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Using Different Methods In Exercises 7-12, find dw/dt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before
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Chapter 13 Solutions
Bundle: Calculus: Early Transcendental Functions, Loose-leaf Version, 6th + WebAssign Printed Access Card for Larson/Edwards' Calculus: Early Transcendental Functions, 6th Edition, Multi-Term
- Concentration of a solute According to the Ficks law, the diffusion of a solute across a cell membrane is given by c(t)=kAV[Cc(t)],(1) Where A is the area of the cell membrane, V is the volume of the cell, ct is the concentration inside the cell at time t, C is the concentration outside the cell, and k is constant. If co represents the concentration of the solute inside the cell when t = 0, then it can be shown that c(t)=(c0C)ekAt/V+C.(2) a. Use the last result to find c(t). b. Substitute back into Equation 1 to show that 2 is indeed the correct antiderivative of 1.arrow_forwardConsider h(x, y, z) = cos (xy) + eyz + ln (xz). Determine the directional derivative of h at the point P(1, 0, −1) in the direction of A = ⟨2, 1, 1⟩ Include interpretationarrow_forwarde joint pdf for X1 and X2 isf (x1, x2) = x1x236for x1 = 1, 2, 3 and x2 = 1, 2, 3.(a) Find the pdf of Y = X1X2.(b) Find the pdf of Z = X1Xarrow_forward
- EXO: Find the phase flows of the systems i-Sinyarrow_forwardFind the linearization of the function a) z = cos(sin y – x); at (-2,0) and use it to approximate f(-1.99,0.01). 10x2 b) z = i at (4, –1) and use it to approximate f(4.01, –0.9). x-y'arrow_forwardExpress the function f(z) = sin(=) in the form f(z) = U (x, y) + V (x, y)i. %3Darrow_forward
- find δƒ/δx and δƒ/δy. ƒ(x, y) = cos2 (3x - y2)arrow_forwardExplain why the function is differentiable at the given point. Then find the linearization L(x,y) of the function at that point. f(x,y)=y+sin(x/y),(0,3)arrow_forwardConsider the function f(x) = ln(x2). Let L(x) be the local linearization of f aboutx bar = a.a) What is the general expression of L(x) ?b) Find the linearization L(x) about a = 1 , a = 2 and a = 3.c) Which one of the above linearizations will fit the best for x = 2.5?arrow_forward
- Use the chain rule to find dz/dt.arrow_forwardfind δƒ/δx and δƒ/δy. ƒ(x, y) = ln (x + y)arrow_forwardExpress dw/ðu and əw/dv as functions of u and v both by using the Chain Rule and expressing w directly in terms of u and v before differentiating. w = In(x? + y? + z²), x= e" sinu, y=e" cos u, z= ue ": (u,v) = (-2,0)arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
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