3 5) S² x ² + 1 dx X+1

Q: dx x²+2x+5

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Q: Solve the differential equation y' =a'y subject to the condition that y = e when x = 0. Preview

A: Y(x)=?

Q: Find the area of the shaded region. r = √cos 20 r = 5 cos 0 NOTE: Enter the exact answer. A

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Q: 3. In evaluating the integral S x² dx (x-1)²(x²+1) you will decompose x² dx (x-1)²(x²+1) into…

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Q: Find the average value ha of the function h on the given interval. ave h(u) = (14 - 13u)-¹, [−1, 1]…

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Q: Evaluate the integral [₁ F. dr. F(x, y) = (x² + y) i+(6x - cos y) j where Cis the boundary of the…

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Q: Solve the differential equation y' = x¹y subject to the condition that y = e¹ when x = 0. e4 y(x):…

A: The detailed solution is given below Thank you

Q: - restaurant depends on the number of its regular cus

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Q: The weekly sales of Honolulu Red Oranges is given by q = 980-10p. Calculate the price elasticity of…

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Q: The average cost function for the weekly manufacture of retro portable CD players is given by C(x)…

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Q: log(is²t) + 1 log; 10 + logn C logn, 10

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Q: Evaluate the line integral [39a²³yzds with respect to s along the 2 curve C: x = t, y t, y = t²,₁…

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Q: The edge of a cube was found to be 20 cm with a possible error in measurement of 0.2 cm. Use…

A: Differential

Q: Find T(t) and N(t) at the given point. r(t) = (t² − 3)i+tj; t=3 T(3): N(3) = =

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Q: The Bernoulli's form of the differential equation x³ydx +(3x² − y³ )dy = 0 is

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Q: The Bernoulli's form of the differential equation x²dy+ (2xy-y³dx=0 is The Bernoulli's form of the…

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Q: s dx x+√2x+1

A: Let  2x+1=u ⇒dudx=12x+1 ⇒dx=2x+1du also x=u2-12  ∫dxx+2x+1=2∫uu2+2u-1du…

Q: Verify Green's Theorem by evaluating both integrals [1²0x + x² +1 = [] (2012 - 31²) A dy (ON-OM) dA…

A: Greens theorm is varified.

Q: Find the curvature and the radius of curvature at the point t = 0. x = et cos(t), y = et sin(t), z =…

A: r(t)=etcost i + et sint j + 11et kr'(t)=(etcost-etsint) i+(etsint+etcost) j                + 11et…

Q: 1.) lim √5-x 2.) lim √5-x 1-5 3.) lim√√5-x

A: We have to find the limit.

Q: Find the centroid of the region by inspection and confirm your answer by integrating. (12,12) x = y…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: We have to find the value

Q: Determine the volume of the solid obtained by rotating the region bounded by x=(y-2)^2, the x-axis…

A: Solution is given below:

Q: d³y d²y dy+y=0 dx3 dx² dx

A: d3ydx3-d2ydx2-dydx+y=0                (1)LetD=ddxTherefore   equation (1)…

Q: Let m(x) be the slope of the tangent line to the curve y=x² x³ 2x² + x at the point (x, y). Find the…

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Q: Obtain the Lagrange interpolating polynomial for a certain function f of which we know that: f (-1)…

A: Lagrange interpolating polynomial: The Lagrange interpolating polynomial is a degree polynomial that…

Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: ∫12v (7+6v2)9 dv Evaluate indefinite anti-differentiation

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Q: Evaluate [12x. (2x - y) dx + (x + 3y) dy. C: arc on y = x/2 from (0, 0) to (4, 32)

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Q: M8 Σ n=1 3 n2 + n

A: Given problem:- Determine whether each of the following series converges.

Q: second derivative of y with respect to x from the parametric equations given 4) x=√1-t₁y = t³ - 3t…

A: We can find the required 2nd derivatives as below

Q: f[in (w) ² ] ^ 4 3 dw

A: ∫lnω24ωdω=∫2lnω4ωdω=∫16ln4ωωdω=16∫ln4ωωdω Substitute u=lnω⇒dudω=1ω⇒dω=ωdu; 16∫ln4ωωdω=16∫u4du…

Q: Solve the differential equation y Pemer 6a y5 subject to the condition that y 3 when = 3.

A: Here we have to solve the given differential equation

Q: 4.) Consider the function defined as Find the following limits. a.) lim f(x) b.) lim f(x) c.) lim…

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Q: "alse 1. The absolute extrema for a function f(x) will occur wherever f'(x) = 0 2. The rectangle…

A: Topic:- function

Q: Find the area of the triangle below. Carry your intermediate computations to at least four decimal…

A: Using herons formula

Q: An oil slick on a lake is surrounded by a floating circular containment boom. As the boom is pulled…

A: Given: drdt= 5 m/min To find: dAdt when diameter = 140m Area of a circle with radius r is defined as…

Q: An airplane leaves City A and flies 144 km due north to City B. It then turns through an angle of…

A: The solution is given in the next step.

Q: = fx x²zdx- dx − yx² dy + 3 dz along the curve C shown in the figure. - Z 2 2 [x²zdx - yx² dy + 3 dz…

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Q: Consider the solid obtained by rotating the region bounded by the given curves about the y-ax 2² y=…

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Q: 1. x²y + 2xy-5y³ =0

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. 12 ti + t²idt = 0

A: To evaluate: ∫012t i+t2jdt

Q: T: P2 P₂ defined by T(a + bx + cx2) = a + b(x + 8) + b(x + 8)² Find the following images of the…

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Q: ∫ sinx √cosx dx

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Q: Prove the following statement: 2² +23+24+... 2+1 = 2" +2-4

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Q: Show complete solution. Let S be the surface with equation y = (4x2/9) + z2 a. Write the equation…

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Q: Activity 2 Find the first derivative of the following: 1. y = ln (12x) 2. y = sin-¹ (x² + 3) 3. y…

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Q: Use the formula k(t) 286 +⁹ k(t) = (4 + 169 +¹2) ² = ¸ ||r'(t) × r"(t)|| ||r' (t)||³ = r(t) =…

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Q: Find Vf if f = 2 2 2 x² + y² + z² V.

A: Given,            f=1x2+y2+z2To find : ∇f

Q: 6. Use Green's Theorem to find the counterclockwise circulation and the outward flux for the field F…

A: This is a problem related to vector calculus. based on the general formula of green's theorem we…