Evaluate the following integrals using (a) Trapezoidal Rule and (b) Simpson Rule by finding such that error is less than 10-6. 1. (1+2 cos x) dx (1-ex) dx -3 3. (x² sin x + tan x) dx

Q: Evaluate S dx √x² +25

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Q: Use Lagrange multipliers to find a relative minimum function value of f if f(x,y,z)= x² + y²+ z²…

A: Here, the given function is: f(x,y,z)=x2+y2+z2 with the two constraints…

Q: 10) x² + y² - 28x - 6y + 189 = 0 12) x² + y² - 32x+22y+376 = 0 2 14) x² + y² - 4x + 24y + 144 = 0…

A: Standard form of a circle is x-h2+y-k2 =r2,    where h, k  is the center of the circle and r is the…

Q: Determine the graph of g = x^2 + sqrt of (x + 1) and solve for its extrema, concavity, and points of…

A: Please see the below picture for detailed solution.

Q: What is (x - 12)² + y² = 144 in polar form? r = 24 sin 0 r= 24 cos 0 O Option 1 r= -24 sin 0-144…

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Q: 10. y (e-3x+4 +2)/(e2+3x +1)

A: The given function is ; y=(e-3x+4+2)/(e2+3x+1).

Q: Find the particular solution of y''-5y'=x-2 when x=0, y=0, y'=2

A: Given that that a non homogeneous differential equation and we find its solution.   Here i attached…

Q: 4. The region is bounded by y = x³, y = 2x + 4 and y=-1. The x coordinate of the centroid of the…

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Q: Find Vf at the given point. 3 f(x,y,z) = x³ + y² − 4z² + z lnx, (1,5,3) Vf|(1,5,3)+(+()k (Simplify…

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Q: dx x²√x² + 1 2 18. 1

A: Use substitution method for solving this integral.

Q: L²x√x-2dx

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Q: By using substitution of x-e' and t = ln(x), find the general solution of the differential equation.

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Q: dx √81+16x² S

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Q: Find the general solution of the given system. dx - 2x + 3y dt dy dt - 6x + 5y Ex(t), y(t)) 0

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Q: Q1/ From the following table of values, find the approximate value of f '(1.5)? X 1.0 1.5 2.0 3.0…

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Q: 2 1) x² + y² + 18x - 26y +246=0

A: Topic = Equations Only question 1 is answered , As per asked by student.

Q: Consider the spherical equation given by p = 4 cos sin p. Determine its corre- sponding equation in…

A: Given

Q: Answer and give the complete solution. Find the dimension of a rectangle whose perimeter is 500m…

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Q: y 4. Find the volume of solid of revolution by rotating y = √√x-2 and x = 10 about the y-axis.

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Q: If x = t² and y = t³, then y O t 3/4t O 3/t Other: = ?

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Q: Given the partial decomposition of the rational function for some numbers A, B and C. What is the…

A: Given :x+1(x-1)(x-2)(x+3)=Ax-1+Bx-2+Cx+3

Q: y = x¹, y = 2 = |x|

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Q: Water stored in an inverted right circular cone leaks out at a constant rate of 2 ft3 per day. The…

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Q: sin (x) dx (2+3 cus(x))² 3(2+3 cos(x)) с

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Q: (ارفق الاجابة) The eigen value of matrix [1] O 1+i, 1-i O 1+i, i 0 1,-1 1-i, 1-i *

A: On solving this we will get

Q: f(t)=sin(-t)- f(t)=1-cos(wt). soo.(10){SI=(1)f

A: We have to find Laplace Transform of given function.

Q: Find the value of (D) solve in detail 1219 = 20.88 * (0.015/60)1.85 4.87 D4 Ans. D= 0.0186

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Q: 4.Determine the area bounded above by y: 5 + x² and below by y = 1 + 2x²

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Q: 2. Find an equation for the plane that passes through the points P=(2,-1,3), Q = (0,0,5) and…

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Q: S dx √4x² - 49 x > 72

A: In order to integrate easily certain assumptions need to be made by using some variables.

Q: Equation Conversion from Polar to Rectangular Coordinates r² = x² + y² r cos 0 = x r sin 0 = y |× y…

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Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = -9x² - 6xy -…

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Q: let W = (x₁ +₁2) be jointly discrete. valid joint pdf a random vector. Contract of W (with atleast…

A: answer is in next step

Q: 1 √3 5) 2 2 / 9) (-1,0) 7) 3√3 3 2 2/3 " 2 ।

A: Topic = Geometry

Q: Part II: Point Conversions 1. Convert (2,7) into a rectangular coordinate. 2. Convert (4,-4) into a…

A: I am attaching image so that you understand each and every step.

Q: 1.30 Find the value of the integral ₁00 √x dx by using simpson method (n = 6)? 1.00

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Q: Find the value of x If f'(3) = 52? X 1 2 4 f(x) -2 8 x

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Q: A plane flies at a speed 580 km/hr at a constant height of 12 km. How rapidly is the angle of…

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Q: -x/3 Jx/4 cscxcotxdx

A: topic- definite integral

Q: Find Maclaurin series for the following functions Ans. Σ 2) 5 sin(-x) Ans. (-5x)" n! 5(-1)"(-x)2+1…

A: The given function is 5sin(-x). Repost the next question.

Q: me rose r = 4 cos 30 has 1 petal cannot be determined 6 petals 3 petals

A: Topic:- application of functions

Q: The sum of two numbers is k. Find the minimum value of the sum of their cubes.

A: Given

Q: dx Consider the integral S (x - 2)³/21 (a) Why is this an improper integral? (b) Determine if the…

A: ∫ 241x-232dx

Q: Question 15 : The altitude of a triangle is increasing at a rate of 2.5 centimeters/minute while the…

A: To solve the following problem

Q: f(x) = -(x − 1)² +4 Use the equation of the function to find each characteristic of the function.…

A: Given:        fx=-x-12+4 y-intercept:      To get y-intercept put x=0       y=-0-12+4…

Q: Find the area under the graph of the function over the interval given. f(x)=e*; [-5,2] The area is…

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Q: Give the domain and range. Then, use the graph to find (a) f(-2). (b) f(0), (c) f Ay 40 & M 2 X and…

A: Answer: The solution is given below:

Q: What is the area of the region enclosed by the graph of r² = 3 + cos 0? √ √3+ cos e de √(3 + cos 0)…

A: We have to choose correct option.

Q: 4x² + 4y² = 4y - 8x + 5?

A: equation can be written as 4x2+4y2-4y+8x-5=0 ⇒x2+y2-y+2x-54=0 Recall: if the general circle equation…

Q: 1) x² + y² + 18x - 26y +246 = 0 3) x² + y² + 16x +10y + 80 = 0 5) x² + y² - 22x+26y +254 = 0 7) x² +…

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