IV. Define f(x, y) 1. 2. 3y √1+x¹ Find the rate of change of f at the point (-1, 1) along the direction (1,-1). = Let C be the portion of the curve y = − to the point (3,-9). Evaluate [₁ -³ from the point (-1,3) f(x, y) ds.

Q: Evaluate F.dr if F(x, y) = (x²y)i + (xy²)j and the curve C is given by r(t)=(t²)i +(t)j, 0≤t≤1.

A:

Q: Analyze and sketch = √2+4+4 intercept relative minimum graph of the function. Find any intercepts,…

A:

Q: y' = = CSC x — y cotx.

A:

Q: Suppose TEL(V) and T² = I and -1 is not an eigenvalue of T. Prove that T = I.

A: We have given that , T ∈ ℒV. Also T2 = I  and -1 is not an eigenvalue of T. We need to prove that ,…

Q: Consider the following problem; max f (x₁, x₂) = -x2² - x² subject to (x₁ - 1)³ ≥ x² Check whether…

A: Introduction: When assessing whether a multi-variable function is optimal, the quadratic surface…

Q: Determine if the matrix does any of the following: • A rotation • A projection • A reflection •…

A: From the graphical structures, we determine the type of matrices.

Q: Let f(x, y) = y²exy. (a) Find the normal vector to the graph of f(x, y) at (0,1,1). (b) Find the…

A: Given That : function f(x,y)=y2exy To find : Normal vector to the graph of f(x,y) at (0,1,1)

Q: ssume that a matrix A is diagonalizable and we have calculated the diagonalization of A, i.e. A =…

A:

Q: How differential equations and may lab helps in architectural engineering field

A: MATLAB is a computer program that provides the user with a convenient environment for performing…

Q: 2b) What are the eigenvalues of (A - σI)-¹? Hint: Your answer should eigenvalues of A−¹ are involve…

A:

Q: Estimate the following definite integrals using the Trapezoidal rule and Simpson's rule. Estimate…

A: To solve the given integral ∫121s2ds using Trapezoidal rule and Simpson's rule. Using n=4

Q: (ii) Determine whether the following functions are continuous at -2, or not, clearly stating any…

A:

Q: Let f(x, y, z) = 9 (√x² + y² + 2² where g is some nonnegative function of one variable such that…

A:

Q: Let f(x) = (x+1) arctan(1-2x) + f(t) dt) Which of the following statements are correct? I. f'(0) +…

A: Introduction: When there is a differentiation under integral sign, we follow Leibniz rule. It is a…

Q: Let S be the negatively oriented surface defined by R(u, v) = (u², v², uv), where (u, v) € [0, 1] ×…

A: Flux ∫∫SF . dS=∫ab∫cdFr(u,v).∂r∂u×∂r∂v du dv

Q: Here is a contour diagram for a function g(x,y) 15 10 0.3 0,6 0.0 0.6 Use the diagram to answer the…

A: contour diagram gives values of function for different combination of x and y . Values given in the…

Q: J dx 4 + x² =

A:

Q: Rachel purchased a car for $23,900; she paid 20% of the cost as a down payment and financed the…

A: The compound interest formula for an initial amount of P at a rate of r%, for t years compounded n…

Q: How did they calculate what T does to the elements of B?

A: You want to know "How did they calculate what T does to the elements of B?" We have  B=1, x, x2, x3…

Q: 2. Let f(x, y) = |x − 1| · yś. (a) Compute, if they exist, the partial derivatives fr and fy at the…

A: Given: fx,y=x-1·y13 We have to determine whether fx,y is differentiable at the point x,y=1,0

Q: Consider the following integral equation, so called because the unknown dependent variable, y,…

A: Introduction: Convolution is used to solve an integral equation through Laplace transformation. Like…

Q: Let G be the solid in the first octant bounded by the planes x = y ₁ Y = 2,2=0 and x = 1. Set up an…

A: Given: Let us consider the given first octant bounded by the planes, x=y, y=z, z=0, and x=1 Let's…

Q: 3) You are constructing a box out of a sheet of cardboard with dimensions 2 m by 4 m. You then cut…

A: Note: As per the Bartleby guidelines, we cannot author hand written solution, so we are authoring…

Q: Two sides and an angle are given. Determine whether the given information results in one triangle,…

A: Two sides and an angle are given. a=7,   b=9,  B=49°   To determine: whether the given information…

Q: R(x) = F/2 π dx

A: We have to evaluate the integral: R→x=∫0π/2sin2x3x+1, lnx2-1,xx2+1dx   .....(1)

