The Divergence Test for infinite series (also called the "n-th term test fo divergence of a series") says that: lim an +0 =→ } an diverges n=1 Notice that this test tells us nothing about > an if lim Σ an = 0; in n=1 that situation the series might converge or it might diverge. Consider the series n=1 The Divergence Test tells us this series: might converge or might diverge diverges converges

Q: 3. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1…

A: Given problem:-  A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine…

Q: 1. Find the particular solution of the DE y" -11y' + 24y = 0 subject to the boundary conditions y…

A: The differential equation can be solved as follows:

Q: Find the radius of convergence, R, of the series. Σ n = 1 R = Find the interval, I, of convergence…

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Q: b. In x? dx

A: According to the company rule we can answer only first question and rest can be reposted.

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. 18.% I cos(m2") dy dz

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Q: (2y²+ x²+3 0. प्रमत्ण ै

A: This is a problem of double integration. Based on the general formula we will evaluate the integral.

Q: Find curl(7z i + 8x j+ 5y k). curl (7z i + &x j+ 5y k) = ( i )i + (i )j + ( )k

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Q: d Caleulate fri(t) - r(t)] and ri(e) x ra(t)] first by differentiating the product directly and then…

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Q: I. Evaluate the following Definite 1.) Sº 6x³+4x²-8x 1.) L,º 2x 3) (3 sin3(x)dr

A: According to rules.. I  need to solve 1st question

Q: Find V · (V × F), if F(x, y, z) = 2e"²i+ 2xe"j – 9ev²k. V· (V × F) =

A: Given F(x,y,z)=2exzi→+2xeyj→-9eyzk→ To find, ∇.(∇×F)

Q: Find curl (7z i + 8x j + 9y k). curl(7z i + 8x j + 9y k) = ( i )i + ( i )j + ( i )k

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

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O 6…

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Q: Hi, I believe the function was not entered correctly in the transcription. It should be x^2-16/x-2.…

A: Apologies for the inconvenience. First two steps were correct in the original solution. Step 3 was…

Q: Find the general solution 5. (D² – 1)y = 0

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Q: -x lim + 169 x→-9 x+9

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Q: The smaller the curvature in the bend of a road, the faster a car can travel. Assume that the…

A: We need to find speed at given point.

Q: 47. f(x) = V(3 – x) on [1,3]

A:

Q: 7. S x4 sec (x5 - 9) dx 8. S tan 3 x dx

A: Question 7 and question 8 are solved.

Q: Solve for k such that 1 | k(x² – 2x + 1)dx = 5

A: Given problem:- ∫ k(x2 -2x+1) dx =5  Solve for k

Q: letter b

A:

Q: Calculus Question

A: Matrices

Q: Use the following graph to answer the questions that follow. 325 Domestic supply 275 225 Price of…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 5…

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Q: Find the area bounded by the curve x = y² + 2y and the line  x = 3.

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Q: Solve using Gauss-Jordan elimination. X1 - X2 + 2x3 - 4×4 = - 3x1 + 5x2 - 3x3 + 13x4 = - 10.9 2x1…

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Q: f 1 1 3. The graphs of f(x) and g(x) are given above. Find the following: (i) S'(1), where S(x) =…

A: Differentiation

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4x?y – 6xyz + 10yz2…

A: Given problem:- Find the first partial derivatives with respect to x, y, and z.   f(x, y, z) = 4x²y…

Q: (d) The curve y = x – x² from r = 0 to r = 2

A:

Q: True or False. Explain your answer The limit of sin(x) as x approaches very large values is 0 or 1.

A: Given

Q: I. Evaluate the following Definite Integral. 1.) L,9 6x3+4x2-8x dx 2.) x²(2x³ + 1) dx 2x 3.) sž…

A: Integration

Q: Find V · (V × F), if F(x, y, z) = e"i+ 3ze'j – 5e"k. V. (V × F) =

A:

Q: 2.) Sž sin"(x)dx

A: sin2x +cos2x =1 dcos xdx=-sin x ∫un du = un+1n+1+C

Q: Find the derivative ofe 11. D[(4x – 5)']

A: Given query is to find the derivative of thw expression.

Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where 0 sts 1.

A:

Q: The integral TT tan x sec?x dx is an improper integral of type I that diverges is an improper…

A: To evaluate the following integral.∫π2π tan x sec2 x dx

Q: y" + 2y' + 5y = 4e¬t cos 2t, y(0) = 1, y'(0) = 0 %3|

A:

Q: 4) Find the critical points of the parametric equations x = 5 – In t y = t + Int

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Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.…

A: Given query is to find rolle's theorem can be used or not.

Q: Try to find the slope of the tangent to the circle x²+y²=5. at the point (-2, 1) Show solution

A: tangent

Q: ||r(t) × r"(t)|| Use the formula k(t) = to find k(t). 13 r(t) = eti+ etj K(t) :

A: Given r(t)=e5t i + e-t j

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. 2…

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Q: The sum of the digits of a three-digit number is 11. The tens digit is three times the hundreds…

A: Let a be the hundreds digit, b be the tens digit and c be the units digit. Thus our required three…

Q: A plane region is bounded by the curves 2x2 + 4x + y = 0 and 2x – y = 0. Sketch the given boundaries…

A: The objective of the question is evaluate the area bounded by the given curves and Sketch of the…

Q: y = 3x - x2 and y = 2x 11 %3D

A:

Q: Find V × (V × F) if F(x, Y, z) 9xyj+ 5xyz k. ▼ × (V × F)

A: The detailed solution is given below Thank you

Q: 1. Using L'Hospital's rule, evaluate lim(1 – x²).

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Q: d. | x In(x + 2) dx

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

Q: the line y =4(USE DISK AND SHELL METHOD) 6.) Find the volume of the solid generated by revolving by…

A: Since the region given in question 5 is not bounded. I answer question 6 for you. Please resubmit…

Q: 9) Given a piecewise function below 1 D)-2y/ n f(x) =] (1– x)× e -k (x>0) , Find lim f(x) = (x= 0)…

A: As we know from the the limit rule: If the limit is limx→afxgx and its result of the form of 1∞ then…

Q: 2. Find the orthogonal trajectories of the family of parabolas y = cx O In(x² + y² ) = c O 2r? + y²…

A: Explanation of the answer is as follows