(t- 1)* 24 24 4 24 24 4 1 85 84 g5 84 82 O Option 1 O Option 2 24 24s 12s² + 4s3 + s4 12s2 + 4s3 + s 24 24s + 12s? - - 4s3 + s4 O Option 3 O Option 4

Q: Select the correct answer. The graph of the function fx) = x3 defined over the interval [0, 1] on…

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Q: 00 Write the Taylor series for f(x) = e* about x = Σ- 3)". 3 as n=0 Find the first five…

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Q: S 23x* + 5 +* x2-16 dx X-4

A: We will use simple Integration rules to solve this question.

Q: Test the series for convergence or divergence using the Alternating Series Test. (-1)^ - 1 5+ 7n n-…

A: Here, the given Alternating series is: ∑n=1∞(-1)n-15+7n

Q: The integral (4 – y²)²dy represents the volume of a solid. Sketch the region, rectangular element,…

A: Here, the given integral is: ∫02π(4-y2)2dy which is of the form  π(outer radius)2-(inner…

Q: Prove the following identity: 1- tan? e cos 20 = sec e

A: solution:-cos2θ=1-tan2θsec2θ RHS=1-tan2θsec2θ        =1-sinθcosθ21cosθ2,      ∴tanθ=sinθcosθ &…

Q: the derivative of the function at P0 in the direction of A ​f(x,y,z) = 9excos(yz)​, P0(0,0,0)​, A =…

A: Given query is to find direction derivative.

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

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Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

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Q: 4) lim (5x-1 + 1)4x x00

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Q: b.

A: answer is in next step

Q: 125 when p n= 410, p=0.25, and q 1-p. Evaluate the formula z= pq (Round to two decimal places as…

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Q: What is the volume of the solid generated by revolving about the x-axis, the region bounded by y =…

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Q: 1 2" 3" 1 Find the sum of the convergent series. n-4

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Q: set D: Problem #G Find the eauation OF the Iine tangent to F Cx) = cos? x - Sin? (x) at X 3r %3D 4

A: To find the equation of the tangent line at x=3pi/4.

Q: Evaluate the integral using the appropriate substitution. You must use a substitution for this…

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Q: Use a calculator to find the approximate value of the expression. Round the answer to two decimal…

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Q: Use the Root Test to determine whether the series convergent or divergent. n2 + 1 9n2 + 8 n- 1…

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Q: Evaluate the double integral over the given region. |6x sin xy dA, R. 0 SxsA, 0sys1 R. O A. 6x 兀 OB.…

A: We will evaluate the double integral.

Q: 1. Using double integrals find moment of inertia about the x-axis of the area enclosed by the lines…

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Q: e 4e2 -8e+5 dx

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Q: Evaluate the definite integral using integration by parts. Do not use any other met od. You must…

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Q: 3. Find the curvature K of the space curve r(t) = (cos³ t)i + (sin³ t)j. (Note: Since you aren't…

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Q: 1. A supermarket employee wants to construct an open-top bax from a 14 by 30 in a piece four corners…

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Q: Find the point-normal form equation of the plane containing the point (1, -3, 5) and the line with…

A: Solution: P(1 , -3 , 5) (2 - x ) = (y+1)/2 = -z/3 = t

Q: oint) Use the graph of f(x) shown below to find the following integrals.

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Q: Solve the system. If the system has one unique solution, write the solution set. Otherwise, deter…

A: The objectives to find the solution of the system.

Q: dz Draw a dependency diagram and write a chain rule formula for and given the functions below. z=…

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Q: 3. A right circular cone has a base radius of 6 feet and slant height of 10 feet. If the approximate…

A: Solved below.

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 6 P4(x) =…

A: Solution

Q: Find the volume of the solid generated by revolving the area bounded by the given curves about…

A: Given:-the region bounded by y=sinx, x=0 and y=1revolving about y=1using washer/disk…

Q: 0:32:4 Consider the solid obtained by rotating the region bounded by the given curves about the…

A: Given problem:- Consider the solid obtained by rotating the region bounded by the given curves about…

Q: Determine the sum of this convergent series.

A: This question can be solved using the concept of infinite geometric progression.

Q: The average amount of time that a customer waits in line for service is given by W(x, y) = y < x…

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Q: A right circular closed cylinder with radius r cm and height h cm is placed on a square block with…

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Q: Assume that the radius r of a sphere is expanding at a rate of 90 cm/min. The volume of a sphere is…

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Q: Find the solution of the given differential equation

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Q: 4 4 Use the transformation u= 4x + 3y, v=x+3y to evaluate the given integral for the region R…

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Q: Find the curvature of the curve 7(t) =(- 2t, – 4t“, – 5t) at the point t = 1. Give your answer to 2…

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Q: Triangle BAC is a 30°°-60°°-90°° right triangle. 600 30° A C If BC = 15, what is the measure of AC?…

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Q: Find the linearization​ L(x,y) of the function at each point.  f(x, y) = x2 + y2 + 1  a) (1,2) b)…

A: L(x,y)=f(a,b) +(x-a)fx(a,b)+(y-b)fy(a,b).

Q: 23л Find the exact value of sin 12 23л State the exact value of csc 12

A:

Q: 2. All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the surface…

A: We have to find changing the surface area

Q: ArcTanx — х 1) lim x→0 х3 Тапx

A: We need to apply l'hopital rule which is described below.

Q: 3 dy dx 0 - 2x

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Q: By considering different paths of approach, show that the function below has no limit as…

A: In this question we have to find the limit.

Q: What is the exact area bounded by the curve f (x) = = and the x-axis on the interval [1, 8]? Write…

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Q: Change the Cartesian integral into an equivalent polar integral. 3 0-x SS (P+y?) dy dx = J JO dr de…

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Q: is this a ratio test or a nth term test

A: Here, the given series is: ∑n=1∞(n+18)!18!n!18n

Q: Sketch the region of integration and evaluate the integral. 1 y || 15y5 e xy dx dy ... Sketch the…

A: To sketch the region of integration and then solve the given integral.