Evaluate the indefinite integral. (Use C for the constant of integration.) [ sin (√x) dx

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A: We have to find the volume.

Q: Find the component form of vector with initial point (-6, 2) and terminal point (7,-3). O v = (-8,…

A: We need to find the component form of the vector with given initial and terminal points.

Q: 11) An animal population oscillates over a 7 year period from a low of 800 in year t = 0 to a high…

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Q: 17. bn = 5n-1 12n +9

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Q: 9. Find all the vertical and horizontal asymptotes for the following function and indi- cate the…

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Q: 1. Which of the following is not a D.E.? A. y"- 3y'=0 B. y dz = w(z)=0 I C. y A sinx + Bcosx D. L…

A: **As per our guidelines, we are supposed to answer only one question at a time. Since you have…

Q: The rate of change of profit for a company is given by p(t) = 327 e thousand dollars per year, t…

A: Given that , pt=327e-0.21t

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Q: 27. f(x, y) = 3x² – 2xy + y² − 8y -

A: The objective of the question is determine to identify any critical points and determine whether…

Q: 11. According to a formula discovered by the French physician Poiceulle, the velocity (in cm/sec) of…

A: According to a formula discovered by the French physician Poiceulle,  the velocity (in cm/sec) of…

Q: 3. For each of the following, compute dy. You do not have to simplify your answer. (a) y =tan(x³)…

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Q: Find the volume of the solid constructed by rotating the region under the curve f(x) = e¯ on the…

A: Volume of solid generated by revolving f( x ) about x axis is given as  V = ∫abπy2dx Given function…

Q: Let S be the cylinder x² + y² = 9, with 0 ≤ z ≤ 5. Evaluate the surface integral ff (y + 3) ds. S…

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Q: Find the arc length s of the curve y=ln(1-x^2) on the interval 0≤x≤1/2. Round your answer to 4…

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Q: A particle moves along the x-axis for 0 ≤ t < 18 such that its velocity is given by the graph shown…

A: Average value of f( x ) from x = a to x = b is given as  Average value = 1b - a∫abf( x )dx Area…

Q: The three series Σ An, Σ Bn, and Σ C, have terms 1. 2. 3. Use the Limit Comparison Test to compare…

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Q: Calculate S3, S4, and S5 and then find the sum for the telescoping series where S is the partial sum…

A: Given: S=∑n=2∞ 1n+1-1n+2 To find the S3,S4,S5,S.

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A: Since the complex number lies fourth quadrant So sin value negative and cos value positive

Q: Q1} Find the differential of ex²

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Q: Use the limit comparison test to determine whether an = n=12 an lim = lim n→∞ bn n-x n=12 (a) Choose…

A: We have to to Check the convergence of given series.

Q: 8) A particle that moves along a linear path has a known velocity of v(t) = 4.3 sin (2.1t), where…

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Q: (c) dx So ² (x² + 1)²

A: we have given integration ∫ 011x2+12dx

Q: Find the four second-order partial derivatives. f(x,y) = 3x³y - 5xy + 8y fxx (x,y)= 216x y y (X,Y)=…

A: To find the four second-order partial derivatives. fx, y=3x9y-5xy+8y

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A: The given integral is xsqrt(1-x2), limit from 0 to 1 to

Q: Marginal Cost A division of Ditton Industries manufactures a deluxe toaster oven. Management has…

A: Give that marginal cost function C'x=0.0006x2-0.14x+25 and daily fixed cost is = $900

Q: Create a limit evaluation problem that requires substitution with an answer of 1.

A: limit evaluation problem

Q: Find two positive numbers whose product is 16 and whose sum is a minimum. (Enter your answers as a…

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Q: 19. an = IN 2 τη

A: The sequence is given as an=12-n

Q: Estimate the error that is made by approximating the sum of the given series by the sum of the first…

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Q: Let g(x) = x² - 1x - 23. Find x such that (x, 7) is on the graph of f(x). Ox=-6 or 5 O x = -5 or 6 O…

A: The function is given by gx = x2-x-23 The point on the graph of the function is x, 7. To determine:…

Q: Optimization 6) A rectanguiar box with an open top is to have 3 a 10m³. The length of its base is…

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Q: Suppose that we don't have a formula for g(x) but we know that g(2) = -4 and g'(x)=√√x² + 5 for all…

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Q: 五 -3-2 5+ -5+ 1 3 6 A H

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Determine convergence or divergence of the series. n=1 In n 4n-5 O Converges O Diverges W

A: The given series is:∑n=1∞ln n4n-5n

Q: Multiply the complex numbers below and leave the result in trigonometric form. [7 (cos+ i sin )] [10…

A: Let's consider a complex number  as defined below: By Euler's identity z=r…

Q: 5) The function g(x) is always negative and has an average value of -12 over the interval 0 ≤ x ≤ 5.…

A: To find the area between the curve y = g(x) and the x-axis over the interval [0, 5], we need to…

Q: For the demand function d(x) and demand level x, find the consumers' surplus. d(x) = 450 - 0.09x², x…

A: For the demand function dx and demand level x, to find  the consumers' surplus. dx=450-0.09x2, x=40…

Q: Use Newton's method with the specified initial approximation x, to find x3, the third approximation…

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Q: Rewrite the sum using sigma notation. Σ 52 1 54 + 5 5 5 + 8 16 32 64 - (-5)+5 (3 5 2 - X + 5 128

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Q: -6 -5 -4 -3 5 2 0 2 Use the graph to estimate the slope of the line tangent to the given graph at…

A: Given that , the curve and the line passes through the point (-3,2) To determine the slope of the…

Q: Express the sum without using sigma notation. Simplify your answer where possible. Σ 3 logio(1) J =…

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Q: Let g(s) es (s³ + 4). 3 a) Find the equation of the tangent line to g at (0,4). y = | b) Find the…

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Q: Find the absolute value of the complex number 1 + 2i.

A: We need to find the absolute of given complex number.

Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. g(x) =…

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Q: x²-2,x 0 [K6] a) Sketch the graph of y = f(x). b) Evaluate lim f(x). x-3 c) Evaluate lim f(x). x-0…

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Q: Find a polynomial f(x) with leading coefficient 1 such that the equation f(x) = 0 has the given…

A: Given: Polynomial f(x) has a leading coefficient of 1, has a degree of 7 andhas roots 4,5,3-i and…

Q: Use the standard Maclaurin series for sin(x) to find the first three non- zero terms in the…

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Q: 18. Determine the volume of the figure bounded by the following planes. z=3 z = -8 Z x - 2y = 6 4x +…

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Q: 6) Find the area under the line y = 3 and above the curve y = sin x on the interval [0, π].

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