The Taylor series for True False 1 at x = 3 is 1-(x-3) + (x − 3)² − (x − 3)³ + ... X-2

Q: 3. What is the arc length of y=e* from x= 1 to x=5? Draw the curve

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Q: Verify Green's Theorem by evaluating both integrals (ON-OM) d [[ y² dx + x² dy = √ √ ( ³x for the…

A: In this question, we want to verify the green's Theorem for the given integral.

Q: Given a = (5, 10) and p = (1, 3), find – ả + 4p. 10 - a + 4p =

A: a→=<5,10> and p→=<1,3>

Q: Find the exact value of each expression:\\ (a) sin¯¹ (√3/2) \\ (b) cos¯¹(−1) \\ (a) \\ (b)

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Q: A person starts walking from home and walks: 6 miles East 2 miles Southeast 5 miles South 4 miles…

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Q: Divide. (8x³-4x²-12x+15) + (2x-2) Your answer should give the quotient and the remainder. Quotient:…

A: Please see the below picture for detailed solution.

Q: "JS" f(x, y) dA by dividing the rectangle R with vertices (0, 0), (4, 0), (4,2), and (0, 2) into…

A: We need to find integral.

Q: Find the Jacobian (x, y) / d(u, v) for the indicated change of variables. x=u-v², y = u + v a(x, y)…

A: Follow the procedure given below.

Q: Suppose 150 trout are seeded into a lake. Absent constraint, their population will grow by 35% a…

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Q: (-tanx) ydx + Inlexy cos x| dy = 0

A: We need to find out the general solution of the given differential equation.

Q: 6. Evaluate the following real integrals by residue theorem 3 • I- 88 151 +47 O dx (x²+1)(x² +9) ans…

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Q: (2xy - x + 2y - 1) dx + (4x²y² - x² + 4xy² - x) dy = 0

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Q: How to evaluate this definite integral: ∫[e^3, e]  (3((ln(x))^3) / x dx

A: The definite Integral will be solved by substitute method

Q: Consider the figures below. (1) 2- 14 (2) 4- O Continually increase the height of all rectangles. O…

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Q: For the differential equation y(n) + P₁(t)y(n-¹)+...+Pn(t)y=0 with solutions y₁, , yn Abel's formula…

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Q: Sketch the solid whose volume is given by the iterated integral and rewrite the integral using the…

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Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary Integer…

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Q: The following table shows worldwide sales of a certain type of cell phone and their average selling…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: of [ $ Example 29 a If the determinant of 5-3 3 is equal to 21, what is the value of x?

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

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: 2. Given the function f(x, y)=3x²y + 2xy-y, a) find the value of the directional derivative of the…

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Q: Determine whether the vector field F is conservative. F(x, y, z) = ye²i + zexj + xe k conservative…

A: We have to check if F is conservative or not.

Q: Find the gradient of the function at the given point. Function g(x, y) = ye-x Vg(0, 9) = Point (0,9)…

A: Given function: g(x,y)=ye-x

Q: ind the equation of the line tangent to the curve 3x² + 16y² = 192 at the point Mx + K. P= (-4, 3)…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, and y are positive.…

A: We will use standard method to solve this.

Q: part, and you will not be able to come back to the skipped part. Tutorial Exercise Solve the…

A: The given differential equation is;  y''+3y'+2y=1/(8+ex).

Q: Integrate f Osin-15x+C ○ -sin-¹5x + C 1 dx 1-25x2 - 5 H|K sin ¹5x + C cos ¹5x + C

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Q: Use implicit ?х ਹੈ: ду = = x + y2 + z? = 6xyz 6- 6x differentiation to find əz/ax and Oz/dy. 6- 2y

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Q: 3. Find the sum of the series 2 3 5 6 1 π 1 7 1 (-)-(3) - 2 (² + 1 (3) - () -- () - () +- ... 2! 3…

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Q: A) Let g(x) (5x+24 =x² 2x+8 x<-3 -3<x<4 x 24 a) lim g(x), lim g(x) X--3 evaluate the following…

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Q: Use the functions below to find the given value. f(x) = x - 2 g(x) = x² | = (1)(₁_ 6+ z_ d)

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Q: 9. Give a geometrical interpretation of the intersection of the planes with equations x+y-3=0…

A: Give a geometrical interpretation of the intersection of the planes with equation. x+y-3=0 y+z+5=0…

Q: eley y³ dx + (27x-x³) dy, where C₁ is the unit circle given by r(t) = cos(t)i + sin(t)j, 0 ≤t≤ 2m.…

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Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary Integer…

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Q: Consider the following problem. Find the distance traveled in 29 seconds by an object traveling at a…

A: Solution ) step 2) velocity is the rate of change of distance  with respect to time  r =  d(s) /dt…

Q: Find a unit normal vector to the surface at the given point. [Hint: normalize the gradient vector…

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Q: 5. The sum of thrice a number and two equals 6 less than four times the number. Find the number.

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Q: 7 .TT/2 *3 [¹²³r r cose dr de dz

A: Given: I=∫-17∫0π2∫03rcosθdrdθdz   We know that; The Power Rule: ∫xndx=xn+1n+1+C The common integral:…

Q: 9 (4) Giver Sifon dx = 37 g(x) dx = 16 So Find S (2 f5r1 + 3 ger)) f(x) dx and

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Q: Consider the following. [[X] = Sketch the graph of the function. Use a graphing utility to verify…

A: Here we have to sketch the graph and then finds its domain and range.

Q: dw = t³ and y = 7. Find dt Let w = cos(8x - 10y), where x =

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Q: Solve for a in the triple integral. (Enter your answers as a comma-separated list. f3-a-y2 ↑4-x-y dz…

A: ∫01∫03-a-y2∫a4-x-y2dzdxdy = 14/15 here we have to find value of a  so integrate this and after  put…

Q: Consider the following second-order differential equation. 5y" + y = 0 Find all the roots of the…

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Q: Find curl(curl F) = x (V x F). F(x, y, z) = 4x³yzi + yj + 4zk

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Q: g'(x) = Find the derivative of the function g(x) = e² 52+3

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Q: Find the gradient of the function at the given point. w = 5x²y-7yz+z², (1, 1, -2) O 15i+ 26j+ 11k O…

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Q: The shape of a colony of bacteria on a Petri dish is circular. Find the approximate increase in its…

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Q: 1 r= 1 + cos !

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Q: The population of mosquitoes in a certain area increases at a rate proportional to the current…

A: Given problem:- The population of mosquitoes in a certain area increases at a rate proportional to…