Evaluate each integral. 1. dr VI² - 1 2. I Cos az dz 7x +1 dr 1² – x – 2 3. -エー|

Q: -Find Taylor or Maclaurin for the following functions: 3) 2) f (x) = e* at a = 2

A: A detailed solution is given below.

Q: On what intervals is the function f(x) = continuous? x(x - 1)(x- 2) 1. (-00,0) 2. (0,1) 3. (1,2) 4.…

A: First draw the graph Uasing limits and the check the countinity of this function

Q: Evaluate the integral / (12x + 18y)dx + (12x – y)dy along the paraboli - arc y = x² from (0,0) to…

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Q: Find the area bounded by the curve r= 2+cos θ

A: Given problem:- Find the area bounded by the curve r= 2+cos θ

Q: 1— 2 — е-7 lim 2.x e sin(8x) →-

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Q: Find r'(t), r"(t), r'(t) •r"(t), and r'(t) x r'"(t). r(t) %=D 흑래- 26j + 하하k (a) r'(t) (b) r"(t) (c)…

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Q: Which type of discontinuity does the function exhibit at x = 3? -x2 + 1, -1 sx <0 2х, f(x) = { -4,…

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Q: Product/Quotient/Chain Rules for Differentiation: Answer the following

A: Differentiation

Q: Evaluate the line integral ( 9х + 5у)da + (х — у)dy along the curve C : x = 6 cos t, y = 12 sin t…

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Q: Solve the differential equation Integrating Factor by Linear Equation: dy — у — 5х* — Зх? + 2х — 0…

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Q: 1 f. dx Vx(Vx + 2)

A: Find your answer below

Q: b. In x? dx

A: According to the company rule we can answer only first question and rest can be reposted.

Q: xdx 1. Find the integral (x+2)3 a. -l +c b. l x+1 а. L(x+2)²! x+1 + C L(x+2)2] x+1 + C |(x+2)3_ с.…

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Q: Find the Laplace Transform of the given function using the definition of Laplace Transform a. f(t) =…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Evaluate the line integral / (6x + 2y)dx + (x – 7y)dy along the 10 cos t, y in (0 <t: curve C: x =…

A: A detailed solution is given below.

Q: Find the Taylor series for f centered at 9 if p(n)(9) = _(-1)"n! 7"(n + 1) (-1)" (x – 9)" 7" (n + 1)…

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Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). ||r(t)||* r(t) = 8 cos(8t)i+ 8 sin(8t)j + 5tk…

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Q: Evaluate the integral / (2x + 12y)dx + (24x – y)dy along the parabolic arc y = x² from (0,0) to…

A: For the arc y = x2 and the range of x from 0 to 1. So, dy = 2x dx. Now,…

Q: Evaluate the integral. 2 (3u - 5)(u + 2) du -1

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Q: dx tan x +sin x+1

A: Solution of the problem as follows

Q: ind the average value of the function g(t) = e' over the interval [0, 8]. ound your answer to one…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Q4: Find the corresponding Spherical polar coordinates of the Cartesian coordinates (6,2,5).

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

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Q: Find the indefinite integral. (Use c for the constant of integrat (4t3i + 4tj – 6vik) dt

A: we use the basic formula ∫xn dx =xn+1n+1+C    ; n≠-1

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 +8 1\ lim t++o \ 5t2 + 6'5t (0,0)

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Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 9x from (9, 9) to (0,0). NOTE: Enter…

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Q: Find the equation of the line tangent to the function f(x) = (x – 1)3 + 2 at x = 1. O y = 2 O y – 2…

A: Given query is to find the equation of the tangent at x = 1.

Q: 7y" – 5y' – 2y = 0 ; y(0) = 4 ; y'(0) = 0 |

A: differential equation

Q: Practice Exercises: Find the area of the plane region bounded by the given curves 343 1. y = x2 – 9…

A: Given

Q: 29. Total cost from marginal cost. Sylvie's Old World Cheeses has found that its marginal cost, in…

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Q: 2. dy dx

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Q: Find curl (2z i + 3x j + 5y k). url(2z i + 3x j + 5y k) = ( i )i + ( )j + ( 3 )k

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Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where 0 sts 1.

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Q: 2. y = x5 + 2x* + 5x3 + 4x² + x +1

A: Find the derivatives by applying basic differentiation rules.

Q: b. S 2*³-4x²-x-3 dx х2-2х-3

A: First we divide the polynomial  using long division

Q: 2. Find the orthogonal trajectories of the family of parabolas y = cx O In(x² + y² ) = c O 2r? + y²…

A: Explanation of the answer is as follows

Q: The temperature T in a metal ball is inversely proportional to the distance from the center of the…

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Q: 5xdx 3. Find the integral (x-1)3 -5 5 а. 2(x-1)2 + C x-1 -5 b. 2(x-1)2 + C x-1 c. In (7DE) – in () +…

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Q: Solve the given differential equation by separation of variables. csc(y) dx + sec2(x) dy = 0

A: This question is related to differential equations, we will solve it using given using given…

Q: Find div F and curl F if F(r, y, z) = 2e*"i– 9cos yj+ 4 sin² z k. div F= curl F=

A: Given: F(x,y,z)=2exyi-9cosyj+4sin2zk

Q: 3) Find and d²y of the following equation then simplify whenever possible. dx dx² x = 3em y = 2mem

A: A detailed solution is given below

Q: Evaluate the line integral -ydr + rdy along the curve C : y² = 6x from (6, 6) to (0,0). NOTE: Enter…

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Q: Find each of the two areas bounded by the

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Q: Use the following graph to answer the questions that follow. 325 Domestic supply 275 225 Price of…

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Q: 1. Find the area of parabola y = x² from 0 to 1.

A: This is a problem related to integration. Based on the integral formula for area calculating we will…

Q: Find curl (5z i + 6x j + 8y k). curl (5z i+ 6x j + 8y k) )i + ( i )j + ( i i )k

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Q: Given x – 3 x 3 - What is lim g(x) ? O 1 O -6 O –1

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Q: Evaluate the integral / (2x + 3y)dx + (6x – y)dy along the parabolic arc y = x from (0,0) to (1,1).…

A: Given

Q: Solve the differential equation Integrating Factor by Linear Equation: dy 1 dx x + y2

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Q: Find V · (V × F), if F(x, y, z) = 2e"²i+ 2xe"j – 9ev²k. V· (V × F) =

A: Given F(x,y,z)=2exzi→+2xeyj→-9eyzk→ To find, ∇.(∇×F)