Using lim 0-0 sin 0 0 =1, find the limit. lim 18x (cot x)(csc 9x) X-0

Q: where a = and b = 16 10% f(x) dx = f* f(x) 10 24 [*1 (2) dz - f(2) f(x) dx

A: To find the value of a and b.

Q: Solve the given differential equation by undetermined coefficients. y" + 2y' + y = sin(x) + 4…

A:

Q: von ² moren notional a from x = 1 to x = 2 8 y = ln x -

A: Given :y=lnx-x28

Q: 16. A plane flying horizontally at an altitude of 1 mi and a speed of 500 mi/h passes directly over…

A:

Q: x² - xy (x,y) (0,0) √√√√y If it exists, find lim Answer: .Write DNE of the limit does not exist.

A:

Q: Use the method of undetermined coefficients to find a particular solution x" + 8x' + 9x = t³ Xp²

A: Solution of given question is written in below steps.

Q: Maximizing the Volume of a Box An open-top box is to be made from a 30 in. by 40 in. piece of…

A: Let's solve given maximizing volume of a box problem.

Q: Solve the initial value problem y" + 10y' + 25y = 0, y(-1) = 6, y'(-1) = 6. y(t) =

A:

Q: 12.) S³ S² (3x - 2y ¹) dy dx

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

Q: Assume that the radius r of a sphere is expanding at a rate of 70 cm/min. The volume of a sphere is…

A:

Q: The following information is given. f(3) = 5, f(5)= 3, 11. (a) Find H'(3) if H(x) = g(f(x)). 11. (b)…

A:

Q: T² T³ T Y pln(y+z) e dxdzdy = [Show your solution.]

A:

Q: * The Simpson's Rule gives the exact result when applied to any polynomial .of degree-➖➖➖➖➖➖➖or less…

A: Simpson's Rule: It is a numerical method for approximating the integral of a function between two…

Q: solve the system of equations by Grammer Method. 3x₁ −2x₂ + 4x3 = 19 x₁ +5x₂ −x3 = -12 2 x₁ + 2x₂ +…

A:

Q: Consider the following equations. 124 O Sketch the region bounded by the graphs of the equations. y…

A:

Q: 18. Two cars start moving from the same point. One travels south at 60 mi/h and the other travels…

A:

Q: Find f if f"(t) = 2e¹ + 3 sin(t), f(0) = −4, ƒ(ñ) = 9. f(t) = 2e^t-3sint-6

A:

Q: B: Find the Cartesian coordinates for the point (6,7) in polar coordinate

A:

Q: The base of a three-dimensional figure is bound by the circle x² + y² = 9. Vertical cross sections…

A: Given that,

Q: 3. The Laplace transform of the f(t) = t²e-2t cos(3t) is (a) 2(+2)(8²+45-23) (s²+45+13)³…

A:

Q: Use the formula for the binomial series: to obtain the Maclaurin series for V1 + x. Ο 1- O Ο 00 1 +…

A:

Q: III. Partial Fraction Decomposition: Evaluate the following integrals using partial fra sition. 1.…

A:

Q: Simpson's 3/8 Rule for integration is mainly based upon the idea of O Approximating f(x) by a 3rd…

A: To Find : Idea on which Simpson's 3/8 th rule is based on

Q: Consider the following functions. f₁(x) = 8, f₂(x) = cos²(x), f(x) = sin²(x) g(x) = c₁f₁(x) +…

A:

Q: Evaluate each integral. √x+Yy dz Jx - "X rx + y 0 Jx-y y dz dy Now evaluate J = = y dV, where E =…

A:

Q: 1. a- Find a result by using variable separation for dy dx b- y³y+x³=0

A: Note:- These are multiple questions and acording to our company guideline we can do maximum 1…

Q: III. Evaluate the given definite integral: ₁*√x edx

A: ∫14 xexdx here we have to integrate using substitute method  so for that lets substitute x = v dv/dx…

Q: Solve the following differential equation Ỳ – (sinx) y = 2 sinx

A:

Q: Find the area bounded by r = cos 0 for -π/2 ≤ 0≤π/2. 2. Find the length of the r(t)= , 1 ≤t≤ 5 .…

A: We have to solve Questions 12.

Q: u - If ü = 43 - 2k and = 2 - 3 + 7k, find 3u - 27.

A:

Q: Evaluate √t (3t-t²) dt

A:

Q: Q4\A: Find area of zone bounded by curves y = x² y = 2x+8

A:

Q: 4. xy = COS (²) + +1

A:

Q: What is the area of the region in the first quadrant bounded above by y = -2x + 8 and below by y =…

A:

Q: Find the general solution of the following differential equation. 64y" + 16y' + y = 0 NOTE: Use c₁…

A: The given differential equation,     64y''+16y'+y=0

Q: B: Solve the following integrations: a- [x³e-2x¹ dx b-fdx +10 c-f3sec³x. tanx dx arks

A:

Q: Determine the number of points of intersection for the planes: T₁: 3x-6y + 12z - 6 = 0 and 7₂: 2x -…

A: We want to find number of points of intersection of two planes.

Q: 2) A: By using partial method solve [2x² cos x dx

A:

Q: A bus has 8 vacant seats in the first rose. If three additional passengers enter the bus in how many…

A:

Q: Given f(x) = cos(x) - 2x² + 3x - 1, then f"(0) is equal to- Ο -5 Ο Ο Ο Ο Ο Ο -3 Ο -1 None of them O

A:

Q: Evaluate the following definite integrals using special techniques for integration: (x³) dx /(x²+1)…

A: I am attaching image so that you understand each and every step.

Q: -1.5 -4.5 -1.5 Let [ f(x)dx = 5, |_^*^* f(x)dx = 6, [*¹*³ f(x)dx = 5. -6 -6 Find and -3 [²₁ f(x) dx…

A: This question is related to definite integration, we will solve it using given information.

Q: 17. A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the…

A: Concept of similarity along with derivative is used.q

Q: Find the average value of the function f(x) = over the interval [0, 6] and find c such that f (c)…

A: We have to solve average value

Q: 1. Equation of the plane passing through the points A, B, and C. 2. Equation of the straight line…

A:

Q: You are driving a car away from home. Your velocity (miles per hour) t hours after noon is given by…

A:

Q: Evaluate the following antiderivatives. f (x sinh x + 1) dx

A:

Q: Question 1. A critical point of the function g(x, y) = ey + 3x²y-y is (0,0). Use the Second…

A: See this solution in below

Q: Find the solution of the initial value problem y" + 6y' + 10y = 0, Y (²7) = 0, y¹ (7) = 9. 2 y(t) =…

A:

Q: Find the indefinite integral of the following function:

A: