Prove that dx x(1+x²) 5 = lnx - 1²/2² (₁4²2²2) + ( C. +x²

Q: The radius of the sphere is decreasing at a rate of 2in/min. What is the rate of change of its…

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Q: Find the area of the region bounded by the curves y = 1 (x+1)21 2 y = 4 and

A: Please refer to the image below

Q: While buying a new car, David made a d payment of $1,100 and agreed to make end payments of $230 for…

A: Please refer to the image below

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

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Q: lim (sech 2x)csch x x² +0+*

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Q: Perform the following integration. 1. (sinhæ)(coth? a+csch® a) dự sec³ x tan x 2. S dx √2 + sec x 3.…

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Q: Find the equation of the logistic function with a maximum value of 1000, an initial value of 500,…

A: Topic:- function

Q: b. Two passenger airplanes left the same terminal at the same time. One plane flew due north at an…

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Q: I. Evaluate the following limits 2. lim (3 + x)² x → +∞0

A: Given problem :- limx→+∞3x+x1x

Q: VI. Determine the instantaneous rate of change of the function √x sin (³) In 2 = = [X² f(x): dt 1 +…

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Q: 5x4y + y² 2x5 + 3xy' - dy dx O x¹y² + xy³ = 48 O x³y² + y³ = 120 о x²y² - y³ 3 = 56 O x³y² - xy³ =…

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Q: Find the volume of the solid generated by revolving around the y- axis, the region bounded by 1 y =…

A: Solution given below

Q: Evaluate the indefinite integral given below using the indicated substitution. /-20 -2(-2x +9)³ dx u…

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Q: Find the y coordinate of the center of curvature of the parabola at (2,2). O -7 -6

A: In this question we have to find the y coordinate of the center of curvature of the parabola at (2,…

Q: Evaluate the integral: fnste" du ds dt

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Q: 2. Evaluate all of the integrals. 2²-x+4 (x + 1)(x²+2) da

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Q: IV. Solve the following problems completely. 3 1. Use local linear approximation to estimate √√(3.…

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Q: Suppose the ball is dropped at rest from the top of the house 64 ft above the ground and the only…

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Q: (x + tan y) dy = sin 2y dx

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Q: Use Cartesian coordinates to evaluate y²2 dV D where D is the tetrahedron in the first octant…

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Q: Q3. Evaluate : IL (2) * dy dx

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Q: x-1 x² + 5x + 8 S dx

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Q: Evaluate the integral S (2x − 8)dx 2 - 6x + 18 x²

A: Evaluate the integral

Q: lim (sech 2x) csch x² +0x f(x) = csch x

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Q: Please do this typewritten only for upvote. I will not upvote if it is handwritten. Make sure you…

A: Given that,

Q: Find the solution of the given initial value problem in explicit form. 1 y' = (1-7x)y², y(0) = 6…

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Q: 64 Lood (vt. 1 √t + √i) dt

A: Given ∫164(t-1t+t3) dtTo evaluate the Integral:

Q: Find the area bounded by the curve 2x² + 4x + y - 0 and the line y+x=0 a. 1.000 b. 1.125 c. 1.525 d.…

A: First we draw the graph,

Q: y = coux, X = Find the are a OF i) sketch the area. ii) Determine the boundarier by ) Set-up the…

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Q: 5. Evaluate : p.v x² -∞0 (x²+3)² 8 dx

A: Concept: Some important integration formulas: ∫1a2+x2=1atan-1xa+C Where C is constant Reduction…

Q: Evaluate the following integrals 2x ·S- -dx 2 5+2x+x

A: We know that ∫duu = lnu+C ∫1v2+a2dv = 1a·tan-1va+C

Q: ng a trig substitation, the integral (A) / sec(0) do dr can be transformed into one of the

A: Please refer to the image below

Q: 2. lim (x - Inx)* x→0+

A: Given problem:- Evalution limx→0+x-ln(x)x

Q: 1. a2 = 6 and a6 = 96 are terms of a geometric sequence, find a4.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3. Determine whether the following pairs of functions are linearly dependent or linearly…

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Q: The population of a municipality in the country varies according to the function…

A: Topic:- Algebra

Q: 2. Evaluate all of the integrals. a. [² sec²rtan r (1+sec x)² dz

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Q: Determine the values of r for which the given differential equation has solutions of the form y = t'…

A: To find for what  values of r the given term becomes solution of differential equation.

Q: A small high school has 35 seniors, 25 juniors, and 15 sophomores. If 3 students are chosen from…

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Q: The position of the sun at sunset, north or south of due west, depends on the latitude and the day…

A: We need to solve sinusoidal problem.

Q: Consider the function f(x)=2x^2 +(−4)x What is the value of the constant of integration such that…

A: Topic:- application of integration

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: Given that  The Region bounded by the curves  y = 4 + sec(x) , y = 6 ,  -π3≤x≤π3  about y = 4…

Q: 7. Sara wants to show that (ā × b) × ĉ ‡ ả × (ỉ × ĉ). Yasmina says that it is impossible and comes…

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Q: 5. If Evaluate the following. (a) F' (9) (b) F (0), by interpreting F (0) as an area x) = √25-1² dt.…

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Q: Write z, and z₂ in polar form. (Express 8 in radians. Let 0 ≤ 8 < 2m.) Z₁ = 4√3-41, 2₂ = -1 +/ Л 2₁…

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Q: X(jw) = 8.8cos (3w) sin(0.5w)

A: Given function is:X(j,w)=8.8cos(3w)sin(0.5w)we have to find the value of X(3,5).value of…

Q: - Let v and w be vectors such that |v| = 2, ww = 36 and the angle between v and w is T/3. Calculate…

A: This question can be solved using the concept of vectors.

Q: Find the derivative of the function. g'(t) = g(t) = (8t + 8)² (8t² – 8)−3 -

A: We need to find derivative of given function.

Q: 2. Given the graphs of f(x) and g(x) as shown, find: ✓✓✓✓ a) f(g(0)) b) f(g(2)) 67. -20 -2-

A: f(g(0))=? f(g(2))=?

Q: S 36x2+25 - dx

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