Find c > 0 such that the area of the region enclosed by the parabolas y = x - c² and y = c - z is 1

Q: Find the equation of line: A. Line passing through (5,-11) parallel to x axis. B. Line passing…

A: Equation of a line passing through (x1,y1) is given by, y-y1=m(x-x1) , where m is the slope of this…

Q: Evaluate the iterated integral. 5 cos(r + y +:) dz dx dy

A: We know that integration of sinx is -cosx + c  and integration of cosx is sinx + c.       Here i…

Q: ローペープ 8-x²-y z?dzdxdy. Use cylindrical or spherical coordinates to evaluate the integral.

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Q: The critical values f(z) = "(1- z)°, for some positive constants a and b on 10, 1[ is/are a. b. tb…

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Q: Question 4 Find the approximate area under the curve of f (x) = x< +1 from x = 0 to x = 2, using 4…

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Q: True/False Indicate whether the statement is true or false. 9. A normal vector to a line is parallel…

A: We have to state whether the given statements are true or false: Statements are as follows: 9. A…

Q: Determine which graph corresponds to the area enclosed by the curves y 3x and y = x2 + 7.

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Q: 7x and y = 5x². Sketch the region enclosed by y Decide whether to integrate with respect to x or y.…

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Q: 5. Use geometry to evaluate (V4- x² dx 2 O 2n O 4t

A: Solution:

Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

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Q: Consider the following planes. 5x + 2y – z =22 X- 4y + 2z = 0 (a) Find the angle between the two…

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Q: y = 6x³ – x-4

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Q: 4. Under the usual addition 47Z/2021Z .

A: A detailed solution is given below.

Q: Find the centroid of the region. NOTE: Enter the exact answers. (ë, g) = | (?,?) y = z

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Q: Consider the function f: R → R define by f(x) = a?x3 + x² with a a real constant , a + 0, We can…

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Q: Use a parameterization R(u, v) of f (x,y) = xe*y to find the tangent plane to f(x, y) at the point…

A: Tangent plane at (x1, y1) to f(x, y) is given by below:

Q: Consider the equation a 4y" + by + cy = 0 the constants a.Gm are real and different from zero, the…

A: To find the inequality between b and c.

Q: Evaluate the integral. n/2 5 cos?0 de

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Q: Find the area of the region inside the circle r = 12sinθ and outside the cardioid r = 4 + 4 sinθ.

A: Area

Q: Calculate the (f(g(x)))' and (g(f(x)))' derivatives if f(x) = x7 1 g(x) 5x + 1 (Express numbers in…

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Q: Use Green Theorem to Evaluate |y x²dx – x²dy where C is left half of x² + y² = 25

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Q: 0, 1, 2, 3, and 4 about x = xo Find the Taylor polynomials of orders n = and then find the nth…

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Q: 3X C-6X)

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Q: Evaluate the double integral over the rectangular region R. y'dA; R = {(x, y): -1sxs1, - 8 <ys 8} |…

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Q: Find the relative maximum and minimum values. 3 3. f(x,y) =x +y° - 15xy

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Q: Evaluate the iterated integral. 1 2r y 8ry: dz dy dx

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Q: Assume the cubic function f(z) = ar+ b +cz+d, %3D has a relative maximum value of 3 at z =-2 and a…

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Q: Use The Formula К(T) = ||R' (T) × R"(T)|| ||R'(T)|

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Q: d d Calculate r:(t) · r2(t)] and r:(t) × r2(t)] first by differentiating dt dt the product directly…

A: r1(t)=cos(t)i+sin(t)j+3t kr2(t)=2 i+t k

Q: Find the Laplace transform of: f (t) = v1+ sin t + (7t)14 + t² sin 2t

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Q: Question The following telescoping series Σ en+1 en+2 - n=1 converges to e - 1

A: The given problem is solved below in detail.

Q: Estimate the area under the graph of f(x) = 36 – x² over the interval [ – 6, 4] using eight…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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Q: Assuming x E Z. Prove 2|(x – 6x + 5) → 2}x a|b b = ke Z a 6. = 2 € Z 3 3|6 is True because 4 3+ 4…

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Q: z = 16 - x2 - y2 10 -8 1768 46 8

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 6 1 lim t→+o \ 8t2+9' 6t (?, ?)

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Q: Find the exact arc length of the curve over the stated interval. 1 1 + from y = 1 to y = 3 x = NOTE:…

A: Aec length of the given curveL=∫131+dxdy2dy    Considerx=16y3+12y-1thendxdy=(16×3y2)+-12y2…

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A: Solving

Q: Given the following functions: f(x) = cos(x) g(x) = x'7 + 1 Find f(g(x)) and (f(x). (Use symbolic…

A: The given functions,  fx=cosx  gx=x17+1

Q: x-3 j. lim cose sine- sin 00 02

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Q: Prove that f : [−4,2] → R defined by f(x) = 7/x+5 is uniformly continuous on the interval [−4, 2]…

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Q: Find f such that the given conditions are satisfied. 17) f(x) = 5x2 - 7x + 4, f(0) = 2 A) f(x) =x3…

A: Given f'(x)=5x2-7x+4,   f(0)=2To find f:

Q: Solve y" +3y'+2y =

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Q: Consider the equation 4y" + by' + cy = 0 the constants b,c,m,n are real and different from zero, the…

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Q: Consider the equation y"+ay'+by=f(x) where a and b are real constants. If the general solution of…

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Q: V4-y? cv8-x²-y² Use cylindrical or spherical coordinates to evaluate the integral. JoJ Vx?+y? A 32…

A: To find the value of the given integral.

Q: Which of the following theorems establishes a relationship between differentiation and integration O…

A: We have to find out relation

Q: Find lim f(x) for the given piecewise function. x-6 2x + 1 if x 6 If the limit does not exist,…

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Q: f(x) e C = 0 %3D - ) = Σ %3D n = 0

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