If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is unique. Let A = Find a single vector x whose image under T is b. X = 1 -4

Q: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region…

A: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region…

Q: E h 501. f'(x) = cosx + sec²(x), (4) = 2 + √2 (7

A: Given: f'x=cosx +sec2x ; fπ4=2+22.We need to solve the above initial value problem.Recall the…

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A: On solving this we will get

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Q: A B Ⓒ Which of the following functions is a solution of (x²+1)y' + y² + 1 = 0 ? 1+x y=1*** y=2+x² .y…

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Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

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Q: a and b are two points in the third-dimenson. Show the equation that describes the set of points…

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Q: If f(a, b) = eab (ab + a), show that fûû(a, b) — àƒÂ(a,b) = a²eab

A: We can solve this as follows:

Q: Find the length of the curve r(t): (4 cos(t) + 4t sin(t))i + (4 sin(t) - 4t cos(t))j + (3-√3²) 2 k…

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Q: Which of the following functions satisfy x²dy+ y(x + y)dx=0 with y(1) = 1 ?

A: A detailed solution is given below.

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Q: 79. f(x) = 4x + 3

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Q: Find a plane containing the point ( – 2, — 1, − 2) and the line of intersection of the planes − 3x +…

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Q: Differential Equations:  Solve the following problem for y(t). dy/dt + 2y(t) = 2x(t);    x(t) = u(t)…

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Q: - For the function, find and simplify f(x + h) – f(x). (Assume h ± 0.) h f(x) = 5x² − 2x + 1 f(x…

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Q: Prove, without graphing, that the graph of the function has at least two x-intercepts in the…

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Q: Find an equation of the line that is tangent to the graph of f and parallel to the given line.…

A: We know that the general equation of a straight line is y = mx+c . Here m is slope of the line and c…

Q: 8x³ + 3x - 1 4x² + 1 dx

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Q: Find the slope of the line through P and Q. P(3, −3), Q(−1, 6)

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Q: Can we use x = vy?

A: The Solution is given below

Q: (A B Which of the following functions satisfy x²dy + y(x + y)dx=0 with y(1) = 1 ? 3x²y = 2x + y x²y…

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Q: If the distance between (b, 6) and (5, 6) is 2.5 units, find all possible values of b. (Enter your…

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Q: 12. Find the equation of the tangent line for f(x)=√x at the point where x=9. Be sure to use the…

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Q: Variable Seperable (Differential Equations) dy/dx= (1-y2)/(x3)

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Q: The function f(x) = √√2x − x² is given graphed below: (A) Starting with the formula for f(x), find a…

A: We can solve this as follows:

Q: Evaluate 6-2x-3y (2 2x dzdydx =

A: Topic = Integration

Q: Use the alternative curvature formula k = r(t) = (7 cost,√√5 sin t,3 cos t) |axv| |v|³ to find the…

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Q: The graphs of f and g are given. Use them to evaluate each limit, if it exists. If the limit does…

A: Graph of the functions fx and gx are given, we have to find the following limits. a) limx→2fx+gxb)…

Q: The graphs of z = 8, y = g(z) (solid) and y=h(z) (dashed) are shown; the graph is not drawn to…

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Q: Find the domain and range of the following graph in interval notation. 54 4 3- 2 -5-4-3-2 - -1- -2…

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Q: Solve the system of equations by using the inverse of the coefficient matrix. 2x - 2y = 7 6y + 12z =…

A: Solve the system of linear equations with the help of inverse of Matrix  2x-2y=7  6y+12z=-2  x+2z=1

Q: The graphs of z-6, y-f(x) (solid) and y-g(z) (dash D Region One B C

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Q: Graph the given functions, f and g, in the same rectangular coordinate system. Describe how the…

A: All the parts are solved below in detailed manner.

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Q: My friend Carlos, a graduate student, loves coffee and it is the one thing he pays full price for on…

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Q: Find the vector w with magnitude 17 that lies in the direction opposite of v = (1, -2,3). Show all…

A: Given vector   v→=1, -2, 3

Q: dy The equation2x = y² is a linear differential equation. dx A True B) False

A: Solution: Given data, 2xdy/dx = y2

Q: dx dt = cos x cos²t

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Q: 3. Evaluate the given limit algebraically, if it exists ²-9 lim- x+³2x²-5x-3

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Q: answer

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Q: 4x²y dx + 2x³ dy-10 y² dx - 15xy dy = 0

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Q: Use the alternative curvature formula k = K= r(t) = (4 e cost,4 e sint,4 e ¹) |vxa 3 |v|³ to find…

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Q: Prove by induction: ■)1 + 4 + 9 + ... + n² n(n + 1)(2n + 1) 6

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Q: 10. State the discontinuities of the given graph of f(x) and the reason why they are discontinuties…

A: We have to find out dis continuity

Q: Use the Shell Method to find the volume of the solid obtained by rotating region above the graph of…

A: Consider the region bounded by the bounded by the curves:fx=x2+2 ; gx=11 for 0≤x≤3.We need to find…

Q: Solve the following problems: a) Find the maximum error in the calculation of the area of a…

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Q: b. Explain what The formula for the above graph that passes through the two coordinates she…

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Q: Which of the following functions satisfy x²dy+ y(x + y)dx = 0 with y(1) = 1 ?

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Q: 3. Find the slope of the tangent line at the point (4,1) on the graph of f-¹ if f(x) = x³ + x + 2.

A: The given function fx=x3+x+2 We have to find the slope of the tangent line at the point 4,1 on the…

Q: 1. Consider the ODE: (2x + 4y) + (4x − 2y + 1)y' = 0. Verify that the ODE is exact and then find its…

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