I. Write 2 – 7i in polar coordinates on the complex plane. II. Find (1+ i)° using DeMoivre's theorem.

Q: 3 3. Vxydydx Vxdx Vydy Select one: True O False

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Q: 1 1) [ (tan³ 0 + tan³ 0) e-tan º d0== 2 (-1)" n! (In x)" dx= (m + 1)"+1 ·

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: d太 2.

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Q: x³ – 4x – 1 = 0 3 Consider the implicit curve throughout this problem. Find dy/dx and use this to…

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Q: Determine (4x³ + 3x2 + 5) from the first principle when x = 2 Determine the differential coefficient…

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Q: + Inx y(In2x – Iny)

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Q: Assume that $10000 is invested at an interest rate of 5% per year compounded continuously. (a) What…

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Q: Consider A = (0, 4, 2), B = (6, -1, 0) and C = (3, 0, 1). (i) Find the unit vector having the same…

A: vector

Q: 24. f)dx + fx)dr =,

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: What are the domain and range of functions? a) f(x) = cos^(-1) (In(tan x)) b) y= In( (x+1)/(x^(3)+1)…

A: A)f(x)=cos-1lntan xdomain of inverse of the function -1,1.-1≤lntan x≤11e≤tan…

Q: (3) Find the domain of f(x) = log(6 + x – x²) (A) (-∞, 3) (B) (-2, 3) (C) (3, ∞) (D) (-∞, -2) U (3,…

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Q: A rectangle is constructed with its base on the x-axis and its upper two vertices on the parabola y=…

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Q: 4. If f(t) = 3 sin(4t + 0.12) – 2 cos(3t – 0.72) determine f'(t) when t 1 5. Evaluate when x 1,…

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Q: Compute the directional derivative and gradient of f(x, y, z) = 4r – yez at (2, -1,0) in the…

A: Given: fx,y,z=4x-y2e3xz       at     2,-1,0 Directional Derivative = Gradient of function x unit…

Q: The angle below measures 5.4 radians, and a circle is centered at the angle's vertex. 5.4 rad,…

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Q: Consider the lines defined by the equations (3 : z – 3 = y – 5 = z – 6 and l4(s) = (-2 – 2s, –2s, 6…

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Q: 4. The surface described by the equation x2 + y + z² = 0 is a(an) (a) elliptic paraboloid symmetric…

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Q: dx If x2 - 2x – 4 is solved by trigonometric substitution, which of the following substitutions is…

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Q: (xcosx + sinx) dx + -sinx + 6 )dy y = 0;x=0;y=1 |

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Q: dx Using Trigonometric Substitution find f(0) 3 (x² + x + 1) 2 4 3 sec? e O 3 sec? e 4 O 3 sec e 4 3…

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Q: Find the area in the first quandrant bound by the parabola y

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Q: For the following function, find the Taylor series centered at z = 8 and give the first 5 nonzero…

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Q: 2) Find the equation of the tangent line to the curve y = cos(2x+ at x =

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Q: Express the polar coordinates (-2, -7) as Cartesian coordinates. (2, 0) (0, -2) O (0, 2)

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Q: If these two y's, y1=e^tcos(t) and y2(t)=e^tsin(t) are both solutions to y''+j(t)y'+k(t)y=0, how do…

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Q: Use the new command from Example 3 above to find the volume of the parallelepiped formed by vectors…

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Q: Convert the polar coordinates (1, 111) to Cartesian coordinates. O(/3/2, -1/2) O (1/2, -V3/2) O…

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Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

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Q: What is the slope of the line 0 = (Use decimal notation. Give your answer to three decimal places.)…

A: Slope of a line θ=a is given by m= tan(θ)=tan(a)

Q: Sketch the region whose area is represented by the integral Só Suz dxdy.

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Q: Find the area (in square units) of the region under the graph of the fu f(x) = 2x + 8 %3D square…

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Q: Find a formula for the total maintenance cost during the first x years. (Total maintenance should be…

A: Follow the procedure given below.

Q: Using Trigonometric Substitution  ∫ dx/ (x^2+x+1)^(3/2) find f theta

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Q: The dimensIons of awater tank are 13 cm, 10 cm and 70cm. If it is half-filled with water, cal-…

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Q: True or False, If f' (3) = f" (3) = 0. then I 3 MUST be an inflection point. (Remember = to give…

A: It is given that, f'(3)=f''(3)=0 then x = 3 must be an inflection point.

Q: Q5/Find the Laplace Transform 3-f(t) = sint cos t

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Q: What is the volume of the region R = {(x, y, z) ER/l < x < 3; 2<y< 4;3 < z < 5} ? Select one: O None…

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Q: Compute the derivative of each function. f (x) = e³x* += (cscx + sec x)² %3D %3D

A: Follow the procedure given below.

Q: Find the derivative of the function y=(4x+1)^5(3x+1)^-4

A: We can find the derivative as below.

Q: Given : S 6x³e**3 dx. Using integration by parts (S udv = uv – dv = 3g(x)dx find h(x) if ſ vdu =…

A: Let's find.

Q: Question 4 of 10 Find the volume of the solid that results when the shaded region is revolved about…

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Q: Find the general solution of ydy/dx =2/(3x2). O a. y?/2 =-2x/3+ C O b. y/2=-2/3x + C O c. y?/2 =…

A: 1. ydydx=23x22. The slope of the curve is 2x+1, passes through the point -3,0

Q: Convert the polar coordinates (2, 57) to Cartesian coordinates. O (1, -V3) O (-1, v3) O (-V3, 1)

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Q: 1 1. X CasCx y) dxdy. 0.

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Q: To evaluate dx using trigonometric substitution, which of the following is the new integral form in…

A: Given integral is ∫x2-x2-1 dx.

Q: I. Evaluate /4x2 + 4x + 5 dx

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Q: 100e0.05z thousands of Over the next 5 years, a company projects its continuous flow of revenue to…

A: profit = revenue - cost here  revenue for next 5 year R(x) = 100e0.05x R(5) = 100e0.05(5) R(5) =…

Q: Express the sum in sigma notation.-1/6+1/7-1/8+1/9-1/10

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Q: Sally is standing on a wharf that is 5m above the surface of the water. She is pulling on a rope…

A: Use the trigonometric ratios and application of derivative.

Q: y- cos(e) ]cix + dy = 0|

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