dy 1. Find for the following: dr :b. y sin y = ry

Q: 21 · 8* cos (8*) dx =

A: ∫21*8xcos(8x)dxSubstitute u=8x→dudx=ln(8)*8x→dx=1ln(8)*8xdu=21ln(8)∫cos(u)du

Q: the velumg of a Gale ungtrude) finm a agn by Caffing tolume of 54d a Tozt Ximia laca of Card toud…

A: We need to maximize volume.

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A: We will solve the surface area problem.

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Q: Write down the nth term of the sequence suggested by the pattern. 12, 15, 20, 27

A: here is the solution:

Q: H.W: Use the comparison test to determine the following series converge or diverge: 1 3" +5 n=1

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Q: if x 2 a) Evaluate each of the following, if it exists. (If an answer does not exist, enter DNE.)…

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Q: Find the centroid of the given region. y = 2-x? y = x A (3/22,45/61) В) (5,15) c) (5/14,38/35)…

A: Centroid is x¯,y¯ , where, x¯ = 1A∫ab xfx-gx dx  and y¯ = 1A∫ab 12 fx2-gx2 dxand A = ∫ab f(x)-g(x)…

Q: Q9. Which of these is not the derivative of the function, y = x": A. -½x-1½ B. –0.5x-1Vx-1 C. –0.5 1…

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Q: Consider the curve parameterized by x(t) = 2(t²-1), y(t) = 5e²t, tER Determine an equation of the…

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Q: How many times will you use double angle identities to solve the integral of (sinx)^2*(cosx)^2dx?…

A: ∫ sin2x cos2xdx

Q: he conclusion of Green's Theorem by evaluating both sides of each of the two forms of Green's…

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Q: _4 JA 2 -D 2 CH

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Q: In the integration of (csc 5t)(cot 5t) dt, what is the correct "u"? * cot 5t 5t csc 5t O (csc…

A: This question is based on indefinite integral.

Q: d Calculate ri(t)· r2(t)] and ri(t) × r2(t)] first by differentiating d dt dt the product directly…

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Q: [6x? arcsin(x)]dx

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

A: This is a problem related to vector calculus. Based on the green's theorem we will answer the…

Q: Find absolute maximum & absolute minimum f define on C0, 2]

A: maxima minima

Q: Find the limit. If you L'Hopitals Rule, make sure to justify why you can use i use lim 2?e

A: We have to find the limit.

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 8 cos(t)i+3 sin(t)j+ 5tk;…

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Q: Find the k component of (curl F) for the following vector field on the plane F=(xe^2y)i + (8ye^x)j

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Q: Evaluate the integral of the following using Miscellaneous Substitution dx 1+ X

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Q: 1. A line, passing through point (6, 3, 2) and is perpendicular to the yz-plane. Find a point on…

A: Question is solved step by step.

Q: The half-life of a radioactive substance is 11 days. After 3 days a sample of the substance has been…

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Q: Use Green's Theorem to evaluate the integral (3x² – y)dx + 3xdy where C is the circle a? + y? = 1…

A: As we know from the Green's theorem; ∫CMdx+Ndy=∫∫D∂N∂x-∂M∂ydA   Given; I=∫C3x2-ydx+3xdy So, M=3x2-y…

Q: Suppose f(5) - 9 and f'(5) = = - 3. - An object moves along the curve y³ - 3x² f(x) = 5x = 649. For…

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Q: Find the derivative of the function. f(x) = (5x + 7)³ (06² +00) ² f1(x)

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Q: Let f(x) = Va (2 – x)2. Use the local linear approximation of f (x) at ro V0.99 (1.01)?. 1 to…

A: To use the linear approximation for the given function

Q: 4x + 2(x+1) ≥7+x

A: Solution: According to your given question, we are solving for x 4x+2(x+1)≥7+x

Q: 2. Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x2…

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Q: Describe several types of line integrals and discuss how they are related.

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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: (a) Put a pair of brackets on the left hand side to make these statements correct. 17-2 + 8-4- 11 -…

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: · ln(1+x) a) dx f (1+x)7 u= du = b) f(2x + 1) tan-¹ √√x dx U= du = c) f x² sin(2x) dx U= du = dv =…

A: I have performed integration by parts for the part a) and for the rest I have mention the u and dv…

Q: In the given integral below, what is the values of u and a? * dx УЗ — х2 — 2х и 3 х+1аnd a — 2 и 3…

A: This question is based on indefinite integral.

Q: ||r'(t) × x r" (t)|| Use the formula k(t) to find k(t). r(t) = t’i + tl5j %3D K(t) :

A: The given formula is; κt=r't×r''tr't3 And rt=t2i+t15j   As we know that; The Power law; ddxxn=nxn-1

Q: Find the average value of f(x)= e^-x on the interval [0,2]

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Q: H.W: vectors u =-2i + 4 j – v5k and v = 2i – 4 j + /5k , find: 1. the vector proj,u 2. the scalar…

A: Given  u=-2i+4j-5k & v=2i-4j+5k

Q: Question :44 A 240 mL pharmaceutical liquid suspension dosage form is settling at a rate of 4.8…

A: This is a problem related to divination concept. Based on the given rate and volume we will…

Q: Solve the inequality R(x) <0, where x-3 R(x) = x(x-4)' function. 4- 2- , by using the graph of the 6…

A: Here we have to find the inequality by using the graph.

Q: 6. For each integral, state which trigonometric substitution you would use to integrate by…

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Q: Determine the behavior of the functions defined below. If a limit does not exist or the function is…

A: Note: According to our expert guidelines only first three subparts are to be answered kindly repost…

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 3 1 lim tto0 2t2 +3' 2t (?,?)

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Q: A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 50…

A: The speed of ripple that travels outward = 50 cm/s

Q: Find T(t) and N(t) at the given point. r(t) = 4 cos(t)i + 4 sin(t)j; t = 3 r() - () V3 1 T .3 2 2…

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