Evaluate the integral below by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents, and find the area using geometry. 1². /5² x² dx

Q: Solve the given initial value problem. O x¹y² - xy³ = = 84 x³y² - y² = 26 x¹y² + xy³ = 78 x³y² + xy³…

A: Let's find.

Q: dy II. Find Do not simplify your answers. dx 1. log; (√2x² + y) + tan(2* — 7³) = sin¯¹ (2²-1) + - Б

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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…

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Q: 8 An acceleration function is expressed as a (s, v) = s²-. ' (v+1)³ determine displacement by…

A: a(s, v)=s2-8(v+1)3v(s)=∫0s a(s, v) dv      =∫0s s2-8(v+1)3 dv     =s2v0s -8 (v+1)-3+1-3+10s     =s2s…

Q: Find the volume generated by revolving the given bounded plane area about the line. Use shell…

A: Volume

Q: Definite Integral and Plane Areas of integration (snow solution) 3 1. dx Sö = 2 1+x 4 dx 2. Sh 25-x2…

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Q: Identify the surface in the xyz coordinate system given by the equation: z=-√(4-y^2) O cylinder O…

A: Let's find.

Q: 7. lim y→∞ y² – е6 y 4y² + e7y

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Q: π/4 x³ dx (x²+4)5/2 (Use trigonometric substitution)

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Q: II. Find Do not simplify your answers. 1. log, (2x² + y) + tan(x − ³) = sin−¹(x² − 1) +

A: Given problem:-

Q: f/² sin (1) 4x ; (**) sin (²) COS (²) dx (Consider initially the first 2 terms)

A: ∫vn dv =vn+1n+1+C

Q: limx→1 (x − 1) tan(x³ − x) - (x+1) sin²(2x - 2)

A: limx→1(x-1)tan(x3-x)(x+1) sin2(2x-2)=limx→1tan(x3-x)(x+1)×(x-1)sin2(2x-2)using propertylimx→af(x).…

Q: Consider the parabola given by the equation: Find the following for this parabola: A) The vertex is…

A: The given equation,    fx=-9x2-18x-7

Q: π/4 x² dx (x²+4)5/2 0 (Use trigonometric substitution)

A: Given integral I=∫0π4  x3(x2+4)52 dx

Q: Evaluate the definite integral. NOTE: Enter the exact answer. S||ti + t²i||dt =

A: The given integral is converted to another form by using the following formula and then evaluate the…

Q: Given: (1+2x) ex dx. Using integration by parts and letting u = -1-2x, dv = f(x)dx, then the value…

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Q: 13-30 Evaluate the integrals using Part 1 of the Fundamental Theorem of Calculus. 4. L_ Ax 4x(1-x²)…

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Q: x+1 1-x In [cosh (x+1) + sinh (x+1) lim 2tanh x=1- lim_ In x=1+ l

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Q: dy/dx of sec^2 (x^pi - pi^y)

A: To find the derivative of given function.

Q: Describe the long run behavior of f(t) = As too, f(t) → ? v As t→→∞o, f(t)→→ ? - 4tº + 2t6-3t5+1

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Q: if it was a bez Prove that لما لها حاطها

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Q: 33. (a) L²₁ let - 11 dx r3

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: d d Calculate[r₁(t) r₂(t)] and [r₁(t) × r2(t)] first by differentiating dt the product directly and…

A: This question can be solved using the concept of dot and cross product of two vectors and…

Q: Find exactly T(1) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct…

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Q: B f(x)da as positive, negative or zero? Note two vertical lines indicate a Is Area = and B. Select a…

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Q: 12. -s-7 (s+1)(S-2)

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Q: d Calculate dt [ri(t) · r₂(t)] and [ri(t) × r₂(t)] first by differentiating . dt the product…

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Q: Use the function to find the image of v and the preimage of w. T(V₁² V₂) = (V₁ + V₂₁ V₁ V₂), V =…

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Q: Question 4 15x²x³43x - 19 The integral (x + 1)²(x² - 6x +13) Ax + B What is the value of ax²+bx+c²…

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Q: Use the formula k(t) k(t) = = ||r'(t) × r"(t)|| ||r' (t)||³ = 10t: r(t) = e¹⁰ti + e-tj to find k(t).

A: This question is related to vectors, we will solve it using given information.

Q: Write an equation for the quadratic graphed below: x-intercepts: (-1,0) and (4,0); y-intercept:…

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Q: Given: (1+2x) ex dx. Using integration by parts and letting u = − 1 − 2x, dv = f(x)dx, then the…

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Q: Give the properties for the equation x 2 +y 2 + 4x + 6y - 12 = 0 Domain -3 ≤ x ≤ 8 -5 ≤ x ≤ 5 -7 ≤…

A: We can find the domain of the equation as below.

Q: Calculate[ri(t) r₂(t)] and [r₁(t) × r2(t)] first by differentiating the product directly and then by…

A: This question can be solved using the concept of dot product and cross product of two vectors and…

Q: - 19 f(x+1)-(x2 - 6x +13) Ax + B √x²+bx+c² dx? (3)-In/x² - 6x + 13| + C The integral What is the…

A: Using partial fraction…

Q: 16. lim x¹/ x→0+

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Q: (measured counter- 1. A circle with radius 2 is centered at the origin (0,0). For an angle clockwise…

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Q: Solve the differential equation: * (D² - 3D + 2)y= 2e-x + 8

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Q: Q2) Which of the following series is converge or diverge Σ{"} ,0.7777777777777 n=1 . Σ n=1 27

A: a)=∑n=1∞ n-1n2=∑n=1∞ 1n-1n2{using p-series test:∑n=1∞ 1np converges only when p>1diverges for…

Q: π/4 x³ dx (x²+4)5/2 (Use trigonometric substitution)

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Q: 8 Given: (В © √³x³sin(2x)dx= F4 5T 6 21 Зд TL 277²-24 64 T Find bif sb st

A: Solution is given below:

Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. (x - 1+1/2/3 1. lim x-1 2x²…

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Q: Find the volume of the solid obtained by rotating about the y-axis the region bounded by y=2x^2-x^3…

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Q: Two copies of the same Rational Function are shown below. On the graph below draw the Horizontal…

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Q: Given: (1+2x) ex dx. Using integration by parts and letting u = -1-2x, dv = f(x)dx, then the value…

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Q: f(x,y) = 3x-2y R: the circle x² + y²

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Q: Determine whether the equation is exact. If it is exact, find the solution. If the differential…

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Q: Find the curvature K of the curve, where s is the arc length parameter. M(²) = (₁ + √2/2 =) ₁ - (₁ -…

A: we have to find curvature.

Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 1+ 3 1. lim x12x² + x1

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 1. lim 1+1/3 x-12x²+x-1

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