Question 5 Test the series below for convergence using the Root Test. 5)₁ ∞ n=1 f(n): 3n 6n + 5 The limit of the root test simplifies to lim f(n)| where n→∞ = < The limit is: (enter oo for infinity if needed) Based on this, the series O Converges O Diverges

Q: f(a+h)-f(a) h a. Use the definition mtan = lim h→0 b. Determine an equation of the tangent line at…

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Q: A polynomial function g(x) has a negative leading coefficient. Certain values of g(x) are given in…

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Q: 62. y + y = 22 +10x X

A: To find out the general solution of the differential equation.

Q: Suppose r' (t) = (cos(t), et, 2t) and r(0) = (1, 0, 3). Find r(t).

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Q: (C): Solve the following equations:- (1) sin 2x + 2 sin² = 1

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Q: Evaluate the function at the given values of the independent variables. Simplify the results. g(x,…

A: We can solve this as follows:

Q: (A): If A = 4 2 -2 Find AB and AC. 2 1 -1 2 3 11 0; B= 2 -2 -2 and 1 l-1 2 1. 3 1-31 C=02 6 l-1 2 1

A: A=420210-2-11B=2312-2-2-121C=31-3026-121

Q: Evaluate the integral and check your answer by differentiating. x8 + 8x5 x7 1 dx +C

A: Firstly expand the fraction of given Integral and then integrate

Q: Given: f(x) = 0.2 + 25x-200x^2 +675 x^3-900 x^4 + 400 x^5 from a = 0 to b = 0.8 and segment equal to…

A: Given that      f(x) = 0.2+25x-200x2+675x3-900x4+400x5   from a=0 to b=0.8 and segment equal to 8.…

Q: C): Solve the following equations:- (1) sin 2x + 2 sin² = 1 (2) sech x - 4 tanh x = 1

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Q: 2: io ue Approximate the area of the region bounded by the graph of f(t) = cos (t/2-5/8) and the…

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Q: Question 5 Find the general solution of the differential equation y" - 10y' + 61y = 0. NOTE: Use c₁…

A: Solution : Given that differential equation                  y"-10y'+61=0

Q: Sketch the function. 4 k(x) = -x² +6x²-8 Part 1 of 4

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Q: 4. y = Ae bx are cosax + Bebx sinax, where a and b(lowercase) parameters. (not to be eliminated)

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Q: ¡¡y y cos x² dx dy Evaluate the double integral by reversing the order Show your answer in details.

A: Change the order of integration and then  change limits respectively

Q: dr. (4+x²)²

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Q: -2 S² g(x) dx -6 if g(x) is an even function.

A: We need to evaluate integral.

Q: Evaluate the integral and check your answer by differentiating. x8+8x5 - 1 x7 S dx = +C

A: To find out the integration.

Q: Use the disk method to find the volume of the solid of revolution generated by rotating the region…

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Q: Evaluate the integral by first modifying the form of the integrand and then making an appropriate…

A: We have to evaluate the integral by first modifying the form of the integrand ∫ [ln(e8x) + ln(e-8x)]…

Q: Find all critical points of the following function. f(x,y) = 10x²-5y²

A: Please see the below picture for detailed solution.

Q: Find the general solution of the following differential equation. 64y" +80y + 25y = 0 NOTE: Use c₁…

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Q: Suppose that f is integrable on [-4, 7]. If the average of f on the interval [-4, 7] is 4.25, fin 4…

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Q: If you were to use a substitution of u = 4x³ - 2 to evaluate the definite integral below, what would…

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Q: First, compute the gradient of the function f(x,y) = 4+5x²-3y². Then evaluate it at the point…

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Q: Q5: Find for the following functions: dx (1) In(x - y) = xy + y³ ; (4) y = x sinh 2x -cosh 2x (2) y…

A: We need to find derivative. As per Bartleby's guidelines we can solve one question from multiple…

Q: -2- 0 y = g(x) 4 7 x

A:

Q: Q3/ A. For the following function f(x). Find: f(x) = x² + 1 i. ii. iii. The slope of the f(x) by…

A: Given function, f(x)=x2+1 Aim: To find slope of f(x) Therefore differentiate w.r.t.x Therefore…

Q: A spherical raindrop evaporates at a rate proportional to its surface area with (positive) constant…

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Q: Given the equation 5 sin 6xy = 3, evaluate dy Assume that the equation implicitly defines y as a…

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Q: 1. Given the space curve r(t) = (2e¹,e²¹.e^¹), find the curvature at t = 0

A: I am attaching image so that you understand each and every step.

Q: dy dx + 4y - e* = 0, dr y(0) = 4 3

A: Given: dydx+4y-e-x=0, y(0)=43

Q: where a = 7 and b = 17 [²* f(x) dx - [1² (2) |ƒ(x) dx = [* ƒ(a) da 9

A: ∫924f(x)dx - ∫917f(x)dx = ∫abf(x)dx find a and b = ? here we use integration by limit part rule here…

Q: Sketch the plane curve. r(t) = 3ti - tj, [0, 3] y O 2 1 -1 -2 y 3 2 - -1 -2 2 4 4 Find its length…

A: This question is related to vectors and parametric equations, we will solve it using given…

Q: Find the general isolation of the following: 1. (x³y³+1)dx +x4y²dy=0

A: Please see the below picture for detailed solution.

Q: 1. Integrate: [x³ sin(2x) dx.

A: As per Bartleby guideline, only the first question has been answered. If you want to get the answer…

Q: dy Q5: Find for the following functions: dx (3) y = ex.sin² x In√x

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Q: Discuss the continuity of the function. 41 √x² + y² + z² f(x, y, z) == continuous except where x² +…

A: The given function,   fx,y,z=41x2+y2+z2

Q: In 100 yrs, 132mg of radium decomposes to 96mg. How many mg will be left after 200 yrs?

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Q: a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the…

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Q: x-1/2c (4) y = x sinh 2x – cosh 2x

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Q: (B): If A = 2i +3j - 4k; B = 3i - 4j+5k and C = i + j-k, find: (iv) (3A + 4B).C (i)A.B (ii) B.C…

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Q: (B): Find the unit vector perpendicular to the vectors: 3i - 4j + 5k 4i + 5j-6k ;

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Q: For f(x) = 7x and g(x)=x+4, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(2); d.…

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Q: Find f'(x) for f(x) = - 8A√x - 5Bx⁹ where A and B are constants. Completely simplify any fractions.…

A: Solution of given question is written in below steps.

Q: Use the divergence of the vector field to compute F(x, y) = (tan-1 (2²)) i + (xy-2 +82²) j 4 fo…

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Q: If y₁ and y2 are linearly independent solutions of ty" + 4y' + te³y = 0 and if W(y₁, y2)(1) = 4,…

A: Need to find out the Wy1,y24

Q: Let f (x) be a polynomial function with a zero of multiplicity of 1 at 3 and a zero of multiplicity…

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Q: Use the method of reduction of order to find a second solution of the differential equation t²y" —…

A: The differential equation is given by,  t2 y'' - 4t y' + 6y = 0  Given,    y1 (t) = t2

Q: Solve the following differential equations: a- cos (x+y) dx +(3y2 +2y +cos (x + y) dy=0 b- y = (x +…

A: Given a- cos (x+y) dx +(3y² +2y +cos (x + y) )dy =0 b-y'=(x+1)e-xy2