If f is a continuous function satisfying f(x) = x* - x+(1-x)[,f'f)dt + x[ (t -r°)f(@dt for all x, then f "(1) = ? A) -1 B) 0 C) 1 D) 2 E) 3

Q: Let f(x, y, z) = In(x² + 2) + y²e== – cos(2yz). Find fzyz- %3D

A: Given that: f(x, y, z)=ln(x2+z)+y2exz-cos(2yz)

Q: (2) Let F(x, y) = (cos(y)+2x, -x sin y+1). Show that F is path independent by finding %3D a…

A: For the given vector function to be independent, it must be derived from a potential scalar function…

Q: Suppose that for each i such that 1 <i<N one has / f(1)dt = i Ji-1 What is / f(t)dt if N = 87?

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Q: The quadratic partial derivatives are continuous and fa (x, y) = x + y? and fy (a, y) = x – y meets…

A: We have to check whether the statement, "The quadratic partial derivative are continuous and…

Q: tinuous at t= 0, it is continuous at every other point. 3 If the autocorrelation function R(t) of a…

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Q: 30. Find the continuous function f(t) satisfying csin z for all r. 2+ f(t)dt = sin2015 /3

A: According to Leibnitz rule:

Q: Find the linearization of the function f (x) = x at a = 1. a Va lal sin (a) L (1) Using this…

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Q: 11) Consider F(x) = S*sec t tan t dt a) Integrate to find F as a function of x b) Demonstrate the…

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Q: 21 (important) Find the fixed point for F(x) = ax + s. When is it attracting?

A: Given Fx=ax+s

Q: f (x, y) = sen (r² – 0²) + In(r® + 0), Vr2 + y? A con arctan

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Q: Find the divergence of U = r cos 0 a, - sin 0 ag + 2r² sin 0 2 sin 0 3 sin 0 - r2 2 cos 0 3 cos 0 r2…

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Q: In Exercises 23-28 explain why fis continuous. 26. f(x, y, z) = sin (xyz – 1) 27. f(x, y, z) = ln(e"…

A: The function is continuous if all partial derivatives exist.

Q: Find the first partial derivatives of at the point (x, y) (1,2). x + y f(x, y) af -(1,2) = 2/3 af…

A: Explanation of the solution is given below...

Q: Suppose f(x,y) is differentiable infinitely many times (so that partial derivatives of all orders…

A: This question can be solved by cross verifying the three conditions for a function f(x,y) to have a…

Q: Since f(x, y) = 1 + y² and ðf/ðy = 2y are continuous everywhere, the region R in Theorem 1.2.1 can…

A: Given data: We are given that y=tan(x+c) is the family of the solution using initial value y(0)=0

Q: Find the first partial derivatives with respect to x, y, and z. fx, у, 2) %3 4x?у - 2хуz + бу2?…

A: Given  f(x, y, z) = 4x2y - 2xyz + 6yz2

Q: Find the first partial derivatives with respect to x and y of f(x,y) = (4x-y)/(4x+y) at the point…

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Q: Show that the function f(z) = e-z",z # 0 and f(0)=0 is not analytic at z=0, although Cauchy-Riemann…

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Q: Calculate the second-order partial derivative of f(x,y) =sin(x³y²) with respect to x and y, that is,…

A: given f ( x1 y) =sin ( x3 y2)   ∂2f∂x∂y=∂∂x∂f∂y

Q: If z = f (x, y) is a function that admits second continuous partial derivatives such that image1 A…

A: Given z=fx,y such that ∇fx,y=300−12x2−12y2,18y2−24xy. Here, ∇fx,y=fx,fy=300−12x2−12y2,18y2−24xy.…

Q: Suppose that z = xy² and x and y are differentiable func- tions of t with x =2,y = when t = -1. Then…

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Q: Compute the partial derivative of the function f(x, y, z) = e'-z cos(y) +ze-/(1+y²) with respect to…

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Q: Show that the Dirichlet function f defined on [0 , 1] by f(x) = { 1 if x is rational 0 if x is…

