Find the trigonometric Faurier Series of the function defined by; flx) = x + # if = < X <... -T..

Q: Problem 1: Determine centroid Y-bar with respect to the x-axis. A = 1.6 m B-3.9 m V A A B B

A: We have to find the centroid.

Q: 10z Sketch the region enclosed by y = 5, y = el, and a = 1. Find the area of the region.

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Q: (3. 7/7) as Cartesian coordinates. Express the polar coordinates (3,

A: We have to express (3 , π/2) in Cartesian coordinates.

Q: Find the area of the region in the first quadrant bounded by the curve y = √√x² + 5, the x-axis and…

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Q: Write the equation of a circle with a center at (2, -3) and a radius of 4. ( x - 2) 2 + ( y + 3) 2…

A: To write the equation of a circle with a center at (2, -3) and a radius of 4.

Q: 7. dx ггтV)

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Q: 1-x² 1-x 10 f(x, y, z) dy dz dx

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Q: The ellipse 3 4 8 16 x²y² 1 = + 9 16 4 has a vertical axis of

A: elipse equation is given  x2/9 + y2/16 = 1/4 here compare with  x2/a2 + y2/b2 = 1

Q: Below is the graph of a polynomial function with real coefficients. All local extrema of the…

A: (a)The function is decreasing in the intervals: (-∞, 9),(-6, -3),(1, 5),(8,∞). (b) The function has…

Q: Gas is $5 a gallon. The vehicle gets 20 mpg. Tech makes $30 an hour. He speeds 15 mph over the speed…

A: Gas costs $5/gal  Mileage = 15 miles/gal  Thus, for every 15 miles he will pay $5 if he is not…

Q: √₁ 5. X x² 2 ²+x-6dx

A: Given:        ∫x2x2+x-6dx For the integrand x2x2+x-6, take partial fraction      =∫-95x+3+45x-2+1dx…

Q: Find the center and radius of the circle whose diameter has an endpoint at (3, -4) and the origin. 5…

A: Given that the endpoints of the diameter are 3,-4 and 0,0.

Q: Evaluate the integrals. a. b. [x√1-x² dx X x sin cos 3 -cos-dx

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Q: Limits 8. Find the indicated limit using the graph of f(x) below. , V lim f (x) x-2 =

A: Topic = Limits

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: Solution: L-1 {1/s7}

Q: Solve right triangle ABC. (Round angle measures to the nearest degree and side lengths to the…

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Q: The marginal revenue for a certain company is given by the function R' (x) = 100x-1/2 where R'(x) is…

A: Given.

Q: Consider the following integral. dx Given the substitution u = x4 - 4, find du. du = ])dx dx Rewrite…

A: The given integral is: I=∫x3x4-4dx   ...1   As we know that; ∫1ax+bdx=1alnax+b+C And…

Q: The volume of the solid whose base is region in the xy-plane that is bounded by the parabola y = 12…

A: Concept: To find the limit of x put equate the values of y  The volume of the solid in the x-y plane…

Q: Use the second fundamental theorem of calculus to evaluate the following: x, x 20 10. [* f(x) dx if…

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Q: dr. T About OX -2 2 y=√16-1²

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 14 Find the slope of the function ƒ(x) = -x - 1, by the definition of a limit. Slope =

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Q: Convert the polar equation r² = 2 cos (-20) to a Cartesian equation. (x² + y²)² = 2x²-2y² (x² + y²)²…

A: In this question, we want to convert the polar equation in Cartesian equation.

Q: -10 5. Given the polynomial: 2x³ + 19x² + 32x - 21 A) List all of the possible rational roots: B)…

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Q: Evaluate spherical 4 √16-4² √16-x² - y² sőösi O -√16-x²-y² cylindrical coordinates. or (x² + y² + z…

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Q: The value of arcsin O KIT X 4 KIO O KIM X 3 KIN 2 (9) is

A: here is given that sin-1(1/2) we now that sin-1(sin(π/6))

Q: Exponential and Logarithmic Functions 11. Use the properties of logarithms to fully expand the…

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Q: II. Coefficients Linear in Two Variables 1. (6x-3y+2)dx-(2x-y-1)dy=0 2. (9x-4y+4)dx-(2x-y+1)dy=0

A: We can solve the given differential equation.

Q: The area enclosed between the two curves x² = 2y and y² = 2x is rotated about the x- axis. Determine…

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Q: (-1)kk Determine whether the series converges absolutely, converges conditionally, or diverges Σk=1…

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Q: R is the region bounded by the functions f(x) = functions on the interval [7, 12]. Enter an exact…

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Q: Find the average value of f(x) = 3 sin (x) + 5 cos (x) over the interval 0, [0]. 3

A: The function f(x)=3 sin(x)+5 cos(x) over the interval 0,π3

Q: Find the exact interest on a loan of $7500 at 13% annually made on July 17 and due November 30.…

A: Given that we need to find the interest on a loan for following interest rate and on time.

Q: Z A Consider the tetrahedron ABCD with vertex A at the origin as shown: (a) Find the equation of the…

A: Given that: A=0, 0, 0; B=0, 0, 3; C=0, 4, 0; D=6, 0, 0 We have to find:  a) An equation of a line…

Q: 15. dx 16x* - 1

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Q: Q4: Let y = √r and 1= x² then y) = Oifn= t= a) 2 b) 3 c) 4 d)5 e) others

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Q: Find an equation of the tangent line to the graph of the given function at the specified point. f(x)…

A: topic- equation of tangent line to the function at point

Q: Use linear approximation, i.e. the tangent line, to approximate √81.3 as follows: - Let f(x) √x.…

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Q: 21 The equation x2 + y2 = 5 has _______. a center at (5, 5) and a radius with a length of five…

A: We know that the equation of circle is: (x-h)2+(y-k)2=r2 where, (h,k)- centre of circler-radius of…

Q: Problem 2. Consider the lines 1(t) and r(s) defined below. l(t) = t+ r(s) = 8+ Your buddy Ron…

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Q: A tank contains 400 liters of fresh water. Brine containing 0.3 kg/L of salt runs into the tank at…

A: We need to find concentration.

Q: Express the polar coordinates (2.) as Cartesian coordinates. (√3,1) (-√3,-1) (√3,-1)

A: Topic = Geometry

Q: Q2: The equation of the tangent line to the graph of y=t² and t = 4x² at t = 1 is (not that x is…

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Q: dx (4+x²)² √

A: Explained below

Q: Given: c= 8, a = 5, C = 67°

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Q: estion 24 Copy of To integrate x³ ²dx' e+² x² Ox we apply integration by parts and in the form u dv,…

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Q: Refer to the graph of f(x) on the interval [-2, 4] shown below. Which of the following would give…

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Q: Direction: Fill in the blanks with the next step in solving the solutions of the differential…

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Q: Use polar coordinates to evaluate: a) SSRdA/(x²+y²+1) where R is the region in the upper second…

A: The value of the given region is (π/4)ln(2)

Q: A tire manufacturer estimates that the demand function for their radial tires will be given by P =…

A: