1) Write a complex number in a standard form z = x + ly:: 2+i (2- i)(3i+ 4)(i+1)

Q: Set up the iterated integral for evaluating f(r,0,2) r dz dr de over the region D, where D is the…

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Q: What are the coordinates of the vertex of the equation (+8)² (x+2)² 36 = 1? 25 O (-2,-2), (-2, 14) O…

A: The given equation is

Q: Compute the matrix exponential eAt for the following system x' = Ax. x₁ = 2x₁ + 2x₂, x 2 = 2x₁ + 5x₂…

A: We have to find the matrix exponential for the given system.

Q: What are the dimensions of the right circular cylinder of greatest volume that can be inscribed in a…

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Q: *Find the general solution of:- dy dx =x√2x + 1 1

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Q: Compute the electric charge on the surface which is the portion of the cone z = √√3x² + 3y2 in the…

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Q: Question 2 Suppose an > 0 for n≥1 and lim Wan < 1 n→∞0 What can you conclude regarding 1 an? The…

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Q: The cost of laying a fibre optic cable underwater is 3 times that of underground. An island is 4 km…

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Q: A company manufactures and sells x television sets per month. The monthly cost and price-demand…

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Q: 11. A car drives towards a 111 m skyscraper at 7.62 m/s. How fast is the car approaching the top of…

A: Given that :Height of the skyscraper =  mSpeed of the car =  m/sTo find :Rate of change of distance…

Q: Find the exact slope of the tangent line to the parametric curve x= 4 cos(t) y = 8 sin(t) at the…

A: {x=4cos⁡(t)y=8sin⁡(t) at the point where t=π6

Q: Consider the function defined by f(x) = sin(sqrt(|x|)).  A) What is the domain of this function?…

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Q: Perform the following operations and simplify the results. State the domain restriction in each…

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Q: We turn now to the problem of finding area under a curve. Suppose we want to find the area between…

A: As per guidelines we can solve only 3 subparts if multiple subparts are posted. So I am solving…

Q: f, o x sin(x − y) dxdy = Jo J, x? sin(x − y)dydx

A: ∫−12∫06x2sin⁡(x−y)dxdy=∫06∫−12x2sin⁡(x−y)dydx

Q: 17. Suppose you want to fence three sides of rectangular region where one side is bordered by a…

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Q: a) x2+5x-14 x²+8x+7 + x²-4x+4 3x²-6x

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Q: Q.1 (B)/ IfD = 3 -2 -2 01 -62, E-first column of D, find K if (K- 10 E'DE). 0 5

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Q: Determine the amplitude, midline, period, and an equation involving the sine function for the graph…

A: A graph of the trigonometric function is given.The aim is to find the equation of the graph.

Q: Solve the following triangles: (a) a = 10, b = 8, c = 7 (b) A = 90°, B = 20°, a = 7; (c) A = 58°, a…

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Q: A 15 inches candle is lit and burn at a constant rate of 1 inches per hour. Let T represent of hours…

A: Given that a 15-inch candle is lit and burns at a constant rate of 1 inch per hour.Let T represent…

Q: Use the Ratio Test to determine the convergence or divergence of the series. Step 1 Step 2 6 Recall…

A: By using the Ratio Test to determine the convergence or divergence of the following series.

Q: 4 Find all critical numbers of fa)=x² (x-23

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Q: 100. Given that f₁² xdx = 11/1, 2 S₁² x² dx = 2 1/37, and ₁² x³ dx = 1, 3 4 Compute ¹ (1 - x)² dx

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Q: Find the sum of the series: n=0 x³n-2 n!

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Q: This problem tests calculating new functions from old ones: From the table below calculate the…

A: The table value of the function and derivative functions are given.The aim is to find the  .

Q: 21. A window is composed of a rectangle with a semicircle above. If the perimeter is 16.0 m, what…

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Q: implicit differentation to find dy/dx use then dx²/da² 2y² = x² + 2x and

A: given equation To find:  and You have asking to find the

Q: Find the areas of the shaded regions in

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Q: 2. Prove that (₁ + ²)" is convergent by using the Monotone Convergence Theorem.

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Q: 9x Find the Maclaurin series of e 10

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Q: (2) Let f(x, y, z) = x²y + y²z. Find the directional derivative of f at the point (1,2,3) in the…

A: The given function is To find :- The directional derivative of f at a point  in the direction

Q: If xy + y² = 1 find the value of dy / dx² at the point (0-1)

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Q: Calculus 1

A: z=2x2+xyx=cost, y=2sint

Q: Find the exact value of each of the following under the given conditions. 6√85 85 5 sin a = 13 (a)…

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Q: Betty's Bathtub company produces two types of tubs: the Jazzy Jets model and the Double Dip model.…

A: We have to find the price of Jazzy Jets model and Double Dip model.

Q: The formula for the braking distance of a car is: 0.03361 v² μl d= where: . d is the braking…

A: given that,and find the d value for the given velocities?

Q: Let z = 5 e5π i/4 Write z, z4, z⁹ and 2-2 in the form a + bi. z = 5 cos (5.) +/-5 sin(5.4) 4 Z4 z⁹…

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Q: Simplify the following complex fraction; State the domain restriction: 1 X|N 2 1 1 X 1 -

A: To simplify the following complex fraction. To state the domain restriction.

Q: tan ¹ (sin x) √√x D) lim-

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Q: Find the equation of the tangent to the curve cos²x - sin²x y = at the point where x = I |4

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Q: Simplify the following rational expression. State the domain restrictions: a) b) x³-8 2x3-8a 9-x²…

A: Given two rational functionsand,.We need to find the domain restrictions.

Q: (4) Let f(x, y) = . Find the equation of the tangent line to the level curve f (x, y) = 0 at the…

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Q: ← The following graph shows the rate of inhalation of oxygen (in liters per minutes) by a person…

A: From the given data and graph,we can useLeft Riemann sumeach width= h =1At x=1, f(x)= 2.7 At x=2,…

Q: Find the arclength of the curve x = 5t 9, y = 12t – 3 with 2 ≤ t ≤ 5. -

A: x=5t-9y=12t-3

Q: Find the area of the surface obtained by rotating the given curve about the x-axis. ㅠ x = 5 cos³(0),…

A: Given curve,The surface obtained by rotating the given curve about the x-axis on the interval,

Q: Find the maximum value of the function z = 5x + 7y subject to the following constraints. x+8y≤48…

A: The given objective function Subject to

Q: A = 90°, b =6, c = 8

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Q: 4. Find the first five terms of the binomial series for f(x) = √√1 + x

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Q: Evaluate this integral | √2 3 (1+x) + C √x(1 + x² ) 5 dx (1+x)³ +C 3 ○ 2 √ (1 + x ³ ) 6 + C Va 3 6 3…

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