Use Euler's Formula to express each of the following in a + bi form. Use symbolic notation and fractions where needed.) -e(31/4)i = Sie-(x/3)i

Q: Evaluate the iterates integrals r*dA D = {(r, y) : 1<r< e, 0< y S In(x)} %3D

A: We will use simple Integration rules to solve this question.

Q: 2 (In x dx

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Q: (a) x = 6t,y = - 7+ 4t O (x, y) = (0, 6) + t{ – 7,4) ai + bj = -7j + t(6i + 4j) O (x, y) = (0, 7) +…

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Q: Given, 1 ) dæ + ( y6 Ах + 1 :) dy = 0 y7 is an exact differential equation. Determine the value of A

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Q: T sec"(evE + 1) dx Vxe-Vx

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Q: (ese e cot e-s cot e de CSC

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Q: Integrate the differential equation in which A is being made at a rate k1and destroyed…

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Q: 2 : x = 1 + 3t, y = 3 – 6t, z = 5 – 3t are parallel and find the distance etween them. FOTE: Enter…

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Q: Consider the Bernoulli's equation: dy - y = 6e*y³. dx A) Find an appropriate substitution and reduce…

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Q: Sx*e-2x dx e-2 (2x* + 4x³ + 6x² + 6x + 3) + C 4 A e-2x (2x* + 4x3 + 6x² + 6x + 3) + C B -2x 3 x*…

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Q: Find the solution set of the inequality 5x2 – 2x + 12 < 6x² – 3x – 18. - Select one: а. [—5, 6] b.…

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Q: v=(5,1,-2), w=(4,-4,3) find the angle of 0 between the vectors v and w.

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Q: Answer(8) Linear First Order D.E. Solve the following differential equations of 1-e" dx +2(xe" -…

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Q: If f(x) = 2x - 1, what is the equation of the normal line to the graph of fat (1, 1) O A. x - 6y = -…

A: 1) f(x)=2x3-1 at (1,1) 2)f(x)=g(u) and g(u)=u(x).

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j…

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Q: Use separation of variable or homogeneous equation to get tye general solution for each differential…

A: A detailed solution is given below

Q: dy + y = y² sin x dx

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Q: Find an equation of the plane through the origin that is parallel to the plane 5x – 4y + 6z + 10 =…

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Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

A: Find your answer below

Q: SEATWORK Solve two problems; one problem from #1 and one problem from #2. Submit clear and upright…

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Q: | (3 + xx) dx

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Q: 2 (In x dx U.

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Q: if -2 <x< 0 f(x) dx where f(x) = 4 x2 if 0 < x< 2 -

A: This question is based on definite integral properties.

Q: Solve the differential equation with appropriate method. Finalize answer equated to ky^n. dy/dx + y…

A: Using bernoulli's differential equations, solve this differential equations.

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y²,…

A: We have to find the equation of tangent plane

Q: 9. sin“ x cos“ x dx

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Q: ) frcos () ->]dx +: - y dx + xdy = 0 %3D

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Q: Find the exact area of the surface obtained by rotating the curve y=÷x², 0<x<12, about the y-axis.…

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Q: A closed rectangular box with a volume of 1296ft is made from two kinds of materials. The top and…

A: answer is in next step

Q: (a) Find an equation of the tangent plane to the surface at the given point. z = x2 - y2, (7, 4, 33)…

A: Given problem:- (a) Find an equation of the tangent plane to the surface at the given point.     z =…

Q: nd Solve:- Qz: Classify dy - 3x +(3メナリ』 = e Jス

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Q: |(x + 1)°sinx dx -(x + 1)³ cos x + 3 (x + 1)² sin x – 6 (x + 1)cosx – 6 sinx + C (x + 1)³ cos x – 3…

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Q: Find the (natural) domain of the function x + 1 2х — 1 f (x) = Select one: a. (-0, –1] U (1/2, ∞) b.…

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Q: Determine that area. 4. A solid is obtained by rotating about the x-axis. The curve is given to be…

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Q: | e" sin® (e") cos" .7 (e²)dx

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Q: Calculate the following sums. (Use symbolic notation and fractions where needed.) 8. (a) i=1 8 (b)…

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Q: Determine the area, in square units, bounded above by f(r) = x2 + 10x + 25 and g(x) = -x +1 and…

A: Topic = Area The area is 323.

Q: Find the area bounded by the graphs of f(x)=x+2, g(x)=3x²+5 , x=-1 and x=1.

A: Explanation of the answer is as follows

Q: A curve C is defined by the parametric equations x = 1– t2 y = t – t3 (a) Show that C has two…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: indefinite integrals: Show complete and detailed solutions. Express your answers in simplest form…

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Q: S sin(ln x)dx A 1 x sin(lnx) – cos(Inx) + C x sin(lnx) – cos(lnx) + C| B D x sin(Inx) + cos(Inx) + C…

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Q: Which of the following is the correct definition of the limit? The lim f(x) = A, if and only if, for…

A: Explanation of the answer is as follows

Q: Evaluate the iterates integrals r*dA D = {(r, y) : 1 <I< e, 0Sys In(r)}

A: Given problem:- ∫∫D x3 dA        D={(x, y) : 1≤ x≤ e, 0≤ y≤ ln(x) }

Q: A general equation of conic section is given as y + 4x + 4(x – 2y) + k =0. Determine the value/s of…

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Q: o S(e*+3 + ex-3)dx +e*-3•

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Q: A wire of length L- 100cm is divided into two parts. One forms a circle and the other forms a…

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Q: Given the differential equation x+2 2y ? find the particular solution, y = f(x), dæ with the initial…

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Q: Please answer each question with solution.

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Q: In V3 dx 1+e2cx

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Q: Find the derivative of the following using General Rule. 7) y = vt3 8) f(x) = 6 + 5 1 9) y =-+ 2 x3…

A: We have to find derivative of Given function.