Find the work that is done by the vector field F = x i + 2xy j + 3xyz k, on a particle that moves along the helix, r(t) = < cos(t), sin(t), t> from t = 0 to t = 2pi.

Q: Find the definite integral of f(x) = x(3x + 2) over the interval [0, 2].

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Q: 2. L{t7}

A: We have given function to find Laplace transform  Using formula  Ltn = n!sn+1 Put n=7 Lt7 =…

Q: at 2- N. 4 -CO be approximating rectangles. -∞ 02468 Using the specified rectangles, approximate the…

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Q: 1)a) What is the area under the curve y = 2³ and above the x-axis between z = 1 and 2 = 3? What is…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: The given curves are  x=4-y2,  x=y2-4

Q: can apply the definitions of even/oddness, absolute value to prove statements that involve cases.…

A: Answer — Exploring different cases and relation between x and 2                      a)…

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: Find the area under the graph of the function over the interval given.   ​f(x)=ex​; ​[−2​,3​]

A: QUESTION - Find the area under the graph of the function over the interval given.   ​f(x)=e^x​ ,…

Q: Find the interest on the following loan. $6000 at 4% for 9 months The simple interest is $ (Round to…

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Q: x+3 20 Find the linearization of f(x)=1-S 2² x+3 The linearization of f(x) = 1 - S 8 8 20 2+t dt at…

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Q: You are given the following information. Function: f(x) = -4x² + 5 Point: (1, 1) (a) Find a unit…

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Q: Find a formula for the sum of n terms. Use the formula to find the limit as n → ∞. lim n→∞ 4 (i-1)²

A: Find the value of limn→∞∑i=1n4n3(i-1)2. The formulas important here are;…

Q: Given the following vectors, calculate -7v u=(6,-8)v=(6,-5)

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Q: Find the interval of convergence of the se- ries Σ n=1 an Vn+3

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Q: Mary Branson invested her summer earnings of $5000 in a savings account for college. The account…

A: Given Principal amount ( P ) = 5000Rate ( R ) = 6.5 % Time ( t ) = 6 months =0.5 years

Q: A retail store estimates that weekly sales s and weekly advertising costs x (both in dollars) are…

A: A retail store estimates that weekly sales s and weekly advertising costs x (both in dollars) are…

Q: In Flatland there are four cities, Abbott, Banchoff, Charlie and Dimension. The distance from The…

A: We can solve it by Dynamic programming algorithm.

Q: The area of the triangle AKMN is A=25√√3 in². If <MKN = 30°, find |KN|=|MN| = ?

A: GivenArea of triangle KMN=253 in2∠MKN=30°   We are required to find the lengths of equal sides KN…

Q: Use left and right endpoints and the given number of rectangles to find two approximations of the…

A: Solve the following

Q: A bacteria culture grows with a constant relative growth rate. After 2 hours there are 400 bacteria…

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Q: Find the total differential. dw = w = eбy cos(4x) + z10

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Q: Compute the percent relative error in computing the area of a square whose side is measured with an…

A: We need to find error in area.

Q: - Do not use a calculator for this problem. Find the x-value where the relative maximum of y = e =…

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Q: Find the Laplace transform of the given function by using integral definition. 2. f(t) = e-πt

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Q: fx³ cos4xdx (you can use short cut method)

A: ∫ x3cos4xdx

Q: Write a linear cost function for the following situation. A ski resort charges a snowboard rental…

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Q: Find the linearization of the function f(x) = x7 at L(x) = | la k 7 sin (a) at z = 1. Using this…

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Q: Sketch the region enclosed by the given curves. -5 -10- O y = 6 cos(x), y 6-6 cos(x), 0≤x≤ x US 1.0…

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Q: 5 a. For f(x)=, find an equation for the secant line through the points where x = 2 and X X = 5. 5…

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Q: Suppose you are the manager of a firm. The accounting department has provided cost estimates, and…

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Q: For the following equation (a) find dy, and (b) evaluate dy for the given value of x and dx. y=x² -…

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Q: centered at x = 0 for f when 1 (4x + 1)¹/2 * f(x) = 2. T3(x) = 1 + 2x - 6x² + 20x³ 3. T3(x) = 1-2x +…

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Q: 2. If f(x) = √2 +4x, find f(3) of definition x → f'(3) using the , derivative. If" (3) is the limit…

A: Let's find value of f'(3) by using derivative of definition.

Q: Find the velocity and acceleration vectors in terms of u, and up. r = sin 2t and 0 = 4t v = (2 cos…

A: Given that , r=sin2t , θ=4t find the velocity and acceleration in terms of ur and uθ.

Q: B. Evaluate the following Laplace transforms by using the formulas listed in the table of Laplace…

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Q: Match the equation with its graph. x² + y² + z² 9 16 9 21 <|||| = 1 3

A: The given equation x29+y216+z29=1. We have to sketch the graph of the function.

Q: Find the solution of the following differential equations. Show your solutions 6. (D6 + 3D + 3D² +…

A: To find the soution of the following differential equation.D6+3D4+3D2+1y=0

Q: Which of the following is the power series representation for the function f(x) = ¹¹:

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Q: L{e-²t cosh 3t}

A: Laplace transform of e-2tCosh(3t)

Q: V. Find the third derivative: 1) y = 10 tan(x) - 2 cot(x) 2) y = x³ - x² sin (x) 1 3) y = 2 sin(x)-4…

A: As per the guidelines I am supposed to do the first question among multiple questions. So here I am…

Q: Given values for x and z to be -12 and 2, evaluate the following ordered triples to determine the…

A: Given system of equation 2x - 4y - 3z = -2 y = x3 - 3 -2x + 2y -4z = 2

Q: A line passing through the origin makes an angle with respect to the positive x-axis. Find how fast…

A: A line passing through the origin makes an angle with respect to the positive x-axis. To find how…

Q: How long, to the nearest year, will it take me to become a millionaire if I invest $200,000 at 4%…

A: Given query is to find the time taken to reach the amount to million.

Q: (d) Given tant =, find csco, cos0, sec, coto, sine if 0 is in Quadrant III. Answer: cote = cose ==…

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Q: E{sinh-t}

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Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers…

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Q: Tx A price p (indollars) and demand & for a product. related by 2 2x²² + 2x p + 50p² = 7400 are alf…

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Q: 1. 2. 3. Let f(x)=-=-2 Find and simplify/(x+h)-f(x) h Let f(x)=√x-2. Find and simplify f(x+h)-f(x) h…

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Q: 4

A: We have to calculate according to the given information

Q: Evaluate the line integral [ xy²³ dx + 2x²y dy where C is the triangle with vertices (0,0), (2, 2),…

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