y = x² + 1 y = 2r- 2

Q: 15. xydx + 2(x² + 2y²)dy = 0

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Q: x/2 2. dy Sin x dy +34 2- X 2

A: A detailed solution is given below

Q: Find the area of the region between the curves y = 12 – a? and y = x² – 6. Area between curves =

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Q: Geometric Sequence A. Find the indicated terms of the following geometric sequences. 4. 3, 6, 12,…

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Q: 3 dx 2 х2+1

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Q: Consider the line which passes through the point P(1, 3, -5), and which is parallel to the line æ =…

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Q: Find each function value and limit. Use -∞ or co where appropriate. 7x* - 14x2 f(x) = 8x° +4 (A) f(-…

A: topic- functions and limits

Q: 3. Evaluate the integral x³ - 2x? – 4 dr x³ – 2x? |

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Q: Sketch the integration region of the following integration aud evaluate the integral (xソー2xり)dy dx…

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Q: Problem 6 Use the rules of differentiation to to find the derivatives of the functions: (a) f(r) =…

A: topic- differentiation

Q: "(x) If t(x) = Vx find ť'(x)" -2x O 2x -1/2x O 1/2x O None of these O o o o

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Evaluate the following indefinite integral. f11 de dx = (Type an exact answer.)

A: To find out the integration.

Q: Which of the following is TRUE about logarithms and logarithmic functions? i. The argument…

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Q: 2X 3- dy + 2 (9e-x) dx = o e SinX dy + Cosx y tan x 4-

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Q: |+ 3t -dt 11t Simplify the integrand by dividing eac .5 |+ 3t -dt = 11t |dt Type an exact answer.)

A: Given:∫1+3t511tdt

Q: Find the volume of liquid needed to filla sphere of radius R to height R y V

A: Given that  Radius of sphere = R       and Find volume of liquid  at height at R/2.

Q: and ue. Find the velocity and acceleration vectors in terms of u, r= 5 sint and 0 = 8t

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Q: PERFORMANCE TASK 1. The population of a city years from now can be modeled by the function P(x) =…

A: Concept: Graph: A graph is a graphical representation of data that is organized on a graphing plane…

Q: Which of the following could be true if f'(x) = -x O f"(x) = 3 f"(x) = 4x f(x) = -æ O f(x) = -x

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Q: x-3 dx r³+9x +9.x

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Q: fi(x)-2• sin(x) -3- R 3- 5- 3.* 4. 4 2 -2

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Q: 3) Explain why the Cartesian equation 2x– 5y+ 3z = 2 does not describe the plane with normal vector…

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Q: Find

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Q: n-1 Consider the series n=1 Find the sum. If it doesn't exist enter "DNE"

A: We have to find out the sum

Q: The graph below shows Bob's velocity as he walks in a straight line from his home. miles min (4,2)…

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Q: Find the arc length parameter along the curve from the point where t= 0 by evaluating the integral…

A: Given problem:-

Q: dy given the dx Use implicit differentiation to determine equation x? + y² = 4. dy dx

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Q: Differentiate the function. t(t² + 1)4 g(t) = In V8t – 1 - g'(t) =

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Q: Find and classify the critical points of the function: f(z, y) = 1' + y* – 144zy + 4 Local maximums:…

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Q: Write an equation for the polynomial graphed below 5 4 3 1 2 -1 -1 2 3 4 5 -5 -4 -2 - -3 -4 -5 +…

A: topic- polynomials

Q: dy given the dx Use implicit differentiation to determine equation x° + y? 10. - dy dx

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Q: Use your calculator to find the area shown in RED. 8 f(x) = sec(.5x+2) + 2 tan(.5x + 2) +3 Round the…

A: The region is bounded by the curve,fx=sec.5x+2+2tan.5x+2+3 from x=0 to x=5

Q: Write a in the form a = a-T+ anN at the given value of t without finding I and N. r(t) = ( - t+ 4)i…

A: Here, r(t)=(-t+4)i+(2t)j+(t2)k⇒r'(t)=(-1)i+(2)j+(2t)k⇒r''(t)=(0)i+(0)j+(2)kSo,r'(-1)=-1,2,-2 &…

Q: Let -1 <r< 1, the series r na" is the power series representation of the n-1 function

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Q: The area of the region that lies to the right of the y-axis and to the left of the parabola æ = 2y –…

A: topic- Area bounded by curves

Q: Vnx" 00 3" n=0

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Q: Consider a rectangle with the following property. Perimeter: 112 meters Let w represent the width of…

A: A rectangle has perimeter 112 meters.

Q: The equation y = log(x – 5) has a vertical asymptote at: - X =

A: Consider the equation  y=logx-5

Q: dy Given the equation below, find de 1722 + 8x8y + y° = 26 dy dx Now, find the equation of the…

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Q: (c) SUPPLY RATE When the price of a certain commodity is p dollars per unit, the manufacturer is…

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Q: Find the limit. lim ---X +4 Step 1 1 x+ 4 as x approaches -4 from the left. Note that we cannot…

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Q: For the given polynomial o find the maximum possible umbers of the positive and the negative root o…

A: Roots

Q: f (x) = x³ + 4xª + 3x³ – x² + & 1. ,2 -

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: Find the volume of the solid obtained by rotating about the y-axis the region bounded by y=x² and…

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Q: Q1): Find the point (x, y, z) that lines on the plane x +y + 2z = 4 that is nearest to the origin.

A: This question can be solved using the concept of distance of point from a plane in three dimensional…

Q: Find the slope of the tangent line to the curve (a lemniscate) 2 (z? + y?)° = 25(x² – y²) at the…

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Q: 1. Which value of k will make the lines: r = (1,2) +s(2,3), s e R and 9x + ky = 0 parallel? 2.…

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Q: Find the indefinite integral. Check your result by differentiating. (Use C for the constant of…

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Q: A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular…

A: A norman window has the total perimeter 8 feet.

Q: Sketch the integration region of the fallowing integration aud evaluate the integral JS (xy-2xy) dl…

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