to the graph of f(x) at the point…

A: The given function is fx=14x+6-17ex we have to find the equation of the tangent line at the point…

Q: 1. Find the maximum value of f(x, y, z) = x + y − z subject to the constraint x² + y² + z² = 6.

A: f(x,y,z)=x+y-z   x2+y2+z2=6 Rewrite it as: x2+y2+z2-6=0 L(x,y,z,λ)=(x+y−z)+λ(x2+y2+z2−6) Find all…

Q: Question Find the average value of f(x) over the interval [0, 2]. Submit an exact answer using…

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Q: Evaluate 09 9121IN N OC 2 01 2 1 2 I -1²-2 dydx.

A: Given query is to find the value of the integral.

Q: Find the derivative. [미 In dx x +3 x-3

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Q: Differentiate y = (2x³ + 3x² - 1)5 30x(x + 1)(2x³ + 3x² - 1) O 5(6x² + 6x)+ 30x(x+1)(2x³ + 3x² - 1)4…

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Q: Find the Taylor series generated by f at x=a. f(x) = 5x , a = 7

A: We have to find Taylor series of f(x) =5x about x=7. Let us see first what is Taylor series…

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: To find : the domain in terms of i,j and k

Q: 4. consider F(x, y) = (y² − 2xy) i + (2xy − x²) j. (a) Show that F is a conservative vector field in…

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Q: Evaluate the integral using the following values. [₁x³ dx x³ dx = 960, ["x dx = 24, "dx = 4 [² (2x -…

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Q: 4. x³+2x+2 2 x²-1 dx

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Q: Problem 1 Solve the first order ODE with an initial condition y(1) = 2. Here yy(t) is the unknown…

A: Given first order ODE is y'+1ty=ty2 and its initial condition as y(1)=2 We need to find solution for…

Q: Find the exact sum of the following series (0.25)" (0.25)³ Σ(-1)n-1 n 3 n=3 (0.25)4 4 + (0.25)5 _…..…

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Q: 1 The volume of a right circular cone of radius a and height y is given by V = ²y. 3 when x = 6 and…

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Q: The function f(x)=√x² + 7x has an oblique asymptote y = mx + b at +∞. Find the values of m and b.…

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Q: Find the Cartesian equation for the curve represented by the polar equation, r = 2 sin 0. O x² + y²…

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Q: Question Use substitution to evaluate the definite integral given below. [V²5 (Enter an exact…

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Q: A rock thrown vertically upward from the surface of the moon at a velocity of 40 m/sec reaches a…

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Q: sinx cosx 4 + sin¹ x X dx

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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: Can you write out the solution in a better format please

A: Integral of (cot(x)csc(x) = - csc(x)   Csc(π/2) = 1 Csc(π/3) =2/√3

Q: -2 1. Ella thinks that if a function is positive over an interval, then its derivative is also…

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Q: Given the following differential equation: y' − 2y = (e^3x)/((e^x) + 1) and the following boundary…

A: Given the following differential equation: y' − 2y = (e^3x)/((e^x) + 1)

Q: A constant vector field F(x, y, z) = ai + bj + ck is a gradient vector field. True O False

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Q: 5. Use the definition of a Maclaurin Series to express f(2) = as a Power Series. Give the 8th degree…

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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 general solution of the given differential equation, and use it to determine how solutions…

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Q: The triangle with side length a=6 cm and angles measures angle B= 45° and angle C= 120° is given.…

A: Given data:- Side length of the triangle, a=6 cm ∠B=45°∠C=120°

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

A: Radius of convergence of the Power Series : Consider the power series                ∑n=1∞ an(x-a)n…

Q: 5. Solve the given differential equation. (Recommend using Variations of Parameters) y"+3y'+2y =…

A: Given that, the differential equation is y"+3y'+2y=sinex. Obtain the complementary solution.…

Q: 2. Find from first principle the derivative with respect to x of the function f(x)= Inx.

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Q: The marginal cost for printing a paperback book at a small publishing company is c(p) = $0.016 per…

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