solve problems involving partial derivatives (TLO8)no. 1 azazA. For each of the following functions z, findandдхду1. z= sin3x cos4y2. z = tan-1 (2)3. yz + xz + ху —D 0a²za?zB. For each of the following functions z, finda²za²zandду?дх?' дудх' дхду'1. Z %3Dz =2x? — 5ху + у?2. z= sin3x cos4y3. Z 3D taп-1

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Answered: əz az A. For each of the following…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Find the derivatives of number 5 using QUOTIENT RULE.
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1. Find the derivative of each of the following functions a) f(x) = cos5x b) g(x) = cos*5x c) h(x) = cos45x + 3x d) l(x) = (cos*5x + 3x)/2 e) m(x) = 10x (cos*5x + 3x)2
An equation representing a vibrating string of one unit long, fixed at both ends, is given in Equation 1. = a² y_a² y at² Ox² (1) Equation 1 can be written in the form of Equation 2 using the central finite difference approximation of the second derivative of their respective variables. The subscripts represent locations, while superscripts represent time steps. y=By+Cy+ Dy₁₁ + Ey i+1 (2) +1 a) Express B, C, D and E in terms of A t and A x. Note that the coefficient of y, is equal to one. b) The string is discretised into five nodes equally distanced, with A t = 0.2. Write down equations as a result of applying Equation 2 to the domain. Subscripts must be replaced with correct node numbers, while superscripts can be retained not required to incorporate the boundary and initial conditions yet. c) Assemble the three equations above in the form of matrix {y}+1 = [A] {y}'+ {y}+{BC}, where [A] is a square matrix, {BC} is a vector containing the boundary conditions, {y}+1, {y} and {y} are…
4. D11: I can use derivatives to solve optimization problems. (a) Part of the graph of f(x) = x + 2x is given below. i. Does the graph indicate that x = 0 is a critical point? Why/Why not? ii. Use calculus and algebra to find all possible x values where f could possibly change direction (change from increase to decrease or vice versa). Does your algebra indicate that x = 0 is a critical point? Why/Why not? lasif (b) Use the first derivative test to show that f does not have a maximum or a minimum at x = 0. (Hint: you may need to look up this test. Show why it is ok to apply the test to this situation.)

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əz az A. For each of the following functions z, find - and дх ду 1. z= sin3x cos4y 2. z = tan-1 (2) 3. yz + xz + xy = 0