Use the Laplace transform to solve the heat equation U = Urr, t > 0, x > 0. и (х, 0) — е т u (0, t) = 0 lim u (x, t) = 0, x → 0 8.

Q: Find r'(t) and antiderivative[r(t)]dt of: a. r(t) = b. r(t) = te3t

A: (a) Obtain the derivative of r as shown below: r't=ddt2tant,ddt-sect,ddtsin2t…

Q: f(1 + /x) 3+ t? .Find dy where t = 1, f(3) = 2, dt 10. Let y %3D X g(1 – Jx)' g(-1) = 4, f'(3) = -2…

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Q: vatty f Z= f(x,y)=4 e In(y), and x = ln (u cosv), yusin v, use chain rule to find: Evaluate : ]]…

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Q: 2 (y – k) y' = 4a Find the Derivative - d/dy Since 4a is constant with respect to y, the derivative…

A: (1). The given expression is:2y-ky'=4a

Q: Use the Existence and Uniquness Theorem to verify, with initial value (-2,-1): y' = xy2

A: Consider the differential equation y'=xy2 with initial condition -2,-1 Compare the differential…

Q: Find the directional derivative of the function f (x, y) = ln (x + 2y) at the point P(1/4, 1/8) in…

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Q: Sara draws the 4 of hearts from a standard deck of 52 cards. Without replacing the first card, she…

A: Given, Sara draws the 4 of hearts from a standard deck of 52 cards without replacing. a) we know…

Q: 2. Let F(x) = x s sin (t2) dt. Find F'(x). (a) sin (x²) dx (b) sin (x²) (c) sin (x²) + C (d) 2x sin…

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Q: etermine whether the function u(x, t)=ecos() is a solution of the heat conduction equa- on u₁=a²uxx-

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Q: Find the derivative of f(x, y) = xey + cosxy at the point (2,0) in the ection.

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: Əz Q3.If Z= f(x,y) = 4 e In(y), and x = ln (u cosv), y = u sinv, use chain rule to find : E * ди Q4.…

A: Note: We are entitled to solve only one question at a time. As the specified one is not mentioned,…

Q: Given f(x, y, z)= 10 x y z-5, use the total differential to estimate the change in f from the point…

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Q: How do we find the linearization of g(x, y) = tan−1(xy2) at the point (1, 1). and use linearization…

A: To find the linearization of g(x,y)=tan−1⁡(xy2) at the point (1,1), we willl use the formula for the…

Q: Let f(x, y, z) = x“y + z* and x = s³, y = st°, and z = s°t. (a) Calculate the primary derivatives ,…

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Q: Find the differential dy. (а) у — ху5 xv5 – x dy = (b) y = (1+x)-9 dy

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Q: əz ди Q3.If Z= f(x,y)=4e* ln(y), and x = ln (u cosv), yusin v, use chain rule to find : (x²) dr du…

A: 3. Given Z=fx, y=4 ex lny and x=lnu cosv, y= u sinv   To Find: ∂Z∂u and ∂Z∂v

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = − 6 e* cos (yz),…

A: The given function is  and the direction  at .The aim is to find the derivative .

Q: Let f(t) be the velocity in meters/second of a car at time t in seconds. Give an integral for the…

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Q: Find the derivative of the function at Po in the direction of A f(x,y,z) = 3 e* cos (yz), Po(0,0,0),…

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Q: Consider z = f(x,y) = x2 + 3xy + e2y. Find the equation of the tangent when x = 1 and y = 0.   Find…

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Q: dw where w = cos 8x sin 4y, x = dt and y =t". 4 Use the Chain Rule to find

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Q: f(«, у, 2) — sec (9г + 3уг) fa = | fy = f: = ||

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Q: 1. Use the differential df to approximate the change in the value of f(x,y) from the point (1,0) to…

A: We will be using definition.

Q: Rocky Mountain Chocolate Factory (RMCF) founder and president Frank Crail employs 220 people in 361…

A: for net price  equivalent rate determine first find the complement of the chain discount rate…

Q: 16xydx- 24ydy = -8x²dy %3D

A: The given differential equation can be written as:16xy−24yy' =−8x2y' An ODE Mx, y+Nx, yy'=0 is in…