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Q: Verify by differentiation that a) / t dt : V1+t2 /1+t² + C; _ b) tan(x)dr = – In(cos(x)) +C, –1/2 <…

A: Given to find ∫t1+t2dtPut 1+t2=udifferentiate 2tdt=dutdt=du2therefore…

Q: Show that the function f defined on [0, 1] by the conditions f)=2rx when <,r=1, 2, 3,. 1 1=1, 2,…

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Q: Assume that z = ƒ(x, y), x = g(t), y = h(t), ƒx(2, -1) = 3, and ƒy(2, -1) = -2. If g(0) = 2, h(0) =…

A: We use the partial derivatives to find dz/dt  Then plug x=g(t) and y=h(t)

Q: 11. The function f(x) is defined on [1, o0) and satisfies VTO dt. 10 Find f(x).

A:

Q: 11. Show that the function 2ry when r + y + 0 h(r, y) = 0; when r = y = 0 has partial derivatives…

A: Given: h(x,y) =2xyx2+y2;     when x2+y2≠00 ;      when x=y=0 To show that the partial derivative…

Q: of Let f (x, y) = tanh-¹(x-y) with x=e" and y= usinh (t). Then the value of dt (u,t) =(4, In 2) is…

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Q: Find the first partial derivative of w = In(1 + )at (2,0, – 1).

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Q: Show that following function xY (x, y) + (0, 0), f(x, y) = x² + y² (x, y) = (0,0) is continuous,…

A: To check the continuity of given function at origin firstly finding the limit of the function at…

Q: 2. Find the first partial derivatives of (a) f(x,y,2)=x°yz* (c) f(x,y;2)= In[}}+ tan "(0=) (b) f(x,…

A: We need to find first partial derivatives.

Q: 46. s(х, у) tan (y/x) -1 =

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Q: Compute F. dr where F (x, y) : (7xy + x cos x) i+ (-yev + 6x²) j and C is a piecewise closed curve…

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Q: Find the divergence of F(x, y, z) =(a -1 Y, y? + 1' 3xz2 + 2y ) at (2,0, – x COS

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Q: д. L. = a(x, y)+b(x, y) +c(x, y). – d(x, y) -

A: Proof: Consider V be any vector space of all functions of two variable x  and y whose partial…

Q: 1+ax' Let f(x) = cos(x) In | be integrable on If | f(x)dx = 0 where a and b are real 1+ bx a+b…

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Q: Assume that all the given functions have continuous second-order partial derivatives. If z = f(x,…

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Q: A certain function f(x,y), which has continuous second-order partial derivatives on R2 , has (0,0)…

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Q: Vf(r, y) = (300 – 12z? – 12y? , 18y? – 24.ry) - - -

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Q: Find all the second order partial derivatives of the function : f(x, y) = In 4ry + sin 3ry + e4z-3y

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Q: Find all the second partial derivatives (including fxy etc.) a) v = sin(2s^2 − t^3)

A: Please see the explanation below

Q: Let f(z) = sin(z'). %3D s'(z) = 3 coslx 3)) 2. 3x cos(X %3D S'(4) = 0

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Q: Assume x and y are functions of t. Evaluate dt for 4xeY12-In 729+61n x, with the conditions -6, x-3,…

A: Given that 4xey=12-ln729+6 lnx and the conditions are dxdt=6 , x=3, y=0  find dydt

Q: (xy(x² – y²) f(x,y) ={ x² +y² si x² + y² + 0 0 si (x, y) = (0,0)

A:

Q: Let x and y be differentiable functions of t, and lets = √(x2 + y2) be the distance between the…

A: Given equation is s=x2+y2. Compute the derivative of s with respect to t.…

Q: What does Peanos EU theorem guarantee for the IVP:  dy/dt = -t/y ,  IC: (to,0)

A: Peanos theorem: "Consider the initial value problem y1= f(t,y), y(t0)=y0. Let f: Domain f →Rn. Then…

Q: ди + 3x- = 1 + u, dx ди -co 0, dt u(x, 0) = f(x).

A:

Q: Find the first partial derivatives of 2х — 4у - f(x, y) = at the point (x, y) = (2,2). 2х + 4y af…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.