Determine the valve of the following define interal first by tinding the appropriate antiderivate then applying the fundamentell the ore m of culculus. Any basic rule from the basic rules must be cited in YOur solutions 5 ex +5X+ + Los 6) dx

Q: Find both first partlal deriva N = sinh(8x + 13y)

A: The function given is z= sinh(8x+13y) and we know that derivative of sinhx is coshx

Q: 5. (x² + y2 + 1)dx + x(x – 2y)dy = 0,x = 2,y = 3 %3D

A: Solution

Q: A cylindrical can, open at the top, is to hold 400 cm3 of liquid. Find the height, h, and the…

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Q: Choose among the following suitable to define the given S(e + +) arctan{ dx O By parts, the red part…

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

Q: 1- Use trapezium's Rule with n = 4 to approximate the integral Vx dx

A: We have to use formula of Trapezoid Rule.

Q: use Taylor’s formula for ƒ(x, y) at the origin to findquadratic and cubic approximations of ƒ near…

A: Given: The function f(x,y)= sin x cos y

Q: A cylindrical can of height h and radius r is to be made with a fixed volume V. Show that the area…

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Q: A uniform volume charge density of 0.2 uC/m³ is present throughout the spherical shell extending…

A: A uniform volume charge density of 0.2 μC/m3 is present throughout the spherical shell extending…

Q: Ue fe Einemial Theorem to ine tre coeficit ofnthe eparsion of ir+ 31

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Q: Show that the equalion Compatible 3olutions are and also find its रिकेपन nd देक.र

A: P2+q2 =1 given therefore 1x =pz P =x/z.  ...(1) q2 =1-p2      =(z2 -x2)/z2 q =z2-x2z ....(2)

Q: Consider the integral Í dx . For which value of n the error in trapezoidal rule will be less than…

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Q: V. A hemispherical basin of radius 4 ft contains liquid to a depth of 3 ft. If the liquid weighs 48…

A: This is a problem related to pumping volume of the spherical basin to the 3 ft above the container.…

Q: 44) Find a horiz antal Cine y=k +hat the between y = x? and area y = 9 into two equal parts.

A: Solve the following

Q: Use geometry to calculate (without integrating): o V16 – x2 dx Note that f (x) = v16 – x² is the top…

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Q: Consider the curve segments: 1 $1: y = x² from x =to x = 3 and 3 1 52: y = Vx from x =to x = 9. Set…

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Q: 2 By using Trapezoidal rule, the value of "h" in evaluating - 2x + 6)dx , by taking 10 subintervals…

A: Solved below

Q: A cylindrical can, open at the top, is to hold 200 cm³ of liquid. Find the height, h, and the…

A: Consider the given: The given volume of the cylinder is 200 cubic cm. V=πr2h200=πr2hh=200πr2 Find…

Q: Compute TOT/ cos(y³) dydx. [Hint: Change the order of the integration.] Show your solution. Select…

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Q: Evaluate the integral [x dx for n=4 by using (a) Trapezoidal rule (b) Simpson's rule. Compare your…

A: The trapezoidal rule uses the formula below to approximate the integral for an interval.…

Q: Which of the following shapes have half the volume of a solid cylinder with radius 3 and height 10?…

A: Given the volume of shape is  HALF the volume of a solid cylinder with radius 3 and hight 10. we…

Q: 1. , Trh. Suppose that the The volume of a right circular cone of radius r and height h is given by…

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Q: Queston Ser x²-4 Composite Trapezoidal rule with n=4 3.1.1. use the to approximate integral. 3.1.2.…

A: Note:- For part (2), you don't mention method name so, i assume it Trapezoidal rule with n=3. If you…

Q: The radius of a sphere is measured and found to be 3 ft. with a maximum error of 0.1 in. Find the…

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Q: A trapezoidal plate with height h and bases a and 2a is submerged vertically in water as shown.…

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Q: The volume of a right circular cylinder of radius X and height y is given by V= TXy, Suppose that…

A: Given Information : The volume of a right circular cylinder of radius x and height y is given by V =…

Q: Suppose that a cylindrical tank initially containing Vo gal- Use Torricelli's law to show that the…

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Q: Choose among the following suitable to define the given integrations: * f(x + 1) sinx dx Not…

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Q: (b) 3 – cos(x) 2

A: Follow the procedure given below.

Q: #z. {valvate the following definite intgrals. .3 elx 9. Cosx Sinx lx

A: We have to solve

Q: * Using integration by parts, the integral sec³dx is equal to 1 1 - secxtanx +In|secx +tanx| + C 2 1…

A: Use by parts method of integration

Q: Evaluate using integration by parts. .5 x° In (x)dx x° In (x)dx=| (Type an exact answer.)

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Q: 2) By compating aderivatives, find the Tay ior for tixl= la x at

A: By using Taylor series expension of lnx

Q: Consider the curve segments: 51: y = x from x =to x = 3 and 1 52: y = Vitrom x =; to x = 9. Set up…

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Q: 4) A spherical tank is full water with the spout at the Lísdest point on the tank

A: Given, a tank has a radius=4 ft                           spout length=1 ft

Q: The shaded region, R, is bounded by the graph of y = x² and y = 4, as shown. y =x? a. Find the area…

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Q: Given: J Vx sinh TV

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Q: How large should n be to guarantee that the Trapezoidal Rule approximation to - 2 | (- x* – 12a –…

A: Given the given integral is ∫-4-2-x4-12x3-48x2+2x+5dx. Use formula for Trapezoidal rule…

Q: Determine h and N to approximate the integral e- dt within an accuracy of G = 10-5 using the (i)…

A: ii)  Equation is f(x)=exp(-x2).The value of the table for x and y x 0 0.25 0.5 0.75 1 y 1…

Q: The uniform beam has a mass of 42 kg per meter of length. Determine the reactions at the supports. y

A: Let us start solving the problem step by step  Acceleration due to gravity is g=9.81N/m2

Q: Compute the defined integral So [1+ e* sin(4x)] dx using the trapezoidal method with two segments.…

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Q: I+tgX dx; 2 COS X cos

A: Given: ∫1+tanxcos2xdx

Q: A tank in the shape of an inverted cone has a base dia- meter of 1.5 m and a height of 2 m. A 4-cm…

A: We have to find time required to empty the tank.

Q: Find the length of the curve y = In x from x = V3 to a = 2/2. o 1+홀 In를 None of the choices. Please…

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Q: Consider the integral dx . For which value of n the error in trapezoidal rule will be less than…

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Q: Find the area enclosed by one loop of the lemniscate with equation  r^2 = 16cos(2theta) with…

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Q: Compare the Trapezoidal rule and Simpson's rule approximations to x sin x dx and find a bound for…

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Q: Each rear tire on an experimental airplane is supposed to be filled to of 40 pounds per square inch…

A: a) value of k: Given density function: f(x,y)=k(x2+y2), 30≤x≤50, 30≤y≤50 Consider,…

Q: A string of length 27 m has both ends free. Initially the string has a vertical displacement of the…

A: The complete solutions are given below

Q: What is the radius (r) and height (h) of a cylindrical can holding 1L of oil that minimizes the cost…

A: 5

Q: A Cylindrical tank below with radius(R) and hight (H) have two holes ,one at the side at distance…

A: we have given a cylinderical tank with radius R and height H , two holes one at side at distance a…