Use the Chain Rule to differentiate the following function. f(x) = (3x² + (4x-5)4)7 f'(x) =

Q: -9-x²-y² L.**** 1 dz dy dx 0 (a) Sketch each of the following: • the solid E . the projection of E…

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Q: Solve the given differential equation. All solutions should be found. dy 3x² – 2y - y³ 2x + 3xy² dx…

A: Given differential equation is dydx=3x2-2y-y32x+3xy2

Q: 6 + 5 4 3 2 H -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 + The graph above is a transformation…

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Q: Question 2: Let E be the solid inside the surface x² + y² + z² = 10% and above the plane z = 5. (a)…

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Q: Q21 By using Adjoint method, find the inverse of the following matrix. [1 -3 -1 A= 4 2 LO 2 Add file…

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Q: f(x) == What is 1 a) Consider the function its domain? b) Now consider the function g(x, y) = ².…

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one…

Q: Find the length of the curve. r(t) = √√2ti + etj+ek, 0≤t≤7

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: or what values of x does the graph of f have a horizontal tangent? (Use n as your integer variable.…

A: For horizontal tangent slope y' = 0

Q: * The following function f(x) = x^4 sinx is odd о neither O O even

A: Replace x with -x

Q: Using the Midpoint Method, calculate y(0.4) for the following: y' = -5x¹y², y (0) = 1, h = 0.2 1 The…

A: Solution is here

Q: Determine whether the differential equation (4x² − 2xy + 6) dx + (2y² − x² + 4) dy = 0 is exact. If…

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Q: 9-1² 9-1²-² 1.****** (a) 1 dz dy da Sketch each of the following: . the solid E • the projection of…

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Q: C

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Q: 3 3 x³ - y³ z = f(x, y) = x² + xy + y² 0 for for (x, y) = (0,0) (x, y) = (0,0)

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Q: Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate…

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Q: Which one of the following is the gradient of the tangent line at the point (6, -3) on the graph of,…

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Q: The figure to the right shows the velocity, v (in feet/second), of a runner for 0 < t < 15 seconds…

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Q: Find the solution of the given initial value problem. ㅠ ty' + 2y = sint, y (-) - = 5, t > 0 Y ||

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Q: 63 x dx 3√ √x²+1 S √(x² + 1)² + C Option 1 O (x² + 1)² + C Option 3 213 √(x² + 1)² + C Option 2…

A: We have to evaluate ∫x dxx2+13.

Q: b) Maximize the volume of this rectangular box. c) What are the dimensions & volume of this largest…

A: Solved below.

Q: Solve the given initial-value problem. Give the largest interval I over which the solution is…

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Q: Solve the equation | +6 - 4. The solutions are 1 = and 2 = where ₁ ≤ x2. This means x₁ is the…

A: Given,  |x+6|=4

Q: In a certain region there is a uniform current density of 15.0 A/m2 in the positive z-direction.…

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Q: Rewrite the given function with a rational exponent. 7|X 8 = y In X + 8 = In x + 1 || In x + 00 8 00

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Q: 8. Find the area bounded by y=ex, y=x² and x=2. a. 3.1 u² b. 4.1 u² c. 5.1 u² d. 6.1 u²

A: Here we have to find the area bounded by the given curves.

Q: Q2: Find the following limits V-V lim x418√√x+√ 友

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Q: Solve the given differential equation. All solutions should be found. dy 3x² - 4y - y³ 4x + 3xy² dx…

A: Explanation of the answer is as follows.

Q: Find the unit tangent vector T(t) at the point with the given value of the parameter t. 2t r(t) =…

A: In this question, we want to find the tangent unit vector of r(t) at t=0.

Q: The height y (in feet) of a ball thrown by a child is 1 -x² + 4x + 3 y = 16 where x is the…

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Q: Consider the region R bounded by the curves y = 2 sin(2x) and y = 0 in the interval [0,1] with a…

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Q: Consider the initial-value problem y' + ey = f(x), y(0) = 1. Express the solution of the IVP for x>0…

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Q: Fill in the blank. The symbol C₁ represents a constant. - (6 + C₁e-⁹x)= Write this result as a…

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Q: • Find the volume generated by revolving area about the given line plane the given

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Q: The dimensions of Roy and Roger's sandbox are t² meters by t5 meters. One cubic meter of the sandbox…

A: dimensions of the Roy and Roger's sandbox : length =  t2  width = t5 height = v2…

Q: need helping understanding this concept And why each statement is false or QUESTION 1 Check all…

A: We have to consider the given statements are true or false according to the given information

Q: A/ By using Linear equation solve the first order differential uation y' + sec(x)y= cos(x)

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Q: Q4\ Solve by Gaussian elimination x-4y-2z = 21 2x+y+2z = 3 3x+2y-2=-2

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Q: State the order of the given ordinary differential equation. (sin e)y"" - (cos e)y' = 3 Determine…

A: The order of a differential equation is the order of the highest derivative present in the given…

Q: Find the derivative of the function. g(x) = (sech(7x))² g'(x) =

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Q: السؤال الثالث Question Three * Q3. For the motion vector r(t) = et cost i + et sint j , find: (i) N…

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Q: Find for THREE of the following functions: dx 1-y()+In(cos(x)) + √2-y=2(cos(x))*(x)

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Q: Use the chain rule to find the indicated partial derivatives. z = x4 + x²y, x = s + 2t - u, y = stu2…

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Q: Q5) Find dw/dt at the given value foe the following functions 1) w = x² + y², x = cost, y = sint at…

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Q: Solutions converge to the function y =

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

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Q: Solve the given initial-value problem. Give the largest interval I over which the solution is…

A: We have to find the solution and the interval.

Q: Solve the following system of linear equations: X₂-5x₂+x3 = 2 If the system has infinitely many…

A: The given system of equations,        x1-5x2+x3=2

Q: Find an explicit solution of the given initial-value problem. 없을 y(7) = 7 1

A: Find an explicit solution of the given initial-value problem.         dydx=y2-1x2-1  ,    y7=7

Q: Q4\ Solve by Gaussian elimination x-4y-2z = 21 2x+y+2z = 3 3x+2y-2=-2

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