If // f(x,y) dA > 0. then f(x, y) ≥ 0 for all (x, y) in D. D

Q: Find the vertices and foci of the hyperbola. 4x² - y² - 24x - 2y + 31 = 0 vertices smaller x-value…

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

Q: da Find at z = 4 if y = 4z² - 1 and dt da dt 11 > Next Question dy dt = -5. 11

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Q: 6. Differentiate: a. f(x) In (In (3x)) b. Find equation of the tangent line to the graph of y-e³x.…

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Q: Question Find the average value of f(x) Submit an exact answer using fractions and/or roots if…

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Q: the answer

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Q: sinx cosx 4 + sin¹ x X dx

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Q: 5. Solve the given differential equation. (Recommend using Variations of Parameters) y"+3y'+2y =…

A: Given that, the differential equation is y"+3y'+2y=sinex. Obtain the complementary solution.…

Q: Find the area of the shaded region. r = sin(20) r = 4+3 cos (8)

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Q: Given the demand function D(p) = √300-2p. Find the Elasticity of Demand at a price of $14 0 X

A: We can find elasticity of demand.

Q: Use the definition of Taylor series to find the Taylor series, centered at c, for the function. f(x)…

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Q: Let P be the point in R^3 with rectangular coordinates (√2, −√2, 2√3). How to find the cylindrical…

A: We have given rectangular coordinates  (x,y,z) = (√2, -√2, 2√3)

Q: Given the following differential equation: y' − 2y = (e^3x)/((e^x) + 1) and the following boundary…

A: Given the following differential equation: y' − 2y = (e^3x)/((e^x) + 1)

Q: 14. Evaluate f at its critical point(s). 15. Evaluate f at the endpoints of the given interval. 16.…

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Q: Can you write out the solution in a better format please

A: Integral of (cot(x)csc(x) = - csc(x)   Csc(π/2) = 1 Csc(π/3) =2/√3

Q: SS₂ (x² + y) dA. R 2 s's 1 0 217 2 2 (r^cos²e +r sine)r de dr integral It is left as an exercise

A: Given:        ∫∫Rx2+ydA=∫12∫02πr2cos2θ+rsinθrdθdr…

Q: Graph the function f(x)=x²-1 over the interval [0, 2]. Partition the interval into four subintervals…

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Q: Match each of the following parametric Equations with a plane curve : x(t) = - 3t y(t) = 1 - 9t² TER…

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Q: Use integration to find the area of the rose curve r = cos 20.

A: Area bounded by the polar curve Area=12∫ab r2 dθ

Q: n=1 n! n - (x − 3)" 2n

A: The series is given by ∑n=1∞n!2nx-3n To determine:  The radius of convergence. The interval of…

Q: fin(1 + √x dx

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Q: Find the exact value of the expressic ܪܕܐ -1 sin sin ၁ 5 သ | O 2n O 2n 5 5 Эт O 3n 5 3 5

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Q: and f(a) f(x) = 4x² + 5x² + 6x-7 3 7 2. Find f(x), f"(0), given

A: Given a function f(x)=4x3+5x2+6x-7 We have to the following of the given function, f''(x) f''(0)…

Q: Find f x² sin(x²) dx using the Maclaurin Series.

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Q: Let S = {-2, -1, 0, 1, 1, √2, 2, 4}. Determine which elements of S satisfy the inequality. (Enter…

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Q: Find the volume of the solid formed when the area of the region bounded by the curves x²- 3y-5 and…

A: Solution

Q: Use implicit differentiation to find dy dx x3 + y = 15xy || dy dx

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Q: For each differential equation, indicate the order as a number. d'y dt4 Order is: d²y dt² Order is:…

A: Yo find the order of differential equations.

Q: Where does the line through (-3, 1, 0) and (-1, 7, 4) intersect the plane 2x + y -z = -2?

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Q: potential

A: Please refer to the image below

Q: = 4 cost, Use an integral to find the area of the region bounded by the curve x = y=5sint, 0≤t≤2π.

A: SOLUTION-

Q: S= 1 dx xinx

A: This is a problem related to integration. Please follow the procedure given below.

Q: 1. Solve x²-3x²10x + 24-0. Show at least one long division process.

A: Let P(x)=x3- 3x2 - 10x+24 P(2)=23- 3(2)2 - 10(2)+24=8-12-20+24=32 When x=2, p(2)=0. Thus x-2 is a…

Q: Find an equation of the sphere with points P such that the distance from P to A(-2, 5, 2) is twice…

A: Let    P(x,y,z)  be the general point  A( -2, 5, 2)  and  B(6, 3, -3)PA=2PB Recall

Q: True or False? Let R be a ring and a, be R. Then a^2 - b^2 = (a-b (a+b) v a,b € R

A: We can check that the given statement is true or false.

Q: 3. I Find all eigenvalues and eigenvectors of: [100] 4-6 A = 0 0 2 0 2 0

A: We have to find eigen values and vector

Q: sinx cosx 4 + sin4 x dx

A: The given integral is sinx cosx/(4+sin4x).

Q: f cos(x³) x² dx. O 1 ¹ cos4 + c 4 1 3 sin x²+ C 1 1 ¹ cos4 + c - 4 -3 si sin x³+ C

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Q: π f(x,y) = sin 3(x+y) over the square 0≤x≤60sys 6. R

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Q: (x-2y) dx + (2x+y) dy = 0 Prove that it is a Homogenous DE using homegeneity test (degree n) and…

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Q: 2π 12171710727 17/1xsin nx dx 2π I need to solve the integration in a table or zero method, a…

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Q: The traffic flow rate (cars per hour) across an intersection is r(t) 200+600t 120t², where t is in…

A: The traffic flow rate across an intersection is rt=200+600t-120t2, where t is in hours and t=0 is 6…

Q: Which of the following functions are solutions of the differential equation y" - xy + y = 0? Oy=0…

A: It is easy to check through the given options.

Q: Consider the function f(x) = 5e on the interval [0, 7]. 13- 12 11 10- 9 8- 7- 6- 5 2 Find the…

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Q: Question Find the change in surface area dA if the radius of a sphere changes from 11 cm to 10.8 cm.…

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Q: Find the explicit solution of the initial value problem: dy dt 3 4ty+y y(1) = -5

A: We can find the solution as below.

Q: Write the sum using sigma notation: 9 +13 + 17 +21+ A = B = A + 45 = ΣΒ, where n=1

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Q: (5x + 4y) dx + (4x8y³) dy = 0

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Q: dy Solve the differential equation: = A - By. Find the general solution to the dx differential…

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Q: You deposited $50 into a bank that offers 2.5% interest for 30 years. A: What is simple interest…

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Q: Evaluate the following integral. Sxe 13x dx Let u=x². Use the integration by parts formula to set up…

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