Q: xy Prove that the function f(x, y) is differentiable everywhere in its do- x² + y? main.

A:

Q: The function f(z) =e² is: u(x.y)=e*cos(y) o u(x,y) =e*sin(y) ¤ contiuous in СО discontiuous in CO

A:

Q: (a) Assume that g(x, y) is a function of the form g(x, y) {} 0 if (x, y) = (0,0). (i) Show that…

A:

Q: z sin (), if (2, y) # (0, 0) 2. Determine if a function f : R2 → R defined by f (x, y) = %3D 0, if…

A:

Q: { z sin a). if (x, y) # (0,0) 2. Determine if a function f: R2 R defined by (. 9) = BE 0, if (KJ) =…

A:

Q: What is the maximum value of f(t) = sin t + cos t in the interval 0<t< =?

A: Given; f(t) = Sin t + Cos t.

Q: Use linear approximation to find y = L (x) of the function f (x) = = COS X about the point xXo = JT…

A: Use formula of  linear approximation

Q: Find and by implicit differentiation, and confirm that the - dy results obtained agree with those…

A: The solution is as follows

Q: ; (xy) (0,0) x +y -- Investigate the continuity of f(x, y) %3D ; (xy) = (0,0)

A:

Q: Determine if the following are homogeneous or non-homogeneous functions f (x, y) = cos = cOS x + y f…

A:

Q: Evaluate lim (csc a) V. x0+ Let f(x) = Va + le¬*. 1. Find the local linear approximation of f at xo…

A:

Q: 4. If f is a differentiable function of x and y with w = f(x, y), x = r cos 0 and y = r sin 0, show…

A: Given: w=fx,y, x=rcosθ, y=rsinθ If w is a multi variable function w(x,y,a,........z) thus the…

Q: y' + sin(t)y = g(t), y(0) = 5, %3D %3D that is continuous on the interval [0, 27] where if 0 <t < n,…

A: We have to find the solution to the initial value theorem.

Q: 4. If f is a differentiable function of a and y with w f(x, y), x =r cos 0 and y = r sin 0, %3D show…

A: To verify the given relations between partial derivatives.

Q: Define the map f : R² → R² as f(x, y) = (e" cos(y), æ²y + sin(y)) . (a) Show that f is…

A:

Q: a sin (), it (, u) + (0, 0) x²+y? 2. Determine if a function f : R² → R defined by f (x, y) = 0, if…

A:

Q: f(x, y, z, w) = (1+x+ sin(z − 2y), ez-w, 2z+tan(w+x²)).

A: we have to find the approximation of ƒ at the point P = (0, 0, 0, 0).  For this we use the proper…

Q: 18. Let ()- xy6 x4 + y8 ' x+ 0, f(0) = 0. %3D (a) Find all the directional derivatives of f at 0.…

A:

Q: Let = (x – 3)(x – 1)2 for a differentiable function f which is defined on the interval [0,4]. %3D dx

A: TO FIND THE CRITICAL POINTS, INTERVALS OF INCREASE AND DECREASE VALUE OF 'X' AT WHICH LOCAL EXTREMA…

Q: (a) If f(x,y) = e" siny – e sinx then verify that fæy = fyx. %3D -

A: Given that  f(x,y)=e^xsiny-e^ysinx To verify the fxy=fyx

Q: Find the linear approximation of the function at the given point: f(x, y) = 2 sin x – 3 cos y at (0,…

A:

Q: Show that f is continuous at (0, 7) where a cos y + y(e" – 1) if r + 0 f(x, y) = ay if æ = 0.

A: In the given question we have to show that the given function f(x,y) is continuous at the point…

Q: 2xy if (x, y) # (0,0) Let f(x, y) = = {x2+yz if (x, y) = (0,0) (a) Examine the continuity of f at…

A: Given function is fx,y=2xyx2+y2If x,y≠0,00If x,y=0,0 aExamine the continuity of f at 0,0bFind fx0,0…

Q: The function f(z) =e² is: O contiuous in C discontiuous in C Ou(x,y) =e*cos(y) Ou(x,y)=e*sin(y)

A:

Q: Determine k so that f(x, y) = kx(x- y) for 0<x <1,-x< y<x is a joint pdf.

