Solve the equation using Exponential Shift (D² - 2D + 2) y = 12x³e²x O y = e (c! COSx + c2 sinx) + e2 (18x – 18r2 + 6x3 y = e* (c₁ cos.x + c₂ sin x) + e²x (8x − 8x² + 16x³)

Q: Find the divergence of the following vector field: 0 O 2z O O F = (y, -x + z², 3x)

A:

Q: 15. Si dt 1³ + 1² - 2t

A:

Q: (D² - 2D+5)y=e* cos x

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

Q: Question 13 Which of the following satisfies the differential equation d²y dx² A. y = e³r B.y = e-3r…

A:

Q: 32 Evaluate the integral ·ƒƒ(6-y²) dy dx. 00 The value is 18. (Type a simplified fraction.)

A: We know, ∫xndx=xn+1n+1, for any real number n.

Q: Let the vector v have an initial point at (2, −8) and a terminal point at (−1, −8). Determine the…

A: Let the vector v have an initial point at 2, -8 and a terminal point at -1, -8.To determine the…

Q: Use polar coordinates to find the volume of the given solid: Insider the sphere x² + y² + z² = 16…

A:

Q: 2 Evaluate r sin rdr using integration by parts.

A: Given∫ xsinxdx

Q: Given cos(x) = 2 on the interval [0, 2π], what is the value of x?

A:

Q: Examples: 1. Use the graph of f(x) to state the following: a) absolute maximum and absolute minimum…

A: Note that, according to Bartleby guidelines, we can answer only the first question in the case of…

Q: Evaluate the double integral over the given region R. xy² dA 2 X + 1 R xy² SS. dA= +1 R (Type an…

A:

Q: Identify the theorem: If C is the boundary curve of a surface S in 3-dimensional space, then the…

A:

Q: 1 Given that 1 1-x a with convergence in (-1, 1), find the power series for 7-x n=0 n=0 Identify its…

A:

Q: Question 1 CD Assume that "Foo is a function defined by Foo = x²-3x+1 288-1 For a ≤x≤3 Prove that…

A: Given: fx = x2-3x+12x-1---------------------------------To prove: Fx is bounded for 2≤x≤3.…

Q: Given the graph which consists of lines and a semicircle determine ₂ f(x) dx (4,2) 2 3 4 5 -1 -1…

A:

Q: V = πT -0.5x Sin 4x 4 +8x-cos2x 2 - X²-4 2²- 19.5x 1.478 -1-082

A: To determine the limit of the following equation.V=π-0.5×sin 4x4+8×-cos…

Q: 4) Determine the value of the 4) -2 6)-1 c) o d) 1 I'm 10,0 хсу e) DNE xy 2x² √x² + y²

A: If the function approach the same value k along any path into (0,0) then the limit is k. If two…

Q: ·Sa 20. x² dx (x − 1)(x² + 2x + 1)

A:

Q: a. Interest is compounded quarterly b. Interest is compounded daily c. Interest is compounded…

A: Follow the procedure given below.

Q: find do if yot' and both de and h = X

A: We will find the derivative.

Q: 11. S x + 4 x² + 5x - 6 dx

A:

Q: (a) Assume that f(x) is a function defined by f(x) = x²-3x+1 2x - 1 for 2 ≤ x ≤ 3. Prove that f(x)…

A: Given.

Q: [1 1) If A = 3 15 2] 4 6] B = [-3 -21 -5 314 4 253 3. [P 91 Find: D = r s tu

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: state whether the following series is convergent or divergent and state which test you used: an =…

A:

Q: A spherical water tank 1 ft in radius, has a spout of length 1 ft at the top of the tank, is full of…

A: Given problem:- A spherical water tank 1 ft in radius, has a spout of length 1 ft at the top of the…

Q: Let f(x) be a function given by f(x) = (a) Prove whether f(x) is a Dirichlet function. (b) Find the…

A: Given

Q: Assume that f(x) is a function defined by f(x) x²-3x+1 2x1 for 2 ≤ x ≤ 3. Prove that f(x) is bounded…

A:

Q: A(4) = A'(4) -

A: Integration gives area below curve area above x axis is positive area below x axis is negative A(4)…

Q: Using Ratio Test the following series +∞ (n!)² Σ 3n n=1

A:

Q: Evaluate the integral. π/4 Jo 0 sin5(x) dx

A: Given query is to find the value of the integral.

Q: find differential equation of the following equation 1) y' = -x y+x

A:

Q: Let C be the circle with radius 3 centered at the origin, oriented counterclockwise. Define a vector…

A:

Q: Q2: Find the determinant of 3x3 Matrix. 5 7-8 4-36 1 7-9

A:

Q: Fill in the blanks to describe the transformations that occur in the the graph from the Parent…

A:

Q: 4. A population of squirrels is currently measured to be 500 squirrels a. Write a function P(t) to…

A:

Q: 5. Let f(x)=log, (x+1). a. Complete the table of values for the function f(x)=log, (x+1) (without a…

A: We are given f(x) = log3(x+1)  We have to find  Values of f(x) for following values of x without…

Q: 2 cosh x +losion2x = 5

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

Q: Suppose F(5) = -4, F(6) = 4, and F'(x) = f(x). Sº f(x) f(x) dx = = Quest

A: Given problem:-

Q: 1. Find the indicated limit 1- cost, (a) R(t) t 1+ cost, i+ (b) R(t) 1-sint = = -i+e¹j+ek; lim R(t)…

A:

Q: 6) Find dy , where is defined as a function of implicitly by the equation below. dx y + 2x²y³ = 1

A: Given function, y3+2x2y5=1

Q: + 1 -оу-х -oy=x2

A:

Q: wait so which option is the correct answer?

A: Solution:

Q: 5) Calculate the area in square units, bounded by g(x)= 4x+8_and_f(x)=x² +19x+62 over the interval…

A: NOTE: Refresh your page if you can't see any equations. . here we have  and the interval is  so…

Q: ol Down: Two Reflections . Graph the function g given by g(x) = -f(x). 2. Graph the function h given…

A: Reflection

Q: Differentiate and simplify this function g (y) = y3 / ln(2y)

A:

Q: Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

A:

Q: What is the vector that results from transforming a by the transformation matrix? 5 ā= [ and B= -3…

A: The transformed vector can be obtained by multiplying matrix B with a→.

Q: Which of the following statements is correct to find the volume generated by revolving about x=0,…

A: using shell method formula of area A = 2πy∫abf(y)dy here a = 0 b = 2 A = 2πy∫02 (8-y3)dy so here…

Q: b) Calculate the following integrals x²(3x³ + 2)²dx (i) (ii) sin3x e³x dx (ii) (2x22+₁ +*²+2) dx S…

A:

Q: 2. Find the limit and confirm your answer using the sandwich theorem 1 - cos x lim 818 1. 2. 3. 4.…

A: