prove that x^2y/(x^2+y^2) is not differentiable at 0,0 when  x^2y/(x^2+y^2) if (x,y) not equal to (0,0)            0 if f(x,y) = (0,0)

Q: f(x, y) = ln (2x) In (3y) + x - y - xy - 3, then fyz (2,-) is equal to

A: Given :fx,y=ln2xln3y+x-y-xy-3

Q: A coat of paint of thickness 0.02 cm is to be applied uniformly to the faces of a cube of edge 21…

A: We know that,

Q: In explicit method of hyperbolic PDES, the second initial condition, the one involving g, gives…

A: Given,

Q: Find Lebesque integral of function on segment (-3,0) 1 f(x) = %3D x+3

A: Given, fx=1x+35 Let, A be the set of all rational number in -3,0. Here, mA denotes the Lebesgue of…

Q: Show that the differential form in the integral is exact. Then evaluate the integral. (1,2,3) Jazy…

A:

Q: 75. F(x) : (t + 2) dt

A:

Q: Suppose a force of 40N is required to stretch and hold a spring 0.1m from its equilibrium position.…

A:

Q: What is the volume of a rotational body formed by rotating the area bounded the = 4-x ² function…

A:

Q: IT ) Verify that ,0) is a critical point of f(x, y) = y² - 2y cos x. Then use the second derivative…

A:

Q: Bounded by the cylinder x 2 + y 2 = 1 and the planes y= z x =0 z= 0 in the first octant

A:

Q: What is frz, fyy, and fyz of f(x, y) = In(y²")?

A: Given:           f(x,y)=lnyx2          fx=∂∂xlnyx2         Treating y as constant variable…

Q: Consider f(x, y) =(ax² + by²). Based on the second derivative test, what are the conditions…

A: Answer

Q: he first derivative of y = 3x ++ 2V - a is %3D 3 10 y' 5 5z 5 3z 3 3 O y' 10 %3D 2V14 3 O y' 3. 10…

A: To find the derivative of: y=3x15-23x+35+2x34-5x23⇒y=3x15-23x+35+2x34-5x-23...(1) Note that:…

Q: tion f defined as xy Ax, y)=- when (x, y)#(0, 0) when (x, y)=(0, 0) =0, is continuous at the origin.

A:

Q: triangle with vertices (-4, 1) (-2,1) (-3,2), rotated about x=1, set up the integral using the shell…

A: Given vertices of triangle are (-4,1) (-2,1) (-3,2) & axis of rotation is x=1 we have to find…

Q: What is the largest value that the directional derivative of ƒ(x, y, z) = xyz can have at the point…

A:

Q: Simplify down to a single integral in terms of . .3 /9-x² 63–42²–4z² Volume = 1 dy dz dx = Σ da.…

A: ∫-33∫-9-x29-x2y3x2+3z263-4x2-4z2dzdx

Q: x2 f (x) = t² sin(2t) dt 1

A:

Q: 2.Evaluate the total derivative of u with respect to x for u = 4x4+3y² + 3z² when y = sinx and z =…

A:

Q: independent

A: We will solve the problem.

Q: Find the Integration of: f(3sin t + esin ty cost dt In 3

A: we have to integrate the following

Q: Find all the critical points of f(2z, v) = - . 1 + 4x – xy? and classify them using the second…

A: The given function is;  f(x)=-x3/3 +4x -xy2.

Q: volume of solid of as revolution y^2=4x and x^2=4y about the x axis

A:

Q: Give 1 problem of partial differentiation of function of U with respect to 3 independent variables…

A:

Q: Let u = x3 + 1. Indicate how the limits of integration should be adjusted in order to perform the…

A: Given

Q: (b) Use the First Derivative Test to identify all local extrema. Local minimum at x = Local maxiтит…

A:

Q: line integral Compute the where part of the cirele x² +yR=9 C is the %3D in the first quarant from…

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Q: How do I find integrals and their boundaries when working with the cylinderical shell method?

A: According to the cylindrical shell method,

Q: Why is integration needed to compute the work performed in pumping water out of a tank but not to…

A:

Q: Find the area of a triangle bounded by lines y=2x and x=1 by double integration

A: Given region, y=2x        ...(1)x = 1        ...(2) Substitute the value of x = 1 in (1), y = 2 So…

Q: Evaluate In (ax) dx using integration by parts

A: Follow the procedure given below and use simple intergation by parts.

Q: (5)Obtain the integral curve for x 2+y = x passing through the point

A:

Q: Find all second order partial derivative with respect to variable x and y. F(х,у)- х сosxу + y sinx…

A:

Q: Find the limits of integration in cylindrical

A:

Q: If we discuss the derivative of the function f(z) = z. Imz by Cauchy- Riemann equations. we see fz)…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: B) Find the derivative of the foiiowing: 1) y = 2sin2(5x) ,2) y = x, 3) xsin-14y = y tan-14x 4) y =…

A: As per the company  guidelines we have to solv first 3 subparts if suborats are not mentioned  So…

Q: Find partial derivative af for the function f(x,y) given below exp 2x. siny .(at the point (In2, 0

A:

Q: Find the linear approximation of the function f (x,y) = ln (x - 3y) at point (7,2).

A: To find the linear approximation of the function fx, y=lnx-3y at the point 7, 2.

Q: Find volume y=3x^2, x=1, and y=0 about x axis

A: y=3x^2, x=1, and y=0 about x axis

Q: A bounded, 3B > 0 such that |f(x)| < B Vx € (0, 1), continuous function on (0, 1) with unded…

A: We will find an example

Q: Find the area of a triangle bounded by lines y=2x and x=1 by single integration

A: A definite integral can be used to compute area bounded by curves. If there are two curves f,g over…

Q: Evalute Sofy ex* dxdy by first reversing the order ex² 3y integration.

A:

Q: The derivative of y=esinh/x + coshVx equals Select one: 1 1 (esinh/cosh/x + Vx² -1 2х 1 O y' = e…

A: We have to solve

Q: if Zcand Zp is complementary function Particular integral for the equation f(x X F(x,y) respectively…

A: This is Partial differential equation.

Q: Give one problem for  partial differentiation of function of U with respect to 3 independent…

A: It is partial derivative problem

Q: Find y(1) for y" = - 4z - 4y, X, = 0, yo = 0, z, = 1, with step length 0.1 using Euler method (2nd…

A:

Q: Find the the Yegion bounded by area y= tanx 4

A: integration gives the area of any function y .

Q: Show that the function f(z)=sin x cosh y+i cosx sinh y is continious as well as analytic every…

A:

Q: What is the Fourier transform of the one-dimensional rect function rect(x) = 1, for |x| |x|…

A:

Q: 2. Determine the centroid of the area bounded by the curves y = 4x + 16, x = -2, x = 5 and x-axis.

A: