1. a. Given the points A(1, 2, 4), B(2, 0, 3), and C(4, 4, 4), i. determine the vector and parametric equations of the plane that contains these three points ii. determine the corresponding Cartesian equation of the plane that contains these three points

Q: Function h is graphed. h -4 -3 -2 L y 4 3+ 2- 1 -1- -2+ -3- 12 3 4 Find h(2) da. Give an exact…

A: This question can be solved using the concept of area under curve.

Q: xy³ = Let f(x,y)=2x²+y² 1 (x, y) = (0,0) Is f continuous at (0,0) ? Is f continuous at every point ?

A: If limit tends to 0 and function tends to 1 then f is continuous.

Q: 5. csc 6x dx

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Q: -valuate the following 3 .4 3 2 x² + 2x³ + 3x² + x + 1 x4+x²

A: A detailed solution is given below.

Q: Set up only an iterated double integral that gives the volume of the solid over the region R, where…

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Q: The graph shown is f(x) = 1⁄x². Y 5 4+ 3 2+ 1 + 54 3-2-11 1 2 3 4 5 -2 -3- 4 -5 X If g(x) = f* f(t)…

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Q: Example 1: Evaluate the integral: ₁²²=238+1² 2r-3 - 3x + 1 dx.

A: The given integral is (2x-3) /sqrt(x2-3x+1), limit from 3 to 5.

Q: Q1.. Find domain and range for following functions: (2 20 a) y = {1x<0 {² D f(x) + D g(x) = D(f(x) +…

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Q: approximation of the function of the function f(x, y) = ln (x - 3y) om and 40 cm : Find the linear…

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Q: the point type of the function [f(x,y) = x^2+xy+y^2 +3x-3y+4 ] is Relative Minima O saddle point O…

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Q: Q4: Solve the following integration corrected to 3 decimal places using: 1. Trapezoidal rule 4…

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Q: 15. Evaluate [sin50 cos²0de. COS

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Q: ∫ 2cos^2(x)sin(3x)dx

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Q: 5) y = tanx secx 6) Y = b x+1

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Q: X 4. f* - 2x² - 6x +1 2 x² - 2x-8 dx

A: We have to find the integral.

Q: Use Chain rule find the derivative w= 4x^2 +3y^2 with respect to t along the path x=sint and y= cost…

A: Note: “Since you have asked multiple question, we will solve the first question for for you. To get…

Q: dx (x² +25)3/2

A: To find the integration.

Q: . The sides of a cube are found to be 6 feet in length with a possible error of no more than 1.5…

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Q: 6. Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

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Q: Solve the following integration corrected to 3 decimal places using: 1. Trapezoidal rule 4 intervals…

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Q: 5. Use the substitution method to evaluate So 3x²+2 x3 + 2x +37 dx.

A: Topic = Integration

Q: Find the area of the region bounded by the curves y = sqrtx and y = −x^2 between x = 0 and x = 1.…

A: Here we have to find the area of a region.

Q: The function f(x, y) = x² + y² √x² + y² +1-1' (a) {(x, y) = (0,0)} (b) {(x,y) = R²2} 2 if : (x, y) =…

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Q: x² −x+3 Can the Fundamental Theorem of Calculus be used to find 52 dx? ○ No, f(x) = x²-x+3 3√x is…

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Q: 2. . If f(x) dx = 4 and 3g(x) dx = -9, evaluate [² [3f(x) + g(x)] dx

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Q: A. Consider a 100-meter track used for foot races. The time it takes for a ru run the track can be…

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Q: Qs/ Find the ave of the region R enclosed by the parabola x = - y²) and the line Y. X +2

A: find the shaded area

Q: hat are all of the solutions for the equation 3cos(3θ) – 8 = –11 on the interval of [0°, 360°)?…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Find the volume of the solid that results when the region enclosed by y = √√√x, y = 0, and x = 49 is…

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Q: Show that the function f(x, y) = 3x - 4y² is differentiable at point (−1, 2)

A: answer is in next step. please give a like !!!

Q: Write out the first four terms of the Maclaurin series of f(x) if f(0) = -5, ƒ'(0) = 10, f(x) = +…

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Q: Let f(x)=x²+2x if x<5 - Cx if x 25. For what value of the constant c is the function f continuous on…

A: We have to calculate the value of c

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: (a) lim x→0+ (sina) 1 (b)…

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Q: 12. A thin 4 cm wire represented by 1 < x < 5 has density function p(x)=19/cm. Find the mass of the…

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Q: 4. Evaluate the double integral that will find the volume of a solid inside the paraboloid z = 1 -…

A: We need to find volume.

Q: xe. xe2x dx

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Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

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Q: Find the general Solution of the following PDES • з Их + 2 Иу , u(x,c) = чех (3У-2х)12 ans3- исх, у)…

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Q: Find the Fourier transform of (x) 3x iPxK1 O if|x1>1

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Q: Evaluate the double integral: 2 So de dy. Sola 0 Jy¹/3 Y x7 +1 (Hint: Change the order of…

A: Application of integration

Q: Q4\ Find the average value of f(x,y) = (+√) where 0≤x≤y and 0 ≤ y ≤ 4.

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Q: find the given differential solution, using homogeneous equations with constant coefficients.…

A: Solution: The objective is to find the general solution of the given homogeneous differential…

Q: 1. Identify the surfaces of the following equations by converting them into equations in the…

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Q: Find the number c that satisfies the conclusion of the Mean Value Theorem for this function f and…

A: This question can be solved using the concept of mean value theorem.

Q: 6. Find the dimensions of a rectangle of the largest area that can be inscribed in a circle. 7. An…

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

A: To find the volume of the solid that results when the shaded region is revolved about the indicated…

Q: Find the value of t(5) if you are give t(3)=-1 and the non-recursive formula is given as…

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Q: let f(x)=x2 -9y  and  g(x)= √x. find the domain of (f o g)(x) and h(x)= 1 / (f o g)(x)

A: Let f(x)=x2 -9x and g(x)= √x. Now,        (f o g)(x)=fx                =x2-9x                =x-9x…

Q: √tanx secox dx

A: Given problem:- ∫√(tanx) sec6x dx

Q: 2. Solve each of the following integrals using integration by part: a) √3x² In 2x dx b) 5x sin 3x dx

A: Integration is evaluated.