5. Use Lagrange multipliers to find the extreme values of the f (x, y) = x² + 2y² subject to the constraint g (x, y) = x² + y² = 1.

Q: Question Let h(x) = f(x)g(x). If f(x) = x² – 2x − 2 and g(x) = -4x, what is h'(x)? Select the…

A: To find the derivative of the given function.

Q: A particle moves along the x-axis so that its velocity at time 0 < t < 18 is given by v(t), whose…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 6t+ 6…

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Q: A function h is dependent on x and is differentiable for all real numbers. Let f be the inverse of…

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Q: y = С₁e-¹/² + С₂e-4t

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Q: INTEGRAL CALCULUS (UPVOTE WILL BE GIVEN. PLEASE WRITE THE COMPLETE SOLUTIONS LEGIBLY. NO LONG…

A: We will find the required.

Q: Find the inverse transform of the given function of s. 3s + 8 s2+8s + 20 F(s)--

A: Follow the procedure given below.

Q: Use logarithmic differentiation to find the derivative of y = (In(4x))(5x) (where x > 1/4 so that…

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Q: Find the Differential Equation whose general solution is y = C₁e-¹/² + C₂e-4t O 2y" -9y' - 4y = 0…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Question 8 Solve the given differential equation (where the function is subject to the given…

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Q: Consider the following integral. Sketch its region of integration in the xy-plane. 1 y So 180x³y³ dx…

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Q: 81.2² 18 3x-2 = For the rational function h(x) a. Find any intercepts of the function. State them as…

A: to find the y-intercepts, take x=0

Q: Graphs of the velocity functions of two particles are shown, where t is measured in seconds. (a) (b)…

A: Speeding up: A particle is said to speeding up on a interval if its magnitude of velocity is getting…

Q: 10. Find the absolute min and absolute max of h(s) = 2s³ + 3s² – 12s for −3 < s < 2.

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Q: Determine R(t) if R'(t) = <2e2+-4,4 =-1) and R (2) R (2) = <3₁-5,0).

A: To determine R→t if R'→t=2e2t-4, 6t2, 1t-1 and R→2=3, -5, 0.

Q: Evaluate the integral 1 Note: Use an upper-case "C" for the constant of integration. 9x² √4x - x² dx

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Q: - Let C be the curve defined by R(t) = (2e²t - 3,1 - e²t, 2e²t). i. Find a vector equation of the…

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Q: Solve the D.E. y" + y = 2tant O y = C1cost + C2sint - 2cost In (sect - tant) O y = C1cost + C2sint -…

A: We can solve the given differential equation by using the method of variation of parameters.

Q: Evaluate f'(x) if f(x) = x¹nx¸ 2 lnx lnx [A] ·X² x In [B] x xnx 2 [C] 2 ln x x ·x² [D] 0 [E] 2 ln…

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Q: Evaluate the definite integral. π/2 x² sin x [12²232² -π/2 1 + x8 - dx

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Q: For the function f(x,y)=x^2−6xy+2y^2, find and classify all critical points

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Q: Evaluate the following integral or state that it diverges. S4e - 4x dx Select the correct choice…

A: Given query is to find the value of the integral.

Q: An implicit function has a vertical tangent line if = 0. Find the four points on the implicitly…

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Q: 2. Determine f'(x). (a) f(x) = √26

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Q: Calculate directional derivatives and gradients in three dimensions. Find an equation for the…

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Q: (f) Evaluate the derivative. Do not simplify. - (2-7) *** y =

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Q: 2. Separation of Variables Determine which of the following differential equations are separable. Do…

A: according to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…

Q: f(x) x² - 2x - 8 { *2-22-3 x-4 x = 4 x‡4

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Q: [ (x² +1) cos +=dx 2

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Q: The general solution to the DE in the initial value problem (IVP) (y" + 8y' +16y = 0 y(0) = 1 y'(0)…

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Q: A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a…

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Q: Apply a second derivative to identify a critical points as a local maximum, local minimum or saddle…

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Q: Solve the given equation.. dy dx a. + 2xy = x, y(0) = -2 C. y(x)= xex-2e-x² ex-5e-x² 2 b. y(x) = 1/2…

A: The given equation is; dy/dx+2xy=x, y(0)=-2.

Q: Evaluate the iterated integral I SV Answer: 1+ eº dw dv.

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Q: Find the smallest nonnegative integer for x such that x = 2 mod 3 x = 3 mod 5 x = 2 mod 7. A

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Q: ategration by parts formula and explain the e indefinite integrals by using the suggeste f6x 6x…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: J 6t³ cos (t¹) dt

A: According to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. || y=…

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Q: Q2. Solve the following ODE with condition y(2) = -4 and y' (2) = 14. y" + 2y + 5y = 50t - 100

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Q: Evaluate i. Integral 6xln(3x^2+5)dx by selecting and using appropriate substitution.

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Q: Find the transform of the given function by use of a table. f(t) = 5t sin (5t) + e-st cos (t) A…

A: Given : f(t) = 5t sin(5t) + e^(-5t) cos t

Q: 9. Find the maximum value of the directional derivative of f (x, y) = x²y + √y at the point (2, 1)…

A: Since gradient of function gives the maximum rate of change of the function.And directional…

Q: r12 Find ſ² ſ¹²(x + ln y) dydx 3 8

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Q: Suppose we have two interesting functions f and g. We have limited knowledge of them as follows: •…

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Q: Find the indefinite integral using the substitution x = 5 tan(0). (Use C for the constant of…

A: Topic- Indefinite integral We are given,∫x525+x2dxx=5tan(θ)

Q: Suppose lim n ---> infinity is known to exist, lim n---> bn= 5, lim n---> bn an ^2  = 245 find lim…

A: Given:- limn→∞bn=5  limn→∞bnan2=245

Q: • Use partial derivatives to locate critical points for a function of two variables. nd the critical…

A: Here is the solution:

Q: 1. Simplify the following expressions without the aid of a calculator. a) log, (81) b) log2 (2525) -…

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Q: Suppose that f(x, y) = x³y². The directional derivative of f(x, y) in the direction and at the…

A: To find directional derivative of given function.

Q: Use the properties of logarithms to exapnd the logarithm as much as possible: 4 log5 ພາ2 x4y³

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