Q: 4 (1) Evaluate the following summation: Σ i + 2 i=2

A:

Q: 5.1 The diagram shows an irregular hexagon with interior angles all equal to 120° made by cutting…

A: Given, An irregular hexagon with interior angles all equal to 120° made by cutting the corners off…

Q: For which je{1,2,3,4} do we have ||A||₁||Aejl|₁, when O a. none A = O b. j=1 O c. j=2 d. j=3 O e.…

A:

Q: (4) Prove that if s and t are odd perfect squares, s + t is not a perfect square. Use contradiction…

A: A square number or perfect square is an integer that is the square of an integer; in other words, it…

Q: Find a 2 x 2 matrix A that has eigenvalues X₁ = 6 and X₂=5 and corresponding eigenvectors: 1 (2)…

A:

Q: 3) Sketch a graph of the helix r(t) = (− cos(2ñt), 4 sin(2πt), 3t), listing the rotation direction,…

A:

Q: Consider the system of first order ODE where x' (t) = Ax(t) 01 1 A = 0 1 1 002 (a) Find the general…

A: Given That : system of First order differential equation x'(t)=Ax(t) where A=011011002 a) Find the…

Q: Which scenario is the best fit for the linear equation? y=200x +1200

A:

Q: Use Simpson's rule to approximate the following integrals: (using n = 8 subintervals a. cos x³ dx

A: # as per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Calculate the Fourier series of function f(x)=x^2 -L<x<L using the Fourier series of function…

A:

Q: 5. Find the equation of the straight line passing through (3,-5) and parallel to the line joining…

A: 5. To Find: The equation of the straight line passing through (3, -5) and parallel to the line…

Q: Determine if the following limits exist: x² + y5 lim (x,y) →(0,0) 1 - cos(x) + y² (a)

A:

Q: Complete the following for plane A. Write an equation of plane B. Sketch the plane in the first…

A: "Since you have asked multiple questions, according to our guidelines we will solve only the first…

Q: A = 2 0 T -2 2 c=[12] 0 1 0 -1 [0.5 0.0] 0.0 2.0 -2 -2 -2 -1 Ce₁ -1 Ae₂ Ce₂ 0 0 Ae₁ 1 1 2 2 B = N O…

A: Since you have added many problem in one question, so here are the solutions of first three…

Q: For a sphere parameterized using the spherical coordinates and , describe in words the part of the…

A:

Q: Determine whether the following series (-1)-1²+2 80 n=1 is absolutely convergent, conditionally con-…

A: Introduction: When there is a series of alternating terms, two different types of convergence are…

Q: Find the area, in square units, bounded above by f(x) = x²+2x+1 and g(x) = 2x + 10 and bounded below…

A: First we identify the region which we need to find we have f(x)=x2+2x+1,  g(x)=2x+10 area is above…

Q: f(x) = = 2, 2x² + 2x " X log₂ (x - 1), x<-2 −2 < x < 2, x‡0 x ≥ 2. 1. Sketch the graph of the…

A: Given function f(x)=2x&lt;-22x2+2xx-2&lt;x&lt;2, x≠0log2(x-1)x≥2

Q: Find the exact area of the region bounded by the curve r = where t is[0,2].  Use the corollary to…

A: Given that r→=4t−t3,2sinπ2t, where t∈0,2. Here, x=4t−t3 ⇒dx=4−3t2dt And y=2sinπ2t ⇒dy=πcosπ2tdt.

Q: where is the answer from the choices?

A:

Q: Use high-accuracy differentiation formula O(h) to estimate the first derivative of f(x)=log.x.…

A: Consider the given function, fx=logx Here we need to estimate the first derivative of the given…

Q: Question 4. Apply Laplace Transform to solve the following Integro-Differential Equation when x(0) =…

A: Introduction: When an integral equation involves a term of derivative, it becomes an integro…

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: Since you have asked a question with multiple subparts we will answer the first three sub parts for…

Q: Find the centroid of a lamina enclosed between the circles of radius 1 and 2 centred at the origin,…

A: Introduction: The centroid is the point where the mass of the object is distributed uniformly.…

Q: f(x, y, z) = g(√√x² + y² + z²) where 9 is some nonnegative function of one variable such that g(2) =…

A: Mass of curved lamina given by R(u,v) with density f(x,y,z) M=∫∫Sf(R(u,v)) ×Ru(u,v)×Rv(u,v)du dv