4. Determine the equation of the plane passing through the point (1, –4, 3) and parallel to x – y +3z = 5.

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A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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A: We have to solve above problem.

Q: 2. Let A = (1,0, 1) and B = (0, 1, 3). Solve for projaB.

A: ProjBA=B⇀.A⇀A⇀

Q: dz az and ду Suppose z is a function of x and y, and tan Vy? + x2 = ze6y. Solve for

A:

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A: To evaluate the given iterated integral.

Q: 6. S 2sin´x sin(2x) dx

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Q: LEARNING TASK 1: Determine the antiderivatives of the following functions: 1. f(x) = (x+1) 100

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: 3. f(x) = (2x + 1)3 4. f(x) = V7 + V3x + 1

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Q: 11. A spherical balloon is inflated so that its radius (r) increases at a rate of (2/r) cm/sec. How…

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Q: 1 - 2 9) Ans. r = 1

A: Given the matrix . We need to find it's rank. As we know that rank of a matrix is number of non zero…

Q: Find the first three nonzero terms of the Maclaurin expansion of the function. f(x) = 8 cos TX ...…

A: The Maclaurin series is given by  f(x)=f(0)+f'(0)1!x+f''(0)2!x2+f'''(0)3!x3+...

Q: x = -2t x - 3 1 – y Given: line l1 : 4 = % – 8 and l2 2 y = 2+ 2t - % = 6 + 2t 1. If the given lines…

A: We have to find angle between the lines L1 & L2

Q: 1. S-7e*dx 2. S(2ex – 6*)dx S(3)dx 3.

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: 2. For the parametric equation shown below, determine the value of (dyldx) and (d²y/dx?). x = 3t? –…

A: To find dydx& d2ydx2 using the given parametric equations.

Q: 1 1 1 dx x+2, x+1

A: We can solve this as follows:

Q: Mary, Martha and Lazarus lives in the same house. It takes Mary 2 h to clean the house alone. Martha…

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Q: Si cos3x cos4x dx 2 TT 6

A:

Q: (6) Use the linear approximation of the following (Answers are to be expressed in 4 decimal places.)…

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Q: Use (a) bisection method and (b) false position method to find the solution to the following within…

A: Note: There are multiple questions. Few questions has multiple subparts.No specific question has…

Q: xチ+1=4 DIDX= 2-2y (ost) X= 3サ-3 *キーに h で3,0) サ=2メー オー×ポーカ toノー4) メッとナ+ム メーリー3

A: Explanation of the answer is as follows

Q: 2) Eliminate the arbitrary enstant, 4 y= x*+ Cix + Cz e-X

A: Given problem:- Eliminate the arbitrary constants. of y= x² + C₁x + C₂ e-x

Q: vertical asymptote z=0 S'(z) > 0 for z -3, (z # 0) f"(z) 0 for z > 0

A: Let's find.

Q: Write a in the form a = a7T+anN at the given value of t without finding T and N. r(t) = (- 2t + 3)i…

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Q: Find the inverse transform, indicating the method used and showing the details: 2s - 10 -5s 1. s3 3s…

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Q: Q2: Evaluate o o" y*(x² + y²)dx dy 1 cV1-y? y² (x? + y?)dx dy

A:

Q: Each side of an equilateral triangle measures 3cm, with a possible error of 0.1cm. Using…

A: The area of a quadrilateral triangle is: A=34x2 where x=side length =3 cm So, A=34(3)2=934cm2

Q: e problems y' + e = 0, y(0) = 1 %3D

A:

Q: Compute the area enclosed by the curves. You must show your work. Express your answer as a fraction.…

A: In this question we have to find the area enclosed by the curves.

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A: We have to check of the objects collide.

Q: Find the set of all values of x at which the line 3x-y+k= 0 is a tangent line to the -3 curve f (x)=…

A: We need to choose correct option.

Q: Зx+1 5. f(x) %3D 3x2+2

A: f(x)=3x+13x2+2Differentiate…

Q: Suppose z is a function of x and y, and z^xe^6y=y2+x2. Solve for ∂z/∂x and ∂z/∂y. [b]

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Q: Expand and simplifyW – 35) · (5 + 2w)

A:

Q: -Sune +1

A: This question is based on solution of Trigonometric equation.

Q: Find, the genetal Solution of the differehtial equation (2x+Y-3) dy= (f+2Y-3)dX

A: Given problem:- Find the general Solution of the differential equation   (2x + y - 3) dy = (x + 2y -…

Q: 27. f(1) = 1 + e*i 28. f(1) = r² - e- + 5 29. f(1) = (1 + e²)2 30. f(1) = (e' – e¯)? 31. f(1) = 41²…

A:

Q: The following question is about the rational function (x + 1)(x - 2) rex) = (x + 2)(x – 6) The…

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Q: ne differe htial equation 25+ソ-3)dy = ($424-3}dy

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Q: 1. Given the vector ū = (2,0, 1). (a) Solve for the value of a so that ữ and i = (a, 2, a) form a…

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Q: Question 1 Determine the inverse Laplace transforms of: 2s2-5s-1 (a) (s+3)(s²+9)

A:

Q: 8x + 1 10. Evaluate the integral / dx. 4.x2 + 12x + 10 11 (a) In |4.x2 + 12x + 10|| tan-(2x + 3) + C…

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Q: dx Evaluate the integral 7+6x – x²

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Q: Consider and know that the function g defined by 1 g(x, y) = cos (TX /y) + log3(x – y) Answer the…

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Q: 1. Consider a point in Cartesian coordinates given by (-2, 2v3, 4). (a) Find a corresponding…

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Q: 2x^ + xt3 dx x+ x a. In lxl+Ź In Cx t1)+ tan-"c) tc b. In \xl-Į m (x2+1)+ tan-' Cx) tc in e, wone

A: The integration of the integral is  (2x2+x+3)/(x3+x).

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A:

Q: Assume that the radius r of a sphere is expanding at a rate of 90 cm/min. The volume of a sphere is…

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Q: lo-2 2 (12y-8x) dy da

A: Given: ∫05∫0z2∫010-2z12y-8xdydxdz

Q: Question 1 Determine the inverse Laplace transforms of: 2s2-5s-1 (a) (s+3)(s²+9) (b) 352+5s+1 (d)…

A: Let's find.

Q: For the function f(x) = xe-2x give intervals of increase/decrease and intervals of concavity.…

A: Let's find.