Find the derivative of the function: y = (e**)e Oy = e (e*+ + 1) Oy - (e") (e*+* +1) Oy = (e +1)e*+e+e Oy = (e")e e+1

Q: Determine the vector field of F. F(x, y) = yi - xj

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Q: Use power series operations to find the Taylor series at x= 0 for the following function. 17x e* The…

A: we want to find taylor series of the function 17 x ex  about  x=0

Q: Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding…

A: The solution is given below.

Q: (x) = V19+r dt , find f'(3)

A: Given query is to find indicated derivative.

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

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Q: Write the sum in sigma notation. 4 3 1. +- 6. 6. 26 | ... 8. 10 12 52 3+n Ce tn an= fram T 26 26 3+n…

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Q: Find the average value of the function over the indicated interval.   ​(B) Graph the function and…

A: To find the average value of the function,      fA=1b-a∫abf(x)dxWe have, f(x)=500-90x, a=0, b=2

Q: Solve the differential equation for general solution y' = 2x - xy; y = 5 when x = 0 %3D O y =…

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Q: about the line, x- | (E'1) puo (!!)'(0) squiad %3D V= T RG) 3-X y= 2x+1 Idy 3 - 23. x- V= T 29 12

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Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: Solution: C′(x)=3x2 −5x​; C(0)=2,000

Q: Optimize Z= In(4x2 - 24x + 2y2 - 20y) optimize the function. Find Zx, Zy, Zxx, Zyy, Zxy. Comment…

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Q: Sketch the region enclosed by y = 4x and y = 7x². Decide whether to inte with respect to x or y.…

A: we have to find the area of the region .

Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 30x from (30, 30) to (0,0). NOTE:…

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Q: A piece of wire 21 m long is cut into two pieces. One piece is bent into a square and the other is…

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Q: dw dw Find ду at the point (w, x, y, z) = (75, – 1,2, – 3) if w = 3xy + 3yz- 3z° and x2 +y? +z? =…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = 3x, x = 4, x = 5 and y =…

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Q: Find div F and curl F if F(x, y, z) = x°i – 6j + yzk. - div F= curl F=

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Q: Evaluate the following definite integrals. dr 5. ? +3

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Q: Use Lagrange multipliers to find the extreme values of the function f(x, y, z) = x² +y² + z2 subject…

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Q: Find V· (V × F), if F(x, y, z) = 3ei+ 4.xe®j – 2ev²k. V·(V × F) =

A: We need to find dot product.

Q: Plot the points with polar coordinates -5, and 4, using the pencil. 11a 6. 4. 4T 3 如不

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Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). r(t) = ellti+etj K(t) ||

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Q: Evaluate the definite integral

A: Given∫pi/40sin62wcos62wdw,

Q: Is the mathematical statement correct. If f(x)=f(-x), then f’(x)=f’(-x). Explain why

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Q: Determine the vector field of F. F(r, y) = yi – xj

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Q: 3. For the given differential equation xy' – 4y = x*e* a) Find P(x) and Q(x) functions of a FOLDE.…

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Q: 2. sin 2wcos 2wchw

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Q: 4x2-3z-2 Given a+1 determine y"

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Q: Use Newton's method to approximate the indicated root of the equation correct to six decimal place…

A: Here, let the given function be: f(x)=x2+ex-9⇒f'(x)=2x+ex Next,…

Q: Express py? dA as an iterated integral in the order dydr, where R is the region in the ry-plane…

A: Integral

Q: Evaluate (2x - y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (5, -5)

A: The objective of the question is evaluate the definite integral.

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 4 y…

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Q: a. Find the derivative function f' for the function f. b. Determine an equation of the line tangent…

A: Given : f(x)=7x+1   To Find : a) Derivative of f(x) b) Tangent at point (a,f(a)) where a=5

Q: Verify the Divergence Theorem by evaluating F.N dS as a surface integral and as a triple integral.…

A: Here, using the Divergence Theorem, ∯F·Nds=∫∫∫v∇·Fdv Here, F=xy,z,x+y So, ∇·F=∂F∂x,∂F∂y,∂F∂z=y,0,0

Q: 2. By differentiation rules , evaluate the derivatives of the following and simplify as possible: d.…

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Q: 2. C sin $ 2wcos° 2wcw 3. If f(x) = Vi19+r² dt , find f'(3).

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Q: EXAMPLE 9 Evaluate the integral. In (dr SOLUTION We let u = In(x) because its differential du = dx/x…

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Q: 6. (ax3+ bx2+cx) dx= 2b | x2dx where a,b and c are constants. -9 A) True B False

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Q: Find all the first and second partial derivatives of the function f(x, y) = x²y – 3y“.

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) x33 sin(x34) dx Submit…

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Q: Describe the graph of the equation. r = 9 sin 13t i - 9 cos 13t j

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Q: Solve the seperable differential equation 10yy' = x. Use the following initial condition: y(10) = 7.…

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Q: Find V x (V x F) if F(x, y, z) = 9xyj+ 6xyz k. V × (V × F) =

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Q: ermine the Interval(s) for which the function is (a) increasing, (b) decreasing, and (c) constant.…

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Q: Find the area bounded by the curve y = 8 – x and both coordinate axes in the first quadrant. Area of…

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Q: Find the series' interval of convergence and, within this interval, the sum of the series as a…

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Q: The astroid curve below is defined by the parametric equations x(t) = 2 cos' t, y(t) =2sin't.…

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Q: 1. The resultant of two forces has a magnitude of 55 N in the southeast direction. What is the…

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Q: Evaluate the integral (12x + 6y)dx + (9x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

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Q: ||r(t) × r"(t)|| ||r"(t)||* Use the formula k(t) to find k(t). 13 r(t) = 3 cos(3t)i+3 sin(3t)j + tk…

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