A:

Q: Suppose f is a differentiable function of x and y, and g(u, v) = f(e" + sin(v), eu + cos(v)). Use…

A:

Q: 3. Find the work done by F over the curve in the direction of increasing t. = (2,x, y) = (sin t, cos…

A: Write the vector field F=zi+xj+yk The equation of the curve. rt=sinti+costj+tk Differentiate…

Q: Find domain of following functions In(e*+e) arctan(x+y) x² – y? а. f(x, у) — b. f(x, y) = - Vx - y…

A: Domain of a function is the set where the function is well defined. Thus, we check the points where…

Q: Find the linearization L(x) of f(x) = cot x at x = 4 %3D -

A:

Q: I sin () if (r, y) # (0,0) 2. Determine if a function f : R2 R defined by f (x, y) = 0, if (r, y) =…

A:

Q: fhow thot te function f depined by f(XrY) = 1 (x,Y) =(1,-リ - 1) %3D x2 +y (x, y) F (I,-1) * t y is…

A: We use the sequential definition of continuity to solve this problem.

Q: (a) Show that the limit xżycos y lim (x.y)→(0,0) 2x+ +y² does not exist. (b) If u = x cos y+ ye»,…

A:

Q: Suppose z = f(x, y) is a differentiable function of x and y, x =r cos 0, and y =r sin 0. (a) Compute…

A:

Q: Find fa, fy, and fz. f (x, y, z) = z In(xʻy° cos(52)) 4,3 COS x*Y fn = fy = fz =

A: Please refer the attached image for complete solution.

Q: (d) The function x²+y? Vx2+y? (x, y) # (0,0) f(x, y) (x, y) = (0,0) is continuous at (0,0).

A: Note: according to Bartleby policy we are allowed to write only one question please post remaining…

Q: The function h(x) = sin væ² + 1, x E R is continuous on: O R\{-1} O R\{-1,1} O R\{0} O R O R\{1}

A:

Q: x2+y? The continuity of f(x,y)={ tanxy xy +0 at (0,0) elsewhere is continous at (0,0)

A: To check the continuity we will check limit of given function at (0,0).

Q: (a) Show that the limit x*ycosy lim (x.y)-(0,0) does not exist. (b) If u = x cos y+ye", wherex=s+2t…

A: The given function is f(x, y)=x2+y23 at point (0, 1) and direction u→=35, -45. The direction…

Q: Find the antiderivative F for f(x) = | sin z|, -T <x <0 satisfying F(0) = 1. (1) F(x) = - cos x – 1…

A:

Q: If z=f(x,y), x= r cos θ and y= sin θ, where f is a differentiable function expressing az/ax and…

A:

Q: 2. i) Give an example of a nonzero continuous function f on [0,1] such that f(x)dx = 0.

A: We have to give an example of a nonzero continuous function f  on [0,1] such that  ∫01f(x)dx = 0

Q: tf(t)dt = xsin(x) + cos(x) – 1. Then f(T) = %3D Suppose that f is continuous and that Select one:

A: the question is taken from the calculus in which we have to find the value of the function at the…

Q: %3D a) Find fyxyx for f(x,y) = In(xy) – cos (xy) at (1,t).

A:

Q: Let L(r) be the linearization of f(x) = sin x + 1 at the point x = . Find L(π/2).

A:

Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a = %3D L(x) = %3D

A:

Q: Find an antiderivative F(x) of the function f(x)= 7sinx / 12+cosx such that F(0)=1.

A: Now,

Q: (d) The function x²+y? Vx²+y? (x, y) ± (0,0) f(x, y) = (x, y) = (0,0) is continuous at (0,0).

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Tir Find the general function M(x, y) so that (xM(x, y) – y) dx + (sec² y – ) dy = 0 is exact y-ln…

A:

Q: Study the continuity of f(x,y) = xe-Vx at p(1,0) ey.

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.