-12 1. ("(25x – 46x + 3)dx -12

Q: The ODE below models a spring, mass, dashpot system with damping constant c, spring constant k and…

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Q: Graph the problem and solve using vertical or horizontal rectangle. Show your solution. 1. Find the…

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Q: Find the limit. 421 (a) lim 7+ 17 (b) lim x-0 X 3

A: Topic = Limits

Q: Colleen's office equipment is depreciating at a rate of 9% per year. She paid $24,500 for it in…

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Q: Differentiate the following using logarithmic differentiation y = x=

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Q: ind 4 using implicit differentiation and evaluate the derivative at point (-1,2) 2.a°y + 5x?y³ = 2x

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Q: Consider the following. h(x) = ex2 − 4   Find  h '(x)=   Solve  h '(x) = 0 for x. x=   Find  h(0)=…

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Q: Determine if the given series is absolutely convergent, conditionally convergent, or divergent. Show…

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Q: Find the limit (if it exists) (а) lim x — 5 (b) lim 5 x-243 x2 + 6x + 8 (c) lim x--2 x + 2 sin x (d)…

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Q: Finding the length of a curve. Arc length for y = f(x). Let f(z) be a smooth function over the…

A: To find the arc length of given function.

Q: 15 dy dt 2-

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Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)…

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Q: Find the area of the shaded region. x = -y x = 2 – y? -2 A B 10 2. 2. 3.

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Q: Find r'(t). r(t) = (tan(10t))i+t cos(t)j – VEk NOTE: Enter your answer in terms of i, j, and k.…

A: Given problem :- r(t) =(tan-1(10t)) i+t cos(t) j-√tk Find:- r'(t)

Q: 3n 8 If tan 0= find the exact value of each of the following. 2 cos (20)

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Q: 7. An analyst has found that Tom's Transmissions Company cost function is: C(x) = 40,000 + 500x –…

A: Marginal cost =C'(x)  To maximize or minimize use double deriveative test

Q: detailed computation in determining the height of the cabin or part of the Ferris wheel at a given…

A: We are given a ferris wheel with the following informational : diameter : 64 m No of cabins : 32…

Q: Let g(x) = | f(t) dt, where f is the function whose graph is shown below. What is the value of g'…

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Q: Problem 4. The third term of a geometric sequence is 9, and the common ratio is 2 Find the fifth…

A: Given :3rd tern of GP is 9common ratio=32

Q: d d Calculate r1(t) · r2(t)] and dt ri(t) × r2(t)] first by differentiating dt the product directly…

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Q: 5. f(x) = (3x² + x)e5x² %3D

A: Explanation of the answer is as follows

Q: Find V. (F x G), if F(x, y, z) = 14.ci + j+ 13yk and G(x, y, z) = xi + yj – zk. V· (F × G) :

A: Vector

Q: short

A: Please refer to the image below

Q: 18. Find xV4x -3 dx 18. SxV4x - 3 dx

A: Use substitution to solve

Q: dr Let A be the area of a circle with radius r. If dt dA = 2, find dt when r = 5.

A: Given :drdt=2r=5

Q: Use the formula k(t) = |r(t) × r"(t)|| ||r(t)||° to find «(t). r(t) = 8 cos(7t)i+ 8 sin(7t)j + 3tk…

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Q: 5 2 dr = dr- 0 (x²+9)½ /(6+zx) 0, 's (x²+9)½ * A) True B False

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Q: Determine the convergence or divergence of the series. (If you need to use co or -0o, enter INFINITY…

A: limn→∞ sech(n)=limn→∞ 2en+e-n=limn→∞ 2e∞+e-∞=limn→∞ 2∞+0=0limn→∞ sech(n)=0

Q: dx sinxtanx

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Q: Evaluate the following definite integral.  4

A: topic- definite integral

Q: Problem 11. Solve the following system and express your solutions (if any) as individual ordered…

A: 3x2-2y2=-5     2x2+4y2=18

Q: Зx* у + tan y dy Given a first order differential equation dx x³ +x sec? y (a) Clarify the exactness…

A: To solve the given differential equation

Q: Find V· (F x G), if F(x, y, z) = 11xi+j+ 4yk and G(x, y, z) = xi+ yj – zk. V· (F × G)

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Q: dw given w = a2 + 2y2 + 22 and a = cos (st), y = -2s Int and Use chain rule to find 2 = 3s' Vi.

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Q: Use the graph of the function f to decide whether the value of the given quantity exists. If it…

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Q: division

A: We will solve using long division method.

Q: Solve the equation on the interval 0s0<2x. sin (30)= - 1 What are the solutions to sin (30) = - 1 in…

A: Given query is to find the solution of the expression.

Q: (2r+1)ar +2r+1

A: Given: ∫2r+1r2+2r+1dr

Q: Find a basis for the eigerspaca conesponding to the eigenvalue 12. 17 141 12 A basis for the…

A: We want to find the basis.

Q: Answer the following questions for the function f(x) = x/x? + 1 defined on the interval – 5 <x < 7.…

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Q: Find the limit of the following sequence or determine that the sequence diverges. 15 Select the…

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Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

A: Taylor series for f(x) centered at x=a :     f(x) = ∑n=0∞ fn(a)n!(x-a)n

Q: 6. The rate of growth of a particular population is given by dp 50t? - 100t3/2, where P is the…

A: Given problem:- The rate of growth of a particular population is given by (dp)/(dt) = 50t2 - 100t3/2…

Q: 16 Indicate the general rule for the arithmetic sequence with a3 = 8 and a8 = 33. a n = 2 + (n -…

A: The nth term of an arithmetic sequence is an = a + (n - 1)d  a is the first term. d is the common…

Q: Find the differential dy and evaluate dy for the given values of x and d.x y = Vx2 + 24, x = 1, dx =…

A: First differentiate with respect to x then find value at x=1 and dx=-0.1

Q: Vcsc² 0 – 1d0 [In (sin 0)]² + 23

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Q: Determine the convergence or divergence of the series. (If you need to use

A: answer is in next step

Q: 4. Show that y=e²* sin 3x satisfies the equation: y" – 4y' + 13y = 0 %3D

A: Topic = Differential equation

Q: Determine the signs (positive, negative, or zero) of y = f(x) (shown in the graph) and f'æ) and…

A: Consider the graph

Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

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