1.) Find the area of the region bounded by the curve ya 12 and the lines y=o, y=x, x=2.

Q: Show that x+iy | g+ix / = 1₁ =1, where X +iy and y+ix are complex numbers.

A: Here, let evaluate x+iyy+ix Using the absolute rule ab=|a||b|: =|x+iy||y+ix|

Q: P Playing a Game-Quizizz…

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Q: Find the 23rd term of the Arithmetic Progression -7, -3, 1, . . .*

A: 1.  The given arithmetic sequence, -7,-3,1,....... Note:     Multiple questions are given, we are…

Q: √ and g(x)= )=x² Let R be the region in the first quadrant bounded by the x-axis and the curves f(x)…

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Q: Problem #10] A kite 100 ft above the ground is being blown away from the person holding its string…

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Q: An open-top rectangular box is being constructed to hold a volume of 400 in ³. The base of the box…

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Q: 0 Compute the integral: I alned

A: LetI=∫01xlnxdxApply integration by…

Q: Two cars started at the same point but at different times (of the same day) and at different speeds.…

A: Car A left at 9am travel to west direction at speed 30kph,  Therefore at 2pm car A travel total…

Q: The function f is defined by the power series X f(x) = X +-목 3 5 7 for all real number X for which…

A: Let's find interval of converges of given power series.

Q: 3 =+1)

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Q: 2. Find the eigenvalues and eigenvectors of A = 2 1 0 1 2 1 1 2,

A: Given

Q: 3 Find x=x-12 lim. x-7-3 x2+ 8x+15)

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Q: Convert each pair of polar coordinates to rectangular coordinates  1. (2,150)  2. (4, 7 pie/ 4)

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Q: 3 1 L₁ dz -3 (x+2) ³0 Compute the integral:

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Q: The doubling time of an investment is the amount of time it takes to double in value. If an…

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Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: s dx 3x²+2x+5

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Q: 7π| A d) S_T/A (sin x + cos x) dx

A: We will evaluate the given integral in the following step.

Q: 5-x Find the family of the curve whose slope at any point is y-3 passes through the point (2.1) and…

A: Topic:- calculus

Q: -1 √₂² (3+2u) du -2

A:

Q: Evaluate the following integrals: O •(Cartesian to Polar) Civen the cartesian coordinate find FOUR…

A: Follow the procedure given below.

Q: Consider the series. 2 3 4 10 (¹) + ( )² + ( )² + ( )* +-- ∞ This series can be written as a…

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Q: Find the extrema of each given function on a specified closed interval. 1.) g (x)= x³ - (3/2)x²,…

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Q: 4. Determine whether the following statements are True or False? y = f(x) (a) _lim_ f(x) = 1 (b) lim…

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Q: 5x-2 Find the member of the curve whose slope at any point is y+s point (3, 2) and passes through…

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Q: You are to form 3-digit numbers from the digits 1 to 5. How many 3 digit numbers can be formed if a)…

A: Solution of given question is written in below steps.

Q: e²x-2x-1 x² f(x) = a) lim f(x) x⇒0+

A: Use limit concept

Q: Calculate the derivative of f(x) = sinh (x²). (Use symbolic notation and fractions where needed.)…

A: Using chain rule of differentiation.

Q: Find binomial coefficient (3)

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Q: (a) From Standard Form to Slope-intercept Form and Vice Versa (b) From Standard to Intercept Form…

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Q: Find Vf at the given point. f(x,y,z) = x² + y² − 4z² + z lnx, (1,1,3) Vf|(1,1,3) = i +(\)j + ()k…

A: Given the function,   fx,y,z=x2+y2-4z2+z lnx

Q: What is the expansion of the binomial expression (x + y)⁵ ? What are the binomial coefficients?

A: Solution of given question is written in below steps.

Q: 11.) Solve using matrices and Gaussian elimination: x+y+z= 9 -x-3y + 2z = 10 2x + z = 9

A: Please see the below picture for detailed solution.

Q: 2 √₁² √√x² - 4x + 8

A: The solution is given in the next step.

Q: Evaluate the integral. π/2 sin³ 0 cos²0 de 3

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Q: Find the slope and the rate of change of the slope with respect to x when x = 2 cos (3t) - 3 sin(2t)…

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Q: 11. Find the limit using algebraic techniques. The limit of f(x) = -4 O- 0 O=¹ x+4 2x²+5x-12 as x…

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Q: . Find the derivative of a composite function using the Chain Rule or General Power Rule. 1.)…

A: As per the company's guidelines, we are supposed to solve first three sub-parts for you, kindly…

Q: Find an equation for the plane that is tangent to the surface z = In (x + y²) at the point P(0,1,0).…

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Q: Σ (-1)" n=0 2n TT (2n)!

A: Given: The series is  ∑n=0∞ (-1)n π2n(2n)!

Q: Find the enclosed area by the curve with equation y = x² - 9 and the X-axis in the region [−1, 2] 24…

A: In this question, we want to evaluate the area of the region enclosed by the curves y=x2-9 and X-…

Q: 6+ З +2 (2x+1)= 8

A: 6x3 + 2(2x+1) = 8 2x + 4x + 2 = 86x + 2 = 86x = 8 - 26x = 6x = 66 = 1

Q: 1. Find the slope and the rate of change of the slope with respect to x when t = 90°. x = 2 cos(3t)…

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Q: 5) Given the price-demand and price-supply equations below, determine the equilibrium price and find…

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Q: 2 cos x = -0.7, 2TT ≤ x < 4T csc x = 2, 0 < x < 2TT sec x = -3, -π ≤ x < T 4

A: Given :cosx=-0.7cscx=2secx=-3

Q: 4. Find f'(x) if f(x)= In (2x) + cos (6x)

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Q: Find the linearization L(x,y) of the function at each point. f(x,y) = x² + y² +1 a. (3,4) b. (0,3)

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Q: 2 (0) IF F(x)= x 'e', Find f'(x) and F (1)

A: Finding the derivative of the function.

Q: 2. Given the function: f(x) 3 x -3 x≤2 2 x² + 1 x > 2 Is f(x) continuous and differentiable at x=2?

A: Here is the solution:

Q: Find the derivative of the function at Po in the direction of u. g(x,y)= x-y 3xy + 2' Po(-1,1), u…

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