Use the gradient descent method in the equation f=2(x_1)^2 + (x_2)^2 with the starting point (1,2) and perform two iterations

Q: Find the slope and y-intercept of the line through the point (6,7) that cuts off the least area from…

A: The line passes through the point (6,7) that cuts off the least area from the first quadrant.

Q: 2. As an application of partial derivative of multi-variable functions, provide one page abou…

A:

Q: Define the term standard linear approximation?

A: we have to define the term standard linear approximation.

Q: Find the 3rd derivative of the function y = (3x³ – 7x2 +5) (x²+5) O y" = 120z2 - 168z + 90 %3D O g"…

A: Recall:Firstly product the givern term and find function of 'x'   i.e;   y=fxSome formula:∙ddx…

Q: Integrate: ∫sec^(3)2xdx

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Q: Use a linear approximation to estimate V65.

A: 653

Q: Find the critical points of the function by using algebraic partial derivatives test. Rx, у) - -х2 -…

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Q: solve e^-x=lnx using bisection method.

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Q: Use the limit definition of the partial derivative to verify the formulas

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Find the slope and y-intercept of the line through the point (9,5) that cuts off the least area from…

A: Equation of line : Y - y = m(X-x) If this passes through point(9,5) Y-5 = m(X-9) Y = m(X-9)+5 X…

Q: Find the slope and y-intercept of the line through the point (1,5) that cuts off the least area from…

A: In the question we have to find slope of line and y-intercept.

Q: Find the derivative. using chain rule 7 5. у %3 V1-14x2

A: The given function y=71-14x2

Q: Find the slope and y-intercept of the line through the point (10,9) that cuts off the least area…

A: Equation of line in point slope form : (y - a) = m*(x-b)  Where, slope = m and point = (a,b)

Q: Explain how to determine Partial derivatives for y-value ?

A: For a multi variable functions like f(x,y) To find its partial derivative for y value, treat x as a…

Q: Find the curve in the xy-plane that passes through the point (9,4) and whose slope at each point is…

A:

Q: Find the slope and y-intercept of the line through the point (4,10) that cuts off the least area…

A: We have to Find the slope and y-intercept.

Q: Integrate

A:

Q: Find the orthogonal trajectories of family of curves x-y=cx^2

A: To determine the orthogonal trajectory of the equation f(x,y)=c Find dydx Replace dydx→-dxdy Solve…

Q: Find the equation for the perpendicular trajectories of the family. 1. x - curve

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Q: Find the general solution using Integrating Factors Found by Inspection

A:

Q: Find the slope and y-intercept of the line through the point (6,6) that cuts off the least area from…

A: Given : Point (6,6)

Q: By using quotient rule, differentiate f(x) = (2x* – 7x² + 3x)(x² + 1)-1. Hence, find the gradient of…

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Q: Find the partial derivative. revIlzy

A: We can find the partial derivative as below.

Q: Use the linear approximation to estimate

A: In this question, by using a linear approximation to evaluate the value of the expression using…

Q: Find the orthogonal trajectories of

A: Given,          y=ax2+4ax+4a, where a being paarameter.

Q: Find the critical points of y= -2x^2 +4x +3 and apply the Second Derivative Test to find the maximum…

A: Critical point and extreme points

Q: Еxample 5 1 1- Vxdx ха 0,

A:

Q: Find the orthogonal trajectories to the family of curves:

A: Consider the given equation. x2=C-12y2lny2-1 Find the derivative of the function with respect to x.…

Q: can we calculate the derivative of a matrix and the nth root of a matrix ?

A: Yes, derivative of a matrix and the nth root of a matrix both can be calculated.

Q: Find the root of equation by using muller method

A:

Q: A curve passes through the point (2,5) and the gradient of the curve at any point is given by…

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Q: As an application of partial derivative of multi-variable functions, provide one page about Lagrange…

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Q: Find the general solution using Methods of Undetermined Coefficient and Variation of Parameters.…

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Q: Explain how to determine Partial derivatives for x-value ?

A: Partial derivatives :- Let z=fx,y be function of two independent variables x and y. If we keep y  as…

Q: What does it mean to eliminate the parameter? What useful information can be obtained by doing this?

A: Query- What does it mean to eliminate the parameter? What useful information can be obtained by…

Q: Please use the conjugate gradient method to solve min구 + z. (): with the starting point r1)

A: We will convert the minimising function into matrix form to apply the conjugate gradient method.

Q: How to calculate a gradient

A:

Q: How does the partial derivative relate to the limit of a function of two variables?

A: Solution

Q: Solve using partial differentiation

A: Given that  uxy=4eycos2x given that y = 0, ∂u∂y=cosx and u=y2…

Q: Determine the root of f(x)=xr – e* using fixed point iteration and false position method with…

A: Given function is fx=x-e-x The initial value is given as x0=3 In the fixed point iteration process…

Q: 3. х %3D у* — 2у3 2y3

A: We can find the answer as below using delta method

Q: Find the slope and y-intercept of the line through the point (2,7) that cuts off the least area from…

A:

Q: The function f (x) = ax³ – bx² has a gradient of 2 at point (1,6). Find its gradient when x = 2.

A: Given  f(x) = ax3-bx2

Q: What is the slope of the curve y= 2 over √x at the point (4,1)

A: To find the slope at a particular point x=a, the first derivative of the function is taken. Once the…

Q: i Explain. Reducible the working procedure of Equation to Homogencous. form.

A: Given: Procedure of equation Reducible to Homogeneous form.

Q: Define Orthogonal Trajectories ?

A: Definition of Orthogonal trajectories:        Given a family of curves , an orthogonal…

Q: Find the slope and y-intercept of the line through the point (1,2) that cuts off the least area from…

A: Given : Point ( 1 , 2 )  It cuts off the least area from the first  quadrant

Q: When should I use partial integration and when should I use substitution?

A: When should I use partial integration and when should I use substitution.

Q: Find the derivative. USING CHAIN RULE 4 y = V3x² – 5x + 2

A: