f[in (w) ² ] ^ 4 3 dw

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Q: Two years ago, $5, 000.00 was placed into an investment in which the amount of money present, P,…

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Q: An oil slick on a lake is surrounded by a floating circular containment boom. As the boom is pulled…

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Q: Determine whether each of the following series converges. (Make sure to state which test you are…

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Q: Find the interval of convergence for xn 5n 8 n=0

A: The given series,     ∑n=0∞xn5n

Q: Evaluate the definite integral. NOTE: Enter the exact answer. S||ti + 1²j|| dt = |

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Q: 3) Suppose g(t) = 1/t represents the position, in meters from the starting point, of some object…

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Q: Use differentials to estimate the relative error in the lateral surface area of a right circular…

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Q: Calculate[ri(t) r2(t)] and [ri(t) x r2(t)] first by differentiating the product directly and then by…

A: r1(t)=6t i+ 4t2 j+ 4t3 kdr1dt=6 i +8t j +12t2 kr2(t)=t4kdr2dt=4t3 k

Q: Find the curvature and the radius of curvature at the point t = 0. x = et cos(t), y = et sin(t), z =…

A: r(t)=etcost i + et sint j + 11et kr'(t)=(etcost-etsint) i+(etsint+etcost) j                + 11et…

Q: Use the graph of g(t) = G'(t) below to answer the following. Make sure to show work and justify your…

A: Area above x axis is positive  are below x axis is negative ∫02 gt dt  = area from 0 to 2=16∫24 gt…

Q: Find all solutions of the equation in the interval [0, 21). COS +1=0 2x 3 Write your answer in…

A: This is a problem related to trigonometric identity. Based on the given interval and function…

Q: Using trigonometric substitution to evaluate: The first thing we'll need to do here is complete the…

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Q: Use the given derivative to find all critical points off, and at each critical point determine…

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Solve the following X 1.0[₁-2x] i. D ii. D[xln (2x) ] iii. D[cosx – 3 sin (2 x) ]

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Q: dx Find -given that dt 7x² + 6y² = 13 x = 1, y = - 1, and Give your answer as a simple fraction. dx…

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Q: Find the length of the curve 3y = 2(x² + 1)2 from x = 0 to x = 3.

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Q: A farmer uses a lb of fertilizer per acre at a cost of $0.20 per pound, leading to a revenue of R =…

A: Given R=700-400e-(x/100)

Q: Select the choice that makes each statement true. x²+x-6 X-2 [Select] x +3 x²+x-6 lim X-2 X-2…

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Q: Identify the appropriate substitution for the following integral: Sesin z cos adx

A: Assume u=sinx then du=cosxdx. Substitute sinx=u and cosxdx=du in the given integral.…

Q: Determine the volume of the solid obtained by rotating the region bounded by x=(y−2)^2, the x-axis…

A: Given:        x=y-22 The volume of the solid obtained by rotating the region about the x-axis is…

Q: 3. Sketch the graph of y=-2 sin Show evidence of transformations. Clearly plot your points. y=-2 sin…

A: Given:       y=-2sin2θ-π3+4  This is in the form of y=asinbθ-c+d       Here a=-2                b=2…

Q: Find T(t) and N(t) at the given point. r(t) = 6 cos(t)i + 6 sin(t)j; t = T(-₁) = (53) 3. N(₁) = Z =…

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Q: A man is lying on the beach, flying a kite. He holds the end of the kite string at ground level and…

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Q: face integral over t xk, portion of t n the octant x, y, z ing normal

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Q: compute the surface area of example 9.10.2 by rotating f(x) = √x around the x-axis

A: Given

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: To find the domain of rt and the value of rt0.rt=cosπt i-lnt j+t-16; t0=17

Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx.

A: This question can be solved using the concept of mid point rule of definite integrals.

Q: dx S x² √√16-(x-3)² Let x 3 = 4sec 0 dx = 4 sec 0 tan 0 de Is the solution on the right track? If…

A: We have to find the integral.

Q: = ||r'(t) × r"(t)|| ||r' (t)||³ to find k(t). 3 r(t) = 5 cos (7t)i + 5 sin(7t)j + 4tk Use the…

A: Given  problem:-

Q: 2 Σ(-1)". n+1 n=1

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Q: Consider the following series. Σ» (#1) (a) Determine whether the series is convergent or divergent…

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Q: Determine the general equation of this differential equation. xy³ dx + e*dy = 0

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: r(t)=cos(πt) i -ln(t) j+t-12 kDomain of:cos(πt): no restrictions.(-∞, ∞)-ln(t): defiend for…

Q: second derivative tests. =) has a relative Choose one Choose one maximum minimum at the point (?, ?)

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Q: Find f(x) by solving the initial value problem. X+1 f'(x) = f(1) = 8 11 #

A: Initial value problem is solved.

Q: Sa cos 2X (2 cos 2X -1) dx

A: Given,            ∫cos2x2cos22x-1dx

Q: 1. x²y' + 2xy-5y³ = 0

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Q: Step 2 1 To find the integral S H x cos 8x dx by the parts formula, use u = x and v = Apply the rule…

A: This is a problem related to integration. Based on the general formula of integral by parts we will…

Q: - Find the extreme value/s of f(x) = 4 sin² x cos 2x on (37 3π 5π 22

A: This is a problem related to maxima and minima of the function. Based on the general formula and…

Q: List the first four terms of the SEQUENCE {3n+1}n=1* Find the limit of the sequence or determine…

A: The given sequence is 2n/(3n+1)

Q: The finate finear pattern 20;17;14...-103.Calculate number of terms in the sequence ?

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Q: Jo (2x - y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (3,-5) X Evaluate -30

A: Here we have to evaluate        ∫c(2x-y)dx+(x+5y)dy    C: x-axis from (0,0) to (0,-5) and (0,-5) to…

Q: 27. Show that the tangent at any point 0 on the curve x = csec 0, y = c tan is y sin 0=x-c cos 0.

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Q: Determine the volume of the solid obtained by rotating the region bounded by x=(y-2)^2, the x-axis…

A: Solution is given below:

Q: Use the formula k(t) k(t) = ||r' (t) x r"(t)|| ||r' (t)||³ - r(t) = t²i+t³j to find k(t).

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Q: Find the equation of the tangent line to the graph of f(x) = x'e- at x = 0.

A: The given function is f(x)=x9e-x at x=0.

Q: (8x4 − 5x2 + 2)dx evaluate indefinite anti-differentiation

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Q: Find for x³+y³ = 2. -4x O O (E) None of these ○ 3x² + 3y² = 0 2x *(*_*) O

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