find the Fourier series of half rang periodic function. f(x) = x|x| -π < x < π

Q: 3. The definition of Antiderivative states that A. A function (x) is called an antiderivative of the…

A: 3. The antiderivative of a function f(x) is a function whose derivative is equal to f(x).

Q: Find the volume of the region bounded above by the sphere x² + y² + z² = 2 and below by the parabo-…

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Q: 3 Evaluate: ³₁²₁ ¹²[z³(x + y)³] dz dy dx -4 1

A: Given

Q: 3 Evaluate: ₁ S 1²,₁ S² [(x²-x²)²] dx dy x+y

A: To evaluate the given double integral.∫-14∫03x2-y22x+y dx dy

Q: Q9. If W = f(u)=u³ +sin ¹u+lnu, and u= ax +by, where a, and b are constants, show that aw Əw b oy Əx

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Q: 5x -3 2 Evaluate: f fx fdz dy dx 3x 2

A: As per our guideline we are allowed to answer only one question. Kindly repost the other question as…

Q: Determine the values of r for which the differential equation y" - 4y = 0 has solutions of the form…

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Q: 2 3 Evaluate: y cos(z5) dx dy dz 0

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Q: Does the Rolle's Theorem applies for f(z) – ln(2 – z²) over the interval [−1, 1]? O Cannot be…

A: This is a problem related to derivative of the function. Based on the general formula and concept we…

Q: Find the area of the region bounded by the curves y = 1 (x+6)²¹ y = 4 and the x-axis using vertical…

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Q: Q4/Find the slope of the line 3x-4y=-8 and then find the distance from the point P(3,-2) to this…

A: Given Equation of line3x-4y=-8To find slope &amp; Distance.

Q: S¹₁₁ S1+₂x² x + 2y dy dx ·12x²

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Q: Find the area of the region bounded by the curves 1 (+6)² = 4 and the x-axis using vertical strip

A: using vertical strip we have  Area=∫-∞∞∫1x+624dydx

Q: (x²-y²)²1 Evaluate: ₁²² du du dt x+y

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Q: Find the volume of the solid generated by revolving the region bounded by y = e-x², the x-axis and…

A: Given problem is :

Q: e: √₂² ²₁₂₁ (4x²yz - ²) dz dy dx 4

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Q: Evaluate: ₂1+ 2y dy dx ₁¹

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Q: Q1. The parametric equations of the lines L1, and L2 are given as: L: x=-2+1, y=3+2t, z=-t+4 L₂:…

A: Let's find distance between two lines.

Q: -X y" + 2y² + y = €²² ln x e^

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Q: The value of √x dx 1+ A. x-2√x+2 ln (1+√√x) + C B. x-2√x-2 ln (1 + √√x) + C C. x-2√x+2 ln (1+√√x) -…

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Q: What will be the orientation of the curve of the graph of the function f(x) = 3 on (-3,0)? z² z+3 O…

A: Given the function  f(x) = x2x+3 on -3, 0.

Q: 2 t √3u Evaluate the integral: №³4 524 4²2 ds du dt s²+u²

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Q: Q1 Solve the following differential equations. 1. (x + 1) = x(y² + 1) dy dx

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Q: Suppose ƒ(x) = 2¹². What is the lim ƒ(x)? 700 O A. It is a vertical asymptote of f. OB. It is a…

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Q: Evaluate: xy² dx dy [√ 0

A: We have to find value of given definite double integration.

Q: Use the table of integrals to evaluate the integral. 2 √2²47x²³ √4x²-x+ d² dx

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Q: 4 Verify that the Mean Value Theorem can be applied to the function f(x) = x 5 on the interval [0,…

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Q: A particle is moving along the curve whose position vector is given as R(t) = (t)i + ( În (cost)) j…

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Q: Solve the differential equation. x dy dx = y + x³ + 3x² -2 x

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Q: n+an-1+an-2+...+ hat is the lim ´x→∞ (n − 1)x¹−¹ + (n − 2)xn−2+...+ï' −‚n €Z+?

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Q: Evaluate the integral: S/2 sin(4t - u) du dt

A: The integration of the double integral is Sin(4t-u), u from 0 to t, t from pi/2 to pi.

Q: 6. The value of A. sin ¹¹x + √1 + x² + C B. sin-¹ x - √1 + x² +C C. sin-¹ x + √√1- x² +C D. sin…

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Q: Find the volume of the solid generated by revolving the region bounded by y = e-x², the x-axis, and…

A:

Q: Evaluate the double integral: 2 JI ਸਰੰਜਨ y²) DA R where R is the unbounded region between 0 ≤ 0 ≤ 2π…

A: Let's evaluate double integral by converting into polar coordinates.

Q: | √x dx 1 + √x A. x-2√√x+2ln (1+√x) + C 3. x-2√√x-2 ln (1+√√x) + C C. x-2√√x+2ln (1+√√x) - 3+C D.…

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Q: 5x 2 Evaluate: f fx fdz dy dx 2

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Q: Evaluate the integral. ƒ ƒ6(x³ - y³)²dA = □ (Type an exact answer.) R

A: ∫-11∫016x3-y32dA

Q: Evaluate: ₂(4x²y - z³) dz dy dx

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Q: Let S be the solid obtained by rotating the region shown in the figure below about the y-axis. y 12…

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Q: Consider the parametric curve: x = 5t² y = 2et Which integral gives the arc length of the curve over…

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Q: Show that (x+2)² = ln(x + 2) - x+2 + C.

A: Topic = Integration

Q: Compute the average value of the following function over the region R. π f(x,y) = cos x cos y…

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Q: 3 -1 0 2 2 х -у 2 x+y 2 dx dy

A: Given

Q: The value of | Je A. -sin-¹ (ex) + C C. sin-¹ (e) + C dx 2x B.-sin-1 (e-2x) + C D. sin-¹ (e-2x) + C

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Q: 4 Find the area of the region bounded by x = 2y²+1 and the y-axis using the horizontal strip.

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Q: Evaluate: ₁ [2³(x + y)³] dz dy dx

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Q: Evaluate: xy² dx dy

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Q: Find Fourier sine series of f(x) = 4x on - L≤ x ≤ L

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Q: Find the transition points. y = 3x6 - 27x4 (Use symbolic notation and fractions where needed. Give…

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Q: Determine how the function f behaves at infinity. f(x) = (x³∕2x³) + (2/5x) -2

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