Use the appropriate limit laws and theorems to determine the limit of the sequence. 3 cos(n) n an (Use symbolic notation and fractions where needed. Enter DNE if the sequence diverges.) lim an = n→∞

Q: Compute all the first partial derivatives for the following functions: (a) f(x₁, x₂) = x₁x²+2x₁ - 7…

A: As per the instruction, I will be answering the first three subparts. For (b), So,       ∂ ∂…

Q: (c) The tangent line is horizontal if y=✔ Using the expression for y' from part (a), we see that…

A: Note:- As per your demand i solve part c for you with details of red underline Given equation:-…

Q: √x 7+x3dx 9. S

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Q: Question #1 - Find the relative extrema for the function f(x)=2-3x-2x² using the first derivative…

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Q: The shaded region between the graphs of y = −2x² + 20 and y = 3x – 15 is displayed below in - 25+ -6…

A: y=-2x2+20and  y=3x-15fot intercetion points  -2x2+20=3x-15

Q: 1. Evaluate each limit below. Clearly show all steps that lead to the answer. This includ rewriting…

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Q: 1. Show that the following ODE is of homogeneous degree. Hence solve it subject to the given…

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Q: Find the area of the region enclosed by y = 1.25x and x = 3.5 - y². -1 1 7 -1 w Use horizontal…

A: Figure:-

Q: Evaluate the integral. √2 √ x8 (1²) dx √2 √x8 (x²) -(Type an exact answer.) dx =

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Q: ich of the following is the solution of [2x+y cos(xy)]dx + x cos(xy)dy = 0 x² + cos(xy) = c x² -…

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Q: Answer the ff. differential equations. Show complete solutions. 1.) (r+sin-cos)dr +r(sin 0 + cos0)d0…

A: Topic: Differential Equation   The answer is given below:

Q: 1 = (0) 1 = (1 + 1 = 0 - 1 - /

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Q: is a differentiable fun

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Q: 4. (a) Write an equation of the tangent line to the graph of g(x) at x = 2 (b) Find the value(s) of…

A: Given g( x ) = x1 + x2

Q: The gradient of f(x, y) = xy at (x, y) = (−2, 1) is

A: To find gradient

Q: Find e > 0 such that the area of the region enclosed by the parabolas y = x² - c² and y = c² - x² is…

A: given y=x2-c2and y=c2-x2given area is 270

Q: Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

A: To be found - area enclosed by following curves, y = 8x2 y = x2 + 4

Q: 3. Consider the curve r(t) = (3t+1)i + (5t cos(t)-2)j + (e² + 1)k (a) Compute F(0). Show your…

A: Note :- Since you have posted multiple questions with multiple subparts, we will provide the…

Q: Consider the functions f(x) and g(x), for which f(0) = 4, g(0) = 7, f'(0) = -4, and g'(0) = −4. Find…

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Q: d the exact location of all the relative and absolute extrema of the function. g(t) = et − t with…

A: Given: g(t)=et−t with domain [−1, 1]

Q: 23π Which angle measure is not coterminal with the angle 36 ?

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Q: Suppose that f(5) = 2, f '(5) = 4, g(5) = -5, and g'(5) = 6. Find the following values. (a) (fg)'(5)…

A: given  f(5)=2f'(5)=4g(5)=-5g'(5)=6(a) frm product rule(fg)'=fg'+gf'

Q: 9. Show that the following functions satisfy the equation Urr +Uyy = 0, known as the two-dimensional…

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Q: If w Au +3v, then the u-elasticity of w is... 2v nw/u nw/u nw/u nw/u 3v 4u + 3v 4uv 4u + 3v 4u 4u +…

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Q: 2. At 2:00 PM, a thermometer reading 80°F is taken outside where the air temperature is 20°F. At…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Assume A = A₁ + A₂ and A, B = 0. If A₂ = kB, show that k = ● (5) (6) Use the formula x = r' (t)…

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Q: f(x)= 2x^3 + 12x^2 -270x The derivative of this function can be shown to equal f'(x)= 6x^2 +24x…

A: Given function f(x)=2x3+12x2-270x As per our  guidelines we are supposed to answer only  three…

Q: O 4 ↓ ? r ? P C(q) 7 9 15 18 23 30 39 48 R(q) 0 4 8 12 16 20 24 28 Estimate the marginal cost and…

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Q: lim sin ¹0 x9 O does not exist 02 D 3

A: To find the limit of the function at x=0.

Q: Find the points on the cone z² = x² + y² that are closest to the point (-4,3,0)

A: To find the point

Q: Consider the following sequence: W-GI 6n {an} = 5n² √√√n=1 Use the ratio +00 an+1 to show that the…

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Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence…

A: To find the general term of the sequence, starting with n=1. T determine whether the sequence…

Q: Which of the following differential equation can be solved using separation of variables? a.…

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Q: 7.f(x) = 10x4 - 3x³ + 8x² - 4x - 8 8.f(x) = 4x5 + 3x² + 9x³ − 8x² + 16x - 24

A: Hi this is your answer.

Q: The graph of y = x² is given below: (to get a better look at the graph, you can click on it). Find a…

A: To determine the formula for transformed function.

Q: Evaluate the integral (√3+1)x√3 2 2 dx = dx. [(√3+1)x √²³6 (Type an exact answer, using radicals as…

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Q: (x + y − 1)dx + (2x − y)dy = 0

A: According to question,Given differential equation,x + y -1 dx + 2x - ydy = 0

Q: Find the derivative of the function using the definition of derivative. y = √x y'

A: Here we have to find the derivative.

Q: 36. 4x² 16x³ 4x + 1 dx

A: here we have to find the integral.

Q: If f(x) = exg(x), where g(0) = 5 and g'(0) = 2, find f '(0).

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Q: Work with your group to come up with 2 different examples in which this formula would be used.

A: To work out for 2 different examples for which permutation formula is used.

Q: What is the particular solution of 2xyy' =1+ y², when x = 2, y = 3 ? a. y =√√5x-1 c. y =√√5x+2 b. y…

A: Given differential equation 2xyy' = 1 + y2

Q: (9) (a) Find the point P on the plane ry+2=-3 that is closest to the point Q(2, 3, 4). Is the point…

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Q: Evaluate the definite integral. 1 6². lo (8v + 1)² 2 dv

A: Given: ∫011(8v+1)2dv

Q: Complete the following problems, Please show all your work and make sure you have answered all the…

A: Note :- Since you have posted multiple questions, we will provide the solution only to the first…

Q: et s(t) (t) = = 4t³ - 12t² – 36t be the equation of motion for a particle. Find a function for the…

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Q: The _____ of a curve shows the point at which the curve intersects an axis.       A)  slope   B)…

A: Given query is to find the correct option for the intersection of curve with the axis.

Q: lim x->3- x2-x-6 / x2-7x+12

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Q: Use the intermediate value theorem to prove that the functions y = cos(x) and y = x intersect at a…

A: Proof: To use the intermediate value theorem, we need to show that the function f(x) = cos(x) - x…

Q: 5. Verify that the following is a Bernoulli equation and find its general solution: 3/ - x² = Y =…

A: To verify that the following is a Bernoulli equation and to find its general solution. x3y'y-x2=-y3…