If north is the direction of the positive y-axis and east is the direction of the positive x-axis, give the unit vector u pointing northwest. NOTE: Enter your answer in the form ai + bj. Enter the exact answer, or round to three decimal places. u = ?i + ? j

Q: Find the Fourier series for the following functions: f(t) = |sin t], -1 < t < n and The function is…

A: Solution is given below:

Q: 8 1 4-x² 4 x¹ +4.x² dx

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Q: Which equation represents a valid first step to solving the following system of equations using the…

A: Given,           2x-2y=5 and -4x+5y=11To find : Solve using elimination method.

Q: tan Find the integration of 1₁ 1+z²

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Q: III. Consider the power series +∞ n(3x + 2)n n³ +4 n=1 -1. 1. Show that the series is absolutely…

A: Given power series is ∑n=1∞n(3x+2)nn3+4 When x=1, the series becomes…

Q: Evaluate

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Q: Find the derivative of the given function. g(x) = sec¹(2πx) a) g'(x) = 87 sec³ (2πx) tan(2x) Ob)…

A: I am attaching image so that you understand each and every step.

Q: dr 4+x² S Choices: tan ¹(x + 2) + C 1 In x² + 4 +C In x + 2+ C 1 tan 2 1 ¹ 1/2 + +C

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Q: Find the volume of a solid obtained by rotating the region under the graph of the function x = √y…

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Q: Use logarithmic differentiation to determine I√I+1 (x+2)(x³+1) Y L2 7 2√2 O_7√2 72 3 at x = 1 for…

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Q: Find the average value fave of f(x) = x³ between -1 and 1, then find a number c in [-1,1] where f(c)…

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Q: By using Green's Theorem, calculate the integral [x²y dx-xy² dy in polar coordinates, where is the…

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Q: Question 12 Find the sum of 6 O 10 05 n=1 O 12 53-2 +1 The series diverges.

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Q: The area of the surface formed by revolving the curve x = 2√1-y in the interval 0 ≤ y ≤ 1 about the…

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Q: 3. Find the domain of f(x) = = 1 1 X X 3.3

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Q: Find the absolute maximum and the absolute minimum for the function f(x)=e−x−e−5x,…

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Q: Find the y-intercept of a quadratic function containing the following points: (2,5), (1,0), and (−2,…

A: First we need to find the equation of the quadratic function.

Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

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Q: 8 №₁ 4-x² x+4.x² dx

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Q: CALCULATE THE AREA BETWEEN THE GIVEN FUNCTIONS. DEVELOP THE PROBLEM WITH ALL STEP EXPLAINED AND…

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Q: Date 3. Determine if the equation is homogeneous in what degree then solve for the general /…

A: Solution

Q: 4. Determine the maximum point of the the graph of y = 1 — 2 sin(π – 2x), for x = € [−π, π). 3.

A: Let's find maximum points of trigonometric function.

Q: Consider the function f(x) = (4-5x)7. Find the second derivative f" (1). O7(4 – 5z)® O-35 (4-5x)6…

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Q: IV. Fill in the blank to make each statement true. Use correct notations. 12π ¹ (sin ¹2) = 5 1. sin¹…

A: We can find the answer in the following steps.

Q: Question 17 > At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 21…

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Q: 3. S 4 dx x3-4x²+8x

A: The given integral is; 4/(x3-4x2+8x).

Q: The decay rate for a radioactive isotope is 1.6% per year. Find the half-life

A: Given that the decay rate for a radioactive isotope is 1.6% per year.Our Aim is to find the…

Q: If [ 2013 |檳 sin ada = −a³ cos x + 3x² sin x + k fæ sin ædæ, find k d. 3/2 a. 6 b. -3/2 C. -6

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Q: Prove that lim 12 √16x +9y¹2 2 6 4x² +3y does not exist by showing that the limits along different…

A: We have to prove that  limx, y→0, 0 16x4+9y124x2+3y6 does not exist.

Q: Solve p = So (S2₁ Aedx) e dy Evaluate p assuming A closest to your answer: = 2.0 and 8 = 3.0, and…

A: Answer must be option 3.

Q: On Integration of Rational Fractions. Distinct linear factors Repeated linear factors 1² +2 x² +2…

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Q: Question 21 Consider the region in the third quadrant between the circles a² + y² = 4 and a² + y²…

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Q: Find the sum 3n

A: Given: ∑n=1∞n2+n3n

Q: What is the instantaneous rate of change of y=y=−2x^2+2x at x=0 ?

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Q: 2. S (x+1)dx x²(x-1)

A: We can find the answer in the following steps.

Q: Given that answer = [*f(x) dx = 45 13 > [². what is f(v)dv?

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Q: Find the volume of the solid with the given base and cross sections. The base is the circle x² + y²…

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Q: Calculate the derivative using Part 2 of the Fundamental Theorem of Calculus. d dx re¹2x d dx x4…

A: This question can be solved using the concept of fundamental theorem of calculus part 2 according to…

Q: B Consider the function f(x) = -4x²+7x+6. Interpret the meaning of f'(-7)= 63. O The average rate of…

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Q: dy+y=x²y² X-

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Q: 3. S (5x-12)dx x3-6x²+8x

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Q: The legs of a right triangle have lengths 3 cm and 4 cm, respectively. A rectangle is inscribed in…

A: This question can be solved using the concept of maxima and minima.

Q: (7) Find sin(5x) cos(4x) dx

A: Topic:- application of integration     Note:- as per our guideline if more than one question…

Q: ftan³ (r) sec5(x) dx (power of tan and sec are both odd, and power of tan is greater than 1. In this…

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: I. Find the solution set of the following. 4. cos ¹(2x) + sin¯¹ √√1 − 4x² = π

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Q: Suppose that the manufacturing cost of a particular item is approximated by M(x, y) = 6x³ x³y² +…

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Q: 19. Which of the integrals below represents the set-up of ff xy dS, where S is th vertices (1, 0,…

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Q: Provide the complete solution (typewritten if possible) for the item below. Consider the plane π…

A: The equation of the plane π is given as , x-2y+3z-1=0 and the line l is x=1-y2=z+1 Find the…

Q: Find for the following: dz y = ln O 2x+3 I O I 2x+3 3 21(2x+3) O In(+3) 2x+3

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Q: 1.0⁰ 7 -2 dy 1+ y² 1 +x³ = π 2x + 3 da is an improper integral 1 - 1 (₂ ² ² ₁ + 2x + 1) dz dx + 1…

A: Given problem:- Which of following  is True? a)  ∫0∞dy1+y2=π b) ∫-2711+x3dx is an improper integral…