The particular solution of the following equation by using the D Operator y" + 2y' + 3y = -2x + 3

Q: Use the properties to evaluate the integrals. 1. S; (1 + ) dx

A:

Q: dr

A:

Q: Verify Green's Theorem by evaluating both integrals Lv = / an_ aM dA dx + x² dy * ax ay for the…

A: Given problem:-

Q: determine which statement is true y = (x + 2)2 + 2  (A) not a function (B) function; domain: R…

A: Given that       y = (x+2)2+2

Q: (a) 2. A bug begins to crawl up a vertical wire at time t=0. The velocity v of the bug at time t,…

A:

Q: Use power series to show that sinh(z) + cosh(x)= e".

A:

Q: Which of the following Cartesian equations is equivalent to the polar equation T= 4 cos 0? Select…

A: We can convert from polar to cartesian equation as below.

Q: a) 2 B: .A card is drawn from a well shuffled pack of 52 cards. Find the probability of: (iv) a card…

A:

Q: 1. Consider the curve C with parametric equations Sx(t) = t3 – 3t +1 lu(t) = t(t +1) defined for t e…

A: Given information:  xt = t3-3t+1yt = tt+1               , where t∈ℝ.…

Q: A cylindrical container with a circular base and open top must have a volume of 1000 m³. Find the…

A:

Q: 1. Find the area bounded by a curve v? = 9 – x and the y – axis.

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

Q: 2 sec" x AX JS -sec? x

A:

Q: y csc's x cot 5x 2.

A:

Q: 1 q(x) = cot-1 ( V1-πx2

A:

Q: Suppose that , g(t) dt = v7 rg(x)] dx 1. g(r) dr 2.

A:

Q: Use power series to show that 1 1 1 e =- + 0! +...** 2! 3! 4! 5! 6! 117

A:

Q: Find the exact length of the polar curve. r = 6 sin ?,    0 ≤ ? ≤ ?/3

A:

Q: is the graph a function?

A: To determine whether the given graph represents a function.

Q: Question An open-top box is to be made from a 12-inch by 42-inch piece of plastic by removing a…

A: An open‐top box is made from a 12‐inch by 42‐inch piece of plastic by removing a square form each…

Q: Assume the coefficient on Age is -0.052 and the coefficient on Age-Squared is 0.0007. Based on this…

A:

Q: 3. Find of the following equations: dx a. y = –3x² + 7x² + In 8x)* b. xy = 2x?y – 8x 7 c. x = sec…

A:

Q: -2 a 3. 22 9. 6 3 7.

A: Given that,-2ab337=229

Q: Find dy/dx: 1. y = J" cos t dt

A: Given

Q: Solve the value of t using quadratic equation (unit must seconds). Include the units while solving.…

A:

Q: A tangent line to the curve c(t) - (- 4t - 5t + 2, t - 15t - 1) has slope 3 at the pointias) 2-1…

A:

Q: ||r'(t) × r"(t)|| ||r'(t)||³ Use the formula k(t) = to find k(t). r(t) = t²i + t5j 390 t14 K(t) = 3…

A:

Q: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

A: This question can be solved using the concept of area of triangle and area under curve. I have…

Q: Given that å = i+ 53 -3k and b = 3ỉ – 23 +k are vectors in 3D. Find the value of ả x b and b xả…

A: Given; a→=i→+5j→-3k→, b→=3i→-2j→+k→

Q: 3. Find the area bounded by a curve y? = 6x + 36 and the y - axis 4. Find. the area bounded by y =…

A:

Q: Sketch the graph of the cardioid r = 1 + cosθ and the circle r = 3cosθ. Shade the region that is…

A:

Q: 3x2 + 4x + 1 dx 2. 2x2

A:

Q: x² – 3x – 2 - if r<-1 x – 1 x + 3 f(x) = if - 1<x < 1

A: limx→-1-f(x)=limx→-1-x2-3x-2x-1=(-1)2-3(-1)-2-1-1=1+3-2-2=-22=-1

Q: Consider the polar equation defined by r= 5 cos(2 sin 6), where 0<0< 2x. Determine the missing…

A:

Q: Find the limit. lim (t i – 3 j + t² k) t→8 Exact number, no tolerance. lim (1 i– 3 j+? k) i+ i j+ i…

A:

Q: Question 9 Find the volume of the shaded region when revolved about the indicated axis. 21 x = V7+ y…

A:

Q: Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x lawn chairs…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Let f(x) = 1, for all x E (0,1). Is f continuous on (0, 1)? Is f uniformly continuous on (0, 1)?…

A:

Q: Evaluate y' of the given functions: xy² = x²

A:

Q: . Consider the polar curves C1:r= 3 sin20 and C2 :r = 3 cose, and let R be the shaded region as…

A: r=3 sin 2θ and r=3 cos θ R is the shaded region: To Find:a. Find all points of intersection of C1…

Q: Let f(x) 5x. %3D Compute f'(64) and find an equation of the tangent line to the graph at x = 64.…

A:

Q: 3. You are designing a spherical tank to hold water for a small village.The volume of liquid it can…

A: Given information: V = Volume of tank m3V = πh23R-h3…

Q: Q1// Find the Area bounded by: x = -y? and x = y- 2

A:

Q: The evaluation of S S 3y³e*ydxdy is e - 1 O

A: Given: ∫01∫0y2 3y3exydxdy

Q: 5 ,2 X |x² + x – 6| dx -5

A:

Q: upper hall of the unit sphere x =) = 32'i+3xj-3 y'k.

A:

Q: x³+2x-1 (x²+9)² The partial fraction decomposition of has the form None of these Ax+B (x²+9)² A x²+9…

A:

Q: Given the three vectors å ,b and ở in 3D. The following question is t termine if operation involving…

A: We can solve this as follows:

Q: 1) Evaluate lim 10 VX-5 X-25 x25

A: We can find the limit as below.

Q: dx 29. Evaluate + sinx + cosx c) h|1- tan | +C D) tan{1- tan +C A) tan 1+ tan +C B) h1+ tan +C

A: To Find : ∫11+sinx+cosxdx     Note : a)  1+cosx=2 cos2x2b)  sinx=2sinx2cosx2

Q: For the following function f, find the antiderivative F that satisfies the given condition. 3 f(v) =…

A: