Find the volume of the solid obtained by rotating about the x-axis the region bounded by the curve y = √√√x - 1 and the x-axis between x = 2 and x = 5.

Q: Using exact Solution, find the general solution of the following differential equation: (cos2y -…

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Q: (1) Let I be a proper ideal of the commutative ring R with identity. Then I is a ........ if and…

A: 1) Let I be a proper ideal of commutative ring R with identity. Then I is a ............. if and…

Q: Let R be the region in the second quadrant that is inside the polar curve r = 2 and outside the…

A: In this question, we want to find the correct representation of area of the region R.

Q: It is given that the radius of the semicircle increases at the rate of 0.5 cms -1 when heated.…

A: Given ,  The radius of the semicircle increases at the rate of 0.5 cm s-1 when heated We have to…

Q: San 4h (x) dx = [ -3 y h 8 2 AN -3 10 4 -1/ -7 -7 7 x

A: From the graph, note that: ∫-30h(x) dx=-1 because area bounded by the curve h(x) is -1 in -3 to 0.

Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

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

A: ∫-11∫016x3-y32dA

Q: Find a differential equation that corresponds to the given direction field. Consider differential…

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Q: an+1 Suppose that an ∞ Σ απ( – 81)" man n=1 →1 as n→ ∞o. Find the radius of convergence.

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Q: 5. Find and classify (local max., min. or saddle point) all critical points for f(x,y) = x³ − y² +…

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Q: Let L(y)=(x-1)y" - xy + y a) with the observation that y, zx is a solution of L(4)=0 on (1,00), by…

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Q: 2. Evaluate the double integral that will find the volume of a solid bounded by 21-2y²-322 and the…

A: Given: z=1-2y^2-3x^2 and xy-plane

Q: Find the volume of the solid that results when the region enclosed by y = √√√x, y = 0, and x = 49 is…

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Q: CSC X csc x - sin x - dx

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Q: X = 2t-2 - y = ln(t³) Which integral gives the arc length of the curve over the interval from t = 2…

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Q: (3) If R is an integral domain has non zero characteristic, then Char(R)=..... (i) 5 (ii) 4 (iii)9

A: This is a problem related to function and number system of the function. Based on the general…

Q: 7) y = exz 8) y = 3 x ²

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Q: Find the solution of the given initial value problem in explicit form. 7x y' = , y(0) = -9 y + x²y…

A: In this question, we will solve the given IVP.

Q: Evaluate: 1+ 2y dy dx •x x2

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Q: xy³ Q3: Let f(x,y)=2x²+y² 1 (x, y) = (0,0) Is f continuous at (0,0) ? Is f continuous at every point…

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Q: a A person's intelligence quotient (IQ) is measured by the function I(m, a) = 100m where a is the…

A: see below the answer and explanation

Q: For the following exercises, use the second derivative test to identify any critical points and…

A: Given :f(x,y)=-x2-5y2+10x-30y-62

Q: 1. Find the Inverse Laplace Transforms of the following. 4) 48-60√s s4

A: A detailed solution is given below.

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

A: We know the following. Fourier series of function fx on interval -L≤ x≤ L is defined as:…

Q: Consider the parametric curve: X y = ln(-t) Which integral gives the arc length of the curve over…

A: We have to find the length of curve.

Q: Using exact Solution, find the general solution of the following differential equation: (cos2y -…

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Q: t√√t + ,2 + t dx

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Q: dy Write down a differential equation of the form dt 13 solutions all approach y = as t→∞. 14 y' = =…

A: The general form of the differential equation is  dydt=ay+b

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

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Q: Identify the surfaces of the following equations by converting them into equations in the Cartesian…

A: Above question is solved.

Q: 1. 3 If the total cost function is given by TC = 300 +5q+ what is the marginal cost when q = 3? q² 1…

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Q: 1. Identify the surfaces of the following equations by converting them into equations in the…

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Q: [x²√1-x² dx

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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: 3 .4 ²³₁₂₁ (4x²y — z³) dz dy dx

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Q: Q1llenn Prove the following using the principle of mathematical induction. For n ≥ 1, 1 1 1 1 3/2 +…

A: Given; 1/52+1/54+...+1/52n=(1-1/25n)1/24.

Q: Q3: A) Find the limits below x² + sin²y 1) lim (x,y) (0,0) 2x² + y² 2) lim (x, y)-(1,1) x² - 2xy +…

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Q: - 2.f(x,y) = y²x¹ey.

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: For each of the following ,find fx fy fxx fyy fyx and fry 1.f(x, y) = x cos+ ye*. 2.f(x,y) = y²x¹e³.…

A: We have to find the partial derivatives of the given function.     According to our guidelines we…

Q: 1. Given vector 2 0-3 is 2. It is known that a à vector : ( 2 ) and 3 = (-1) is a vector in 1R³ with…

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Q: -2 Evaluate: ²₁5²[(x²-²²] | du dt x+y

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Q: +∞ (x²+4)3/2 dx

A: To find: Integration

Q: Consider the parametric curve: x = ln(t + 5) y = −6t5 Which integral gives the arc length of the…

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Q: Find the area of the region enclosed by the curves y =

A: answer is in next  step

Q: Determine y = Yc+yp using Non-homogenous equations: Method of Undetermined Coefficients Given: y" +…

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Q: derivative of (√2)^csc4x

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Q: Function h is graphed. h -4 -3 -2 L y 4 3+ 2- 1 -1- -2+ -3- 12 3 4 Find h(2) da. Give an exact…

A: This question can be solved using the concept of area under curve.

Q: Let F(x,y)=ln(x² + y²), then answer the following (4) Find the boundary of the function's domain.…

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Q: B) Solve the equation (x+y-1)³ dx+4(x-2) dy=0.

A: Solution

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

A: To find the integral , ∫π/2π∫0t  sin(4t-u) du dt