1. Using properties of definite integrals, given f(x)dx = 10 and | g (x)dx = – 2, evaluate 2 6. a) [-f(x) + g(x)]dx b) [f(x) + 2]dx

Q: Consider the following. u = (4, 7, -7), v = (-9, 3, -4) (a) Find the projection of u onto v. (b)…

A: Projection of u onto v is given by projvu=v·uv2vAnd the vector component of u orthogonal to v is…

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Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

A: The given function is;  f(x,y,z)=xyz x2+y2+z2=243.

Q: 5g is moving horizontally with speed v o. Question 1: A bullet of mass m= hits a block of mass 100m…

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Q: Evaluate the iterated integral. T/2 x sin(y) dy dx

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Q: (10re", 2.r3 + 3.r² – 12.r, r>0 I<0 Given: ƒ(x) (a) Identify all critical numbers of f. (b)…

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Q: To evaluate sin e de , factor sin³e as (sin²e) ² sin® and let sin²0 =-(1- cos20). A True B False

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Q: rental bus fee of Php. 2000 .00 per day plus Php. 10.00 per mile traveled. How much does the rental…

A: Detailed explanation is attached.

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Q: 1. The lincar differential equation has the integrating factor equal to (Note: Simplify or solve the…

A: Given : dydx=1-xxy=-2x   To Find : Integrating Factor

Q: Find the area of the shaded region Blank 1 Note: Enter exact answer ... x = Y 20 1000 y? 20 Blank 1…

A: Find your answer below

Q: A ship leaves Port A and travels 67 miles due west to point C. It then adjusts its course 41°…

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Q: х-у If z=x²sinh then дхду 4-

A: Find partial derivatives.

Q: Find T(t) and N(t) at the given point. x = e' cos t, y = e' sin t, z = e'; t = 0 1 1 1 T(0) = V3'…

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Q: Determine if the following statement is true or false. The points P(1, 0, 1), P2(3, - 4, - 3), P3(4,…

A: Use the distance formula to determine whether given lines laying on a same line or not.

Q: Find the directional derivative of f(x, y, 2) 2y at P(5, 1, –4) a + z in the direction from P to…

A: Given: fx,y,z=2yx+z, P5,1,-4, Q2,3,-1   The expression for the directional derivative of the…

Q: Evaluate the double integral using polar coordinates. R is the region in the first quadrant bounded…

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Q: There is a 4 km long straight beach. At one end, there is a boat anchored at A, 3 km off the beach.…

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Q: iven that y = sin? (t) and x = cos ( 4t?), hence find dx dy a. 8t sin (8t) sin 2t 8t sin ( 8t2 ) b.…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 3 b. Compute the integral S 6x 2 dx using a limit of Riemann sums. Use right endpoints as evaluation…

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Q: If z=x²sinh then дхду O A. (-x³– 3x²y+2xy² – 32x) / 16+x²- 2xy + y² (16+x²-2xy + y²) ² O B. (x³–…

A: Given  z = x2 sinh-1x-y4 We have to find  ∂2z∂x∂y.

Q: Write an equation of the form y=a sin bx or y=a cos bx to describe the graph below. NAA 4- 3 37 2 4…

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Q: Integrating factors found by inspection.: y(x² – y² +1}dx– x(x² – y² – 1\dy = 0

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Q: Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x - y + z = 2…

A: This question can be solved using the concept of planes in three dimensional geometry.

Q: Given f (x,y) =4e** In y with x = In(u cos t) and y = u sin t. The correct value of dz evaluated at…

A: Given fx, y=4e3x ln y, with x=lnu cos t, and y=u sin t.To determine the correct value of ∂z∂u…

Q: Consider and remember that A = (0,4,2) , B = (6,-1,0), C = (3,0,1> %3D %3D 1 1) Determine the unit…

A: Here, the given vectors are: A=0,4,2, B=6,-1,0  C=3,0,1

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

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Q: A. Bisection method 1. Consider finding the root of f(x) =x - 3. Let ɛstep = 0.01, ɛabs = 0.01 and…

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Q: A (R - 5) Given the power series E (n - 3) A, xla - 5) n = 2 Use the technique that we covered in…

A: Here, the given series is: ∑n=2∞(n-3)Anxn-5...(1)

Q: 1. Linear equation of order one: dy-x -2xy zx = 0

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Q: sin (20) do 2 1+ sin? (0)

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Q: S(sec; - sin) do

A: We know that integration power rule is  Integration of (xn) = xn+1/n+1.   Here i attached the…

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Q: ƏM aN 6. In the differential equation (y² –x² - 4x-1dy+2y(x+y+2)dx = 0, what is

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Q: 1) Sketch the curve. a) r=-2 sin O r = -2 sin O Show All Work

A: Explanation of the answer is as follows

Q: 3. Evaluate the following series: 1 а. с. 4n n=1 11 1+ 2" b. d. 3n n=0 n=1

A: To find the sum of the given infinite series.

Q: A frameless painting with a size of 2 meters by 2 meters hangs on the side of a wall where its…

A: Solution of the problem as follows

Q: Consider the vectors: å = ỉ– 3j + 2k , b' = 4j – 2k and ở = i + k in 3D A. Write 3a – 4 b - 2¢ in a…

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Q: x²– y² Consider the function f (x,y) = Which ONE of the following statements x²+ y² is TRUE? f (x,y)…

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Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

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Q: L Sketch the plane curve by plotting points. Indicate the orientation of the curve. (Hint: Create a…

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Q: Evaluate the double integral where D is the region bounded бy у %3Dх, у%3D2х, х%3D1, х%3D2- 4ху dA

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Q: A floodlight is positioned on the ground shining on a white wall 10 m away. A woman 1.6 m tall…

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Q: Find the general solution of the given differential equation. y dx - 5(x + y') dy = 0 x(y)

A: This is a problem related to differential equation. Based on the general formula we will answer the…

Q: Find two unit vectors in 2-space that make an angle of 45° with 8i + 5j NOTE: Enter the exact…

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