Evaluate the iterated integral. T/4 '5 y cos(x) dy dx

Q: (c) Show that the differential equation ry" – 3y + zy = 0 has a general solution of the form y(z) =…

A: given that differential equation   xy'' - 3y' + xy = 0…

Q: use the definition of the derivative to compute f'(x) given f(x) 3x+2

A:

Q: The height of a right circular cone is always three times the radius. Find the volume of the cone at…

A:

Q: _13. If y = sin(4x – 5), then what is y'? а. у'3 сos (4x -5) b. у'- 4cos (4x — 5) c. y' = -cos (4x -…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 8.) A box with a square base and no top must have a surface area of 48 square inches. Find the…

A:

Q: --1

A:

Q: Determine the vector field of F. F(x, y) = yi – xj

A: Given that,  F(x,y)=yi-xj

Q: Use the following information to answer the question below. lim f(x) = 3 lim f(x) = ∞ lim f(x) = -3…

A: Information of the function is given, we have to find the required values

Q: Of all rectangles with a perimeter of lo meters, which one has the maximum area? (GIve both the…

A:

Q: 19. What is the seсond derivative of y бх* - 3x1 + х2 -57 а. у 24х1 — 9х2 + 2х b. у"3 144х — 18 с.…

A:

Q: Find volume of the solid obtained by rotating the bounded region determined by curves y = In x, y =…

A: We have to calculate volume of solid obtained by rotating the region bounded by y=lnx, y=0 and x=2.…

Q: Calculate the area enclosed by the curve f(x) = x³ – 6x2 + 8x and the x-axis.

A: Given query is to find the area enclosed by the curve and x Axis.

Q: At which point will the plane 2x + 4y – 3z = -48 and the line given by the parametric equations x =…

A:

Q: A lighted candie burns outr according to the equation y'(1) =ky (1) where y is the length (in…

A: see below the answer and explanation

Q: Test the convergence of cach of the following two scrics. n" 2n +3 (1) 2 n! (ii) Зп + 2 n=1 n=1

A:

Q: dz and ду dz Find z = a° In (1+ cy) az dz ду ||

A:

Q: Use the Comparison Test to determine whether the series is convergent or divergent. 00 ,7/8 n' n = 2…

A: The given series,    ∑n=2∞1n78-1

Q: Find div F and curl F if F(x,y, z) = x°i – 5j + yzk. - div F= curl F=

A: A detailed solution is given below

Q: 2 4 Find an equation of the normal line to the curve 3x¯y' – x°cos(ny) + 4x + 2 = 0 at the point…

A:

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: Here,  a→(t)=3t i^+6 sin(t)j^+cos(2t)k^⇒v→(t)=∫3t i^+6 sin(t)j^+cos(2t)k^dt⇒v→(t)=3t22 i^+6…

Q: Evaluate lim, (-5x + 5 – 5 - ) 12 O + O 5 O-5

A:

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A:

Q: manager sells 75 cakes per week at 650 pesos each and he knows that for every 10 pesos crease in the…

A: Given query is to find the price tk maximize the revenue.

Q: dx хV х2+2х-1

A:

Q: B. Find the value of (r+1)dx in the following three ways: a. Using elementary geometry, interpreting…

A: answer is in next step

Q: Problem 37: Convert the following complex numbers from rectangular form to polar form: a. 4+ j3 b.…

A:

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

A: f(x)=x2-x2The linear approximation of f(x) at x0=1

Q: 1 2 3 1+3* Use substitution to find the Taylor series at x= 0 of the function ... 1 What is the…

A:

Q: Solve the following indefinite integrals, using substitution or integration by parts where needed 10…

A:

Q: Find curl (3z i + 4x j + 7y k). curl(3z i + 4x j + 7y k) = ( i Di + ( i Oj + ( )k

A:

Q: 3 da Evaluate a+2 A. 3 B. 2 С. 1 D. 0

A:

Q: Find the value of the derivative of g (x, y) when we restrict to the curve defined by x = cos t and…

A: Differrtiate with respect to t

Q: ||r'(t) × r"(t)|| ||r(t)||³ Use the formula k(t) to find k(t). r(t) = 2 cos(4t)i+ 2 sin(4t)j + 9tk…

A: We have to solve k(t)

Q: ||r(t) x r"(t)|| Use the formula k(t) = to find k(t). ||r"(t)||° r(t) = t'i+ t°j K(t) =L

A:

Q: Evaluate the derivative of the function: x2 f(x) = ( x²+1 8x (æ²+1)° O 8a(a² –1) (2²+1) O 1 4x…

A: Use the chain rule for finding the derivative

Q: Evaluate the following limit: lim x→2+ x – 2 O No answer text provided. |- 1/2

A:

Q: Find curl (4z i+ 5x j+ 8y k). curl(4z i+ 5x j+ 8y k) = ( )i +( i j+( i )k

A: To Find : curl(4z i + 5x j +8y k)   Note that : If F=〈P,Q,R〉 is a vector field in ℝ3, and Px,Qy, and…

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

A: Explained below

Q: View Policies Current Attempt in Progress Find curl (6z i + 7x j + 9y k). curl (6z i + 7x j + 9y k)…

A: Solution:

Q: lim 3 1. x+00

A: To evaluate the given limit.limx→+∞1-3xx

Q: Evaluate the following limit: 2x2 – 3x + 5 lim x→+∞ 5x² – x + 12 - - 12 o 3 25

A:

Q: Calculate the first eight terms of the sequence of partial sums correct to four decimal places. E…

A: We can solve as follows

Q: (y – x) dx + 15x?y? dy

A: answer is in next step

Q: Evaluate x2 lim За - 10 - x→-2 x + 2

A:

Q: Evaluate the integral (2x +3y)dx + (27x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

A:

Q: 10 dx J6 x² – 25 (a) the given integration limits (b) the limits obtained by trigonometric…

A:

Q: d²y of the following equation then simplify whenever possible. 3) Find and dx dx- x = 3em y = 4e-m

A:

Q: Find the average value of y = sin x between x = 0 to x = π.

A:

Q: Find the volume oF the solid that results when the region enclosed by the give N curves y=e ソ=o, ×=…

A:

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

A: