Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) an = e^6/n lim n→∞ an =

Q: Show that the following function is not continuous at (0,0). { 3 x2+y6, 0, , if (x, y) # (0,0); if…

A: The given function is continuous.

Q: 1. Perform the following integration: S 3sec?x dx - 2x+3 b. а. S(1+) dx с.

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Q: Let f(r) = r³ – 3x² + 4. Using the Mean Value Theorem, determine the value of c € (0, 3) such that…

A: A detailed solution is given below.

Q: (In billions of dollars per year) can be modeled D'(t) = 841.51 + 815.24t- 189.51?+19.16t where t is…

A: Given

Q: Fill in the missing values to make the equations true. (a) log, 4 - log, 5 = log, %3D (b) log,+…

A: logarithm expressions are given,. we have to find the missing values

Q: 5-e* 2x

A:

Q: 1. Let f be a function satisfying the following properties: continuous on R\{1} • f(0) = 0 and f(3)…

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Q: dz (a) Find of the following functions: dx 2+1 +cos y? = sin(y'+ 22z) COS 7 ZX %3D

A: Solving

Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

A: Given functionf(x)=32x2/3differentiate w.r.t.xf'(x)=32*23x23-1f'(x)=x-13f'(x)2=x-132f'(x)2=x-23we…

Q: a) Find the fifth term of the sequence

A: Part a,Given,           The sequence is 169,3115,4621,6127,.....To find : Find the fifth term of the…

Q: Evaluate the integral. In(x) dx, y > 0

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Q: れお! /0 fi23)=4 4 (か) 2,十 F) Eanals it Ofiles)= 12 D Not if tha above

A: Given: Fx,y = x3y2 To find: Fx2,3 We know that Fxx,y is differentiation of Fx,y with respect to x ,…

Q: 1 у 3 2 y (х + 2)

A: y = (x+2)-1/2 dy/dx = (-1/2)(x+2)(-1/2 - 1) dy/dx = (-1/2)(x+2)(-3/2) dy/dx = -1/2(x+2)3/2

Q: A clothing company determines that its marginal cost, in dollars per dress, is given by the function…

A: Here we will find the cost of producing 201st through 260th dress,

Q: Find the arc length of the parametric curve. x = 3 cos(t), y = 3 sin(t), z = 4t; 0<t<+ L =

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Q: Find the curve given by x = vt and y =(? – 4), t 2 0 find the slope and concavity at the point (2,…

A: Here, the parametric curve is given by: x=t, y=14t2-4, t≥0

Q: Solve for what is asking (show complete solution). Your final answer must be in POLAR FORM. 2. Find…

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Q: Eliminate* the arbitrary constants c1 and c2 from the relation y = cje-2* + cze³* у" -у — бу %3D 0 O…

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Q: cos (4x)dx

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Q: Use the quadratic formula to solve forx. 5x+5x-1 0 (If there is more than one solution, separate…

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Q: Which of the following answer choices correctly graphs the equation below? y=cos(x+ 3π/4) −5

A:

Q: Consider the function f(z) =1-4x on the interval -4, 5]. Find the average or mean slope of the…

A: f(x)=1-4x2f(5)=1-4(25) =-99f(-4)=1-4(16)=-63The average or mean…

Q: 1. Let f be a function satisfying the following properties: • continuous on R\{1} • f(0) = 0 and…

A: Solution is here

Q: For each of the following series determine if the series converg for series convergence or…

A: Given

Q: 3. Find the derivative of y = sin² 3x two different ways, a. Use the product rule. b. Use a power…

A: Here is the solution:

Q: Find the absolute maximum value on (0, 0) for f(x) = 5x– 4x In x. %3D Select the correct choice…

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Q: Use the given graph to estimate the value of each derivative.  (a) f ′(−3) (b) f ′(−2) (c) f ′(−1)…

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Q: Use the given information to sketch the graph of f. Choose the correct graph below. Domain: All real…

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Q: Eliminate c from the equatia cxy + c²x + 4 = 0. O x* (y')? + x?yy + 4 = 0

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Q: Convert the equation, 5r csc(0), from polar coordinates into rectangular coordinates. Hint: Enter an…

A:

Q: Find the equation of the tangent line to y = 7et at x = 3. (Use symbolic notation and fractions…

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Q: 2.) Use the comparison test to determine if the series is convergent or divergent: 2n+3 Σ n=7 3n2+2

A: Given that ∑n=7∞  2n+33n2+2using comperision test2n+33n2+2&gt;2n3n2  for n≥7∑n=7∞…

Q: Find the if yvx- 8 = xy + 2 Vx - 8 = xy + 2 – 8 dx

A: We can find the derivative as below.

Q: Find the directional derivative of f(x, y) 12x at P(4,0) in the x + y direction of Q(1,–1). NOTE:…

A:

Q: 1. F(x) ; (3, 7), [-6, 4], (-co, 0), (-5, +∞), [-5, +∞), [10, -5) %3D x+5 2. F(x) =: (0, 1), (-1,…

A: To find the domain of the function.

Q: Frank wants to know the length of a tunnel built through a mountain. To do so, he makes the…

A: Solve the following

Q: Use the information about values of the functions and their derivatives to calculate H'(5), where…

A:

Q: If the equation of motion of a particle is given by s = A cos(@t + 6), the particle is said to…

A: See below the answer and explanation

Q: Find the absolute maximum and minimum values of the function over the indicated​ interval, and…

A:

Q: c) Determine a pattern for the value of the even, (2k)", derivative of f(x) at x 37T th d) Determine…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Consider a triangle ABC like the one below. Suppose that a=32, b=31, and c= 18. (The figure is not…

A: The given question can be solved as shown in step2.

Q: a) Find the fifth term of the sequence 16 31 46 61 9. 15 21' 27 b) Find the general term of the…

A: See the answer below

Q: of the curve defined by x=3t-t anc

A:

Q: d y' (-9 csc 3x cot 3x – 9 csc 3x) dx

A:

Q: f (x) = x²In x + sec x; find f"(x)

A: Given ,f(x)=x2ln(x)+sec(x)DIferentiate…

Q: 2. There is an element from the group Qu of order: (a)3 (b) 5 (c) 6 (d) 4 The correct answer is (a)…

A: We know order of an element in a divides the order of the group. We know center of Sn is trivial for…

Q: Determine if the sequence is increasing, and/or bounded. 3 — п (b) { (a) 1 — Зп - 3n n=1

A: Given

Q: Jse the graph of the parabola to fill in the table. (a) Does the parabola open upward or downward? O…

A: We have to find the vertex

Q: 10 11 Suppose f(x) dæ = 6 and | f(x) dæ = 5. 10 11 Then f(x) dæ -

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Q: Sketch the region in the plane consisting of points whose polar coordinates satsfy the given condi…

A: formula  r2=x2+y2   condition  1&lt;r≤3   for r = 1 r2=x2+y2x2+y2=1 which is equation of circle with…