Calculus lll  May I please have an explanation about how to calculate the derivative of the surface (the dS) on the surface integral, and then explain the essentials of the surface integral?

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Q: Find the derivative of the function. y= (8x²-6x²+3)4

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A: Step 1: concept  Step 2: solution  Step 3: Step 4:

Q: x The function of is shown below. If I is the function defined by g(x) = [* f(t)dt, write the…

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A: Step 1: The given vector field is, F=−ϵ Let′s verify the relation ∇⋅F(0,0,0) = limϵ→0+​ volume…

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Q: 1. Suppose f(x) = 2 4 == x+3 and g(x) = ½-½. Find and fully simplify ƒ(g(x)). Be sure to show all x…

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Q: The boom OA carries a load P and is supported by two cables as shown. Knowing that the tension in…

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A: (a)  g(x)=x1.4+2x2.5+1​ Step 1: Identify the numerator and denominator Let u=x2.5+1 (numerator)Let…

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Q: Find the distance from the point (-9, -3, 0) to the line ä(t) = (−4, 1, −1)t + (0, 1, −3) .

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Q: Use Euler and Heun methods to solve y' = 2y-x, h=0.1, y(0)=0, compute y₁ys, calculate the Abs_Error.

A: Given Differential Equation :-         y′=2y−x,y(0)=0,h=0.1     We solve this using  Euler's Method…

Q: 5 4. ·3. -2+ 1+ AN -5 -3 -4- 1 x 3 ད Graph of f The graph of the function f is given in the xy-…

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Q: 3. Find the derivative of each function. Label with appropriate derivative notation showing both…

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Q: For the given function, find (a) the equation of the secant line through the points where x has the…

A: Step 1:Step 2:Step 3: Step 4:

Q: Let 4x³ +3y3+42³ + 2xyz – 125 = 0. მ: მ Use partial derivatives to calculate and at the point (2,…

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A: Note- open circle at any point means value of function at that point is not defined or not included…

Q: Use the product rule to find the derivative of the following. p(y) (y¹ + y²) (6y¯³-10y¯4)

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the slope of the line secant to the curve F(x) = 13-x³ (from x=1 to x=2]

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Q: (10 points) Let S be the surface that is part of the sphere x² + y²+z² = 4 lying below the plane 2√3…

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Q: 1. Abel's Theorem. The goal in this problem is to prove Abel's theorem by following a series of…

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A: Horizontal Tangents: A horizontal tangent to a curve at a point indicates that the instantaneous…

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Q: answer a, b, and c

A: ANSWER : Let's solve this problem step-by-step.Problem 4: Suppose a renewable population grows…

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Q: 1. Using the definition of the derivative, find f'(x). Then find f'(2), f'(0) and f'(3) when the…

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Q: Let I = f(x) dx, where f is the function whose graph is shown. 4 2 y f X 1 2 3 4 (a) Use the graph…

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Q: A function f is even if f(x) = f(x) for all x in the domain of f. If f is even, with lim f(x) = 4…

A: Step 1: concept  Step 2: solution Step 3: Step 4:

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A: Solve this question step by step with full calculations.

Q: 5. Find the arc length of the curve y = 3x³/2 from x = 0 to x = 4.

A: Step 1: Step 2: Step 3: Step 4:

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A: We need to evaluate the definite integral,∫17​w2lnwdw Since we have a product of two functions, we…

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A: Since R(x) is a polynomial with real coefficients, its complex roots must occur in conjugate pairs.…

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Q: the correct answer is A could you show me why

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Q: Two forces are applied as shown to a hook support. The magnitude of P is 38 N. 50 N 25° DC a…

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Q: 15. A spring-mass system is governed by the differential equation 2x′′ + 72x = 100 sin(3ωt) .For…

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Q: 3. Compute the profit corresponding to 12,000 units. 5. A rectangular box is to have a square base…

A: STEP 1 : ​​  STEP 2 : ​​   STEP 3 : ​​ STEP 4 : ​​ STEP 5 : ​​

Q: Cable AB is 103 ft long and the tension in the cable is 3900 lb. 56 ft D y A B 20° 50° x C Identify…

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Q: The graph of the function f in the figure below consists of line segments and a semicircle. Let g be…

A: First, we need to understand the problem. The function g(x) is defined as the integral of another…

Q: A tank contains 200 gal of fresh water. A solution containing 4 lb/gal of soluble lawn fertilizer…

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A: a) Life expectancy of a jawbreakerWe can solve this by finding the value of t when we equate r(t) =…

Q: 4 In the integral dxf1dy (7)², make the change of variables x = ½(r− s), y = ½(r + s), and evaluate…

A: Introduction: We are asked to find the value of the double integral ∫021​​dx∫x1−x​dy(x+yx−y​)2with…

Q: Show how to use "Change of Variables Formula for Integrals" to solve "Separable Differential…

A: Step 1: Step 2:Step 3:Step 4:

Q: Find a parameterization for a circle of radius 4 with center (-4,-6,-3) in a plane parallel to the…

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Q: Find the interest earned on $10,000 invested for 6 years at 6% interest compounded as follows. a.…

A: Given:Principal (P): $10,000Time (t): 6 yearsAnnual Interest Rate (r): 6% or 0.06 Compound Interest…