Listen Use the Ratio Test to determine if the series converges or diverges. ne-Sn n=1 Converges Diverges Previous Page Next Page P.

Q: In a certain environment, a colony of bacteria grows according to the model A = A0e^0.06t, where A…

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Q: n3 - 2 1. Find Lt n+0 2n° + 3n - 4

A: Simplify the fraction and solve the limit.

Q: Find the particular solution determined by the initial condition. f'(x) = 3x273 - 6x; f(1) = - 7…

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Q: In the following exercises, suppose →1 as n→>∞. Find the radius of a, that convergence for each…

A: We have to find the radius of convergence.

Q: Find the angle (in degrees) between the planes 4y + z = 4 and – 4x + 2z= - 3.

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Q: 4. Use the definition of derivative to compute the derivative of the following functions at x 1: a.…

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Q: Let a=ci+ja=ci+j and b=9i+45jb=9i+45j. Find c so that a and b are orthogonal.

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Q: ee) Using the Laplace transforms to solve the following equations: y" + 3y' + 2y = e', y (0) = 0, y'…

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Q: Use the Comparison Test to determine if the series converges or diverges. Sn + n=1 diverges…

A: Solution: ∑n=1∞55n+6n Apply constant multiplication rule : ∑c·an =c·∑ an =5·∑n=1∞15n+6n

Q: Find the distance from the point (0,8,9) to the plane – 2y + 3z = 11.

A: In this question, we will find the distance from the given point to the given plane.

Q: Evaluating a Limit In Exercises 13-44, evaluate the limit, using L’Hô pital's Rule if necessary. 14.…

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Q: A driver accelerates when the car is traveling at a speed of 30 miles per hour (i.e., 44 feet per…

A: This question can be solved by applying the equation of motion.

Q: Find a formula for f'(x) and determine the slopef'(2) for the following function. f(x) el+8r' In(x+…

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Q: Find the vector component of v = 2i – j+ 3k along b = i+ 4j + 8k and the vector component of v…

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Q: Find an equation of the plane with the given characteristics. The plane passes through the point…

A: Find an equation of the plane with the given characteristics.   The plane passes through the point…

Q: Find the exact volume of the solid formed in the first octant bounded above by the cone z = 2 - /x2…

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Q: Compute the gradient of f(x, y) = 9 - 5x² – y² and evaluate it at the po (4, – 1). %3D - The…

A: Use gradient formula for finding at given value .

Q: A bulk food storage bin with dimensions 3 feet by 4 feet by 5 feet needs to be increased in size to…

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Q: Find the consumers' surplus at a price level of p = $130 for the price-demand equation below. p=…

A: p=400-0.02xat p =130130=400-0.02x0.02x=270x=2700.02=13500x=13500TE=px =130(13500)TE=1755000

Q: 47. Minimum material. A rectangular box with no top and two parallel partitions (see the figure)…

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Q: 43. fry(x, y) if = e"* f(x. y) en?

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Q: Question A tank is shaped like an upside-down square pyramid, with base of 2 m by 2 m and a height…

A: The volume of square pyramid with side of base a and height h is given by, V=13a2h At any height the…

Q: Find the location at t = 3 of a particle whose path satisfies - (1- dr 7 14t 2t – 4 dt (t + 1)² r(0)…

A: To find the location at t=3 of a particular whose path satisfies.

Q: Find the gradient of the function at the given point. w = x tan(y + z), (2, 15, -4) Vw(2, 15, -4) =…

A: Use gradient formula and partial derivative formula for finding the gradient.

Q: 4. Let f(x) be a function that satisfies f(3x) dx = 1 and 3f(x) dx = 15. Calculate f(x) dx. Show all…

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Q: 2. In the following Exercises, graphs of f or, f' are given. Whichever is shown, sketch graphs of…

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Q: Let z(x, y) = xy where x = r cos(20) & y = r sin(30). dx dy ду az & dr az Calculate by first finding…

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Q: 1. Budgeting for least cost. A manufacturing company pro- duces two models of an HDTV per week, xr…

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Q: dx Ifz = x + y = -2, dt dy = 3, and z> 0, find dt dz at (x, y) = (4, 0). dt Please give an exact…

A: We know that derivatives power rule is  d(xn)/dx = nxn-1 Here i attached the solution of this…

Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 5z + 10 =…

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Q: Sa413 - 3x5/2) dx x4/3, 5)

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Q: Maximize f(x, y) = 3xy Зху subject to x + y = 1

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Q: 4. The measurement of a side of a square is found to be 16 in. The possible error in measuring the…

A: We have to find the error in the area.

Q: Simplify (x) and find any vertical asymptotes. x²_ 4 f (x)= x+ 2

A: Vertical asymptote of the rational function f(x)=p(x)q(x)is given  q(x)=0

Q: Find a, and r for a geometric sequence {a, from the given information. a, =24 and as=648

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Q: Find the particular solution of the differential equation as determined by the initial condition. dB…

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Q: Identify the equation associated with each graphed surface. (a) O z? – 1 = y? + 2? O 22 + y² = z O…

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Q: Consider the triangle shown in the figure. Let A = 11 and B = 5 (in feet) and the angle 1 = radians.…

A: Consider the triangle shown in the figure. Let A=11, B=5 in feet and the angle t=π4 radians. To…

Q: A farmer plans to enclose a rectangular pasture adjacent to a river (see figure). The pasture must…

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Q: Consider the following problem: a box with an open top is to be constructed from a square piece of…

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Q: Assume s is an angle with sin (s) = .t is an angle with cos (1) =. and both angles are between 0 and…

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Q: Evaluate the integral. (Definite Integrals 6 r dr 15) V16+ 3r2

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Q: Maximize and minimize f(x, y, z) 3x + y + 2z subject to 2x + 3y2 + 4z² 210 %3D

A: We have to use lagrange multipliers.

Q: 12) (sin (4x - 9) dx

A: Given function : sin (4x -9) To find : Integral of the function.

Q: 18g(x) - f(x)]dx =] %3D 2 (Simplify your answer.)

A: This question is based on substitution of given integral.

Q: Let A(z) represent the area bounded by the graph, the horizontal avis, and the vertical lines att=0…

A: Given data÷

Q: 2. Let -x2 12x – 32, x 6 2 (a) Sketch the graph of f. (b) Identify the domain, range, and zeros of…

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Q: Please show your answer to at least 4 decimal places. Suppose that f(x, y) = xy. The directional…

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Q: Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use C for the…

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Q: If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) =…

A: Average Cost = C(x)x. Marginal Cost = C'(x)