A cylindrical can without a top is made to contain 10,000 cubic cm of liquid. Find the dimensions that minimize the cost of the metal to make the can.

Q: 9x²-4 :) Tax² ² (x² − 4)(x²+4) dx

A: Topic:- application of integration

Q: 20. A store finds that its sales revenue changes at a rate given by S'(x)=-3x² +300x dollars per…

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Q: Find the arc length (s) of the curve r(t) = (3t, 2 sin(2t), 2 cos (2t)) for -4 < t 5 S = Check…

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Q: у=ех

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Q: If the relation represents a function, find the domain and range. (have it in interval notation.

A: Question: If the relation represents a function, find the domain and range. (have it in interval…

Q: a) Use the Newton-Raphson method to solve the following equation for x to six decim x - ln x=8 (Use…

A: Here we have to use the Newton's raphson method

Q: 3. a. f(-2)= b. f(1) = c. lim f(x) =

A: Note :- This is multiple sub parts questions and according to our company guideline we can do…

Q: Find the volume of the region bounded by z = x²,0 ≤ x ≤ 5, and the planes y = 0, y = 2, and z = 0.…

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Q: For y=5x^−2+8x^−3−7x−4, find dydx.

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Q: Basic Level 1. The graph shows the total cost of making compact discs. 250 Namibian Dollars…

A: According to the graph :-cost of 0 compact disc=N$50 thousandscost of 5 thousands compact disc=N$80…

Q: The graph below is the function f(x) -5-4-3-2 Find lim 4 3 02 1 82 -2 -3- -4 -5 2-1- Find lim Find…

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Q: Evaluate (2 - xy) ds where C is the curve given below. -2 -1 -2

A: Given   ∫C2-xyds Curve C

Q: 2 1 Expand 2y 0.013 2 3. ✓0.0004:

A: Given problem:- Expand 2y210.013y2230.0004

Q: Let f(x) = x¹ - 50x² 3 (a) Use the definition of a derivative or the derivative rules to find ƒ'(x)…

A: "since you have posted a question with multiple subparts,we will solve first three subparts for…

Q: 2. cotx = sin xsin π 2 --x+cos² x cotx

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Q: 1 Given the differential equation dy = y³xex² уз хеха dx a. find the general solution

A: The objective of the question is evaluate the differential equation.

Q: A piece of cardboard measuring 13 inches by 12 inches is formed into an open-top box by cutting…

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Q: Part A The population p, in thousands of bacterial colonies on a kitchen bench can be modelled by…

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Q: The cross product is anti-commutative. This means that axb=-bxa. Show this is true for a=(2,3,4), b…

A: Given  a→=2,3,4 and b→=-5,-4,-3. We have to show that  a→×b→ = -b→×a→.

Q: 10. Explain what it means if a. 6 = 0

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Q: What is the max area of a rectangle placed between the x-axis and the function f(x)= -x^4 + 3

A: Answer : Maximum area should be 4.225 unit2 .

Q: 2. Find the MacLaurin polynomial of degree 16 for the function F(x)= So sin (6xt²) dt.

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Q: a. Find the linear approximating polynomial for the following function centered at the given point…

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Q: Evaluate the Integral using the following values. -206 [³x² dx = 260, [°x dx = 10, [° dx = 2 (22-7x…

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Q: Find the unit tangent vector T(t) for r(t) = 4ti + 7t²j + 3tk. T(t) =

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Q: A factory selling cell phones has a marginal cost function C(x) = 0.01x² – 3x + 229, where…

A: Given that: Cx=0.01x2−3x+229Rx=429−2x To find the area between the graph.

Q: Evaluate the definite integral by the limit definition. L²(x² + 4) dx Submit Answer

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Q: Imagine you want to enclose a field in the shape of a rectangle with a semicircle on one end. If you…

A: Imagine you want to enclose a field in the shape of a rectangle with a semicircle on one end. If you…

Q: Find the particular solution of the following second order differential equation d² y dy dx² --4-…

A: The given differential equation is :d2ydx2-4dydx-21y=-105x-209given that y0=11 ; y'0=39.

Q: 12. Find the area bounded by the curve y = 3x(x - 2)² and the x axis.

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Q: Which if the following is a power series representation of the function f(x) a. Σ(-x - xn+¹) n=0 Ob.…

A: We have to find the power series representation for given function.

Q: Solve for the General or Particular Solution of the following Linear Differential Equation. dr de 4…

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Q: 1. Which of the following functions grows the fastest as x goes to infinity? O 2x О 3x O Ox20 ex

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Q: JENCES AND SERIES: onvergent or divergent and, if convergen 23 an 20 ,n=1,2,3,...

A: The answer is given below:

Q: 3 -2 7 4 3 2 1 -1 2 3 X

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Q: Find the flux of F across S, [/F. Nds where N is the upward unit normal vector to S. F(x, y, z) =…

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Q: 2. 3. (32²+7)dx=(2,₁¹²₁ )dy = 0 4) 1 xe²x dx + (5-1)dy = 0, y(0) = 0 1

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Q: 10. Find the area bounded by the curve x = y² + 2y and the line x = 3.

A: Area Bounded by the Curves : If f(y) and g(y) are two continuous function on a,b and f(y)≥g(y), then…

Q: Use cylindrical coordinates to calculate: Sw(x² + y²) dV = [[[_x² + y²³ av W: x² + y² ≤64, 0≤ z ≤ 16

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Q: Which of the following is a linear differential equation? O da-t{1+t²) sec² ædt = 0 O…

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Q: 2. (xy + x) dx = (x²y² + x² + y² + 1)dy

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Q: 1. The function f is continuous on the interval [3, 13] with selected values of x and f(x) given in…

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Q: Find the domain of f(x) = √6x +9

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Q: The annual rainfall in a certain country varies from 0 to 9 inches and is a random variable with…

A: It is given that the probability density function for the annual rainfall value is given by below…

Q: 1. Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Q: Find the domain of the vector function r(t) = Domain: {t |} ≤t≤

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Q: Let à = = (2, 4, 5) and 6 = (3, -5, - 2). - Find the angle between the vector (in radians) Check…

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Q: 3. a) Examine if the following limit exists, x + y + 1 lim (x,y) (0,0) In(x2 + y²)* If the limit…

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Q: 4. [2 marks]. Solve the following system of equations using the Gauss-Jordan elimination method: -2x…

A: If you don't understand any step please comment.

Q: Suppose that the position of a particle is given by s(t) = 5t³ + 6t+9. (a) Find the velocity at time…

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