An approximation using four terms of a series for the number x3 cos (22) dx

Q: x = y² – y, x = y – y² |

A: The solution is given in the next step.

Q: he vectoi the given maghitude and the same direction as u. Magnitude Direction ||v|| = 19 u = (0, 2,…

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Q: Q1. Evaluate the integrals below using the integral rules derived in Lectures 13-15. For each…

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Q: E. Determine which equations are exact and not exact. Afterwards, solve for the equations that are…

A: use the definition  of exact or non exact.

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y² + 8, (2, 1) Vf(2, 1) = 4i +…

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Q: True/False: The saddle point of the of the function f(x,y) = x² – e occurs at (0,0). - O True O…

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Q: Solve the given initial-value problems. 4.43. re dr +(y-)dy 0; y(0) 0

A: x ex2 dx + (y5-1) dy =0x ex2 dx =(1-y5) dyvariable separable;∫ x ex2 dx=∫ (1-y5) dyx2=tx dx =dt212∫…

Q: Which of the following is 2 equivalent to tan x + cot x where x = -? 2 sin 0 2 sin 0 2 Option 1…

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan 2, (1, 0,…

A: This question is based on finding equation of tangent plane of function having two variables at a…

Q: Q3.3

A: We have to find the value of the given definite integral according to the given information

Q: Consider the following. u = -9i – 2j - 4k, v = 4j + 4k (a) Find the projection of u onto v. (b) Find…

A: Explanation of the answer is as follows

Q: A cubical container that measures 2 inches on a side is tightly packed with 8 marbles and is filled…

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Q: *** . ***** ******* . Determine whether the lines intersect, and if so, find the point of…

A: To find the point of intersection of given lines.

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

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Q: For what value(s) of z on [0, 7] is the value of f(z) = sin z +1a maximum?

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Q: Q2. Evaluate the integrals below by first using trigonometric identities to simplify the in-…

A: We have to find value of given definite integral.

Q: An open box is to be made from a 16 cm by 30 cm piece of cardboard by cutting out squares of equal…

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Q: Question For the function f(x) given below, evaluate lim f(x) and lim f(x). X00 X-00 -5 + 2e-* f(x)…

A: The objective is to evaluate the limit.

Q: Find the centroid of the solid generated by revolving the region about the indicated axis the area…

A: There is more than 1 question, as per the Q&A guidelines, We are answering the 1st question. If…

Q: dy – (x - y + 1)?dx = 0

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Q: Let the region R be the area enclosed by the function f (x) = e® + 2 and g(x) = 6x + 3. Write an…

A: Given: f(x) = ex +2,    g(x)=6x+3

Q: what is the minimum value of f(x)=3x2-18x+25 a. -2 b. 3 c. 6 d. -18

A: Given  f(x)=3x2-18x+25

Q: Find the general solution for the following equation: y''' + 3y'' – 4y' – 12y = 0

A: Solve the differential equation by assuming eλx for some constant λ.

Q: Solve the following items and show your solutions. c.) Find the general solution and solve for the…

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Q: Direction: Eliminate the following arbitrary constants to obtain the DE. 2. у — С1 3D С2е -4х 2. у —…

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Q: A function f(x) has a critical number x=c. Which of the following statements is always true about…

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Q: Find the Laplace Transform of the following functions s? – o? 1) f(t) =t cos(@t) Ans. F(s)= (s² + w*…

A: According to our guidelines, we can answer only three subparts of a question. Kindly repost the…

Q: uantity of cookies sold when the price per cookie, in cents, is x. Use this information to answer…

A: Since we are given with the multiple number subpart answered according to the guidelines

Q: 4. Find the equation of the tangent to h(x) = x´sin(2x) at x = 1 [no unit circle needed]

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Q: 11 2

A: We can solve this as follows:

Q: Given the hyperbola with the equation y – 9x? = -9, find the vertices, the foci, and the equations…

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Q: Which of the following is NOT a solution to the trigonometric equation 2 cot 0 cos 0 – cot 0 = 0? 2…

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Q: 4) rotation 90° clockwise about the origin YK U

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Q: Solve bernoulli equation (dy)/(dx) - y = x * y ^ 2

A: Given problem:- Solve bernoulli equation (dy)/(dx) - y = xy2

Q: Find the centroid of the region in the first quadrant bounded by the given curves. y = x?, x = y7…

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Q: 1) y= 3cos 4 +2 4 a: b: Period: d: Phase Shift: S C:

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Q: 4. What is the geometric relationship between the two integrals below? et dx, In x dx Evaluate the…

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Q: 2. -7-8X-x²

A: Use substitution method to solve this integration.

Q: sino Given that 0<0 < I 2, what is the exact value of sin(20)? 3 and

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Q: Is it log or ln that should be used?

A: You are right. There was a mistake from our end.  Here is the correct explanation: y=x3x Take ln on…

Q: Consider the following planes. 3x + 2y - z = 42 x - 4y + 2z = 0 (a) Find the angle between the two…

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Q: Find the complex zeros of the following polynomial function. Write f in factored form. f(x) = x° -…

A: Here we have to factorize the given cubic equation.

Q: f(b) – f(a) Find the value(s) of c that satisfy the equation = f'(c) in the conclusion of the mean…

A: We can find the value of c that satisfy the equation  f(b)-f(a)b-a = f'(c) .

Q: Learning Task 4: Given the equation x2 +y² =9. 1. Differentiate using implicit differentiation. 2.…

A: Since, the student has mentioned to solve only part numbers (4) and (5), so we are solving part…

Q: What is the amount of material in a hollow cylinder of height 20 cm, given that the sum of the…

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Q: If a cylinder, a hemisphere and a cone stand on equal bases and have the same heights, what wil be…

A: Cylinder, Hemisphere and Cone have same bases i.e. all three have same radii (say r) Also the height…

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y² + 8, (2, 1) Vf(2, 1) =

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Q: Determine whether the area of the given unbounded region is finite. If the area is finite find it.…

A: The region is bounded by curves y=1x4 , x=1 and y=0 which is to the right of the vertical line x =1.…

Q: What value of x minimizes C = 0.005x2 provided that C must be positive and x is within (0,1)

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Q: (b) dx (1+ x²)² 0,

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