2² – y? a² + y? f (x, y) be the function (x, y)) # 0 and f(0, 0) = 0 if f is differentiable in (0,0)? justify vour answed

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

A:

Q: Compute div F, where F(x, y, z) = (x² + 3y, y? – 4z, sin r cos y – 22). A. (4 – sin r sin y, – cos r…

A: Given : F(x, y, z)=(x²  + 3y ,  y² -4z ,  sin(x )cos(y) - z2 )  Now we find div F = ?

Q: Integrate f(x,y) = x + y over the curve C: x2 + y? = 9 in the first quadrant from (3,0) to (0,3).

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Q: 2x + 7x +3. If Ax = 0.3 at x = 4, use linear Let y approximation to estimate Ay %3D %3D %3D Ay =

A: Given y=2x2+7x+3 if ∆x=0.3 at x=4 we have to approximate ∆y using linear approximation.

Q: Let x and y be differentiable functions of t and let s = 2x2 + y2 be the distance between the points…

A: Differentiate both sides with respect to 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 fr and fy- S(x, y) = /"9e" dt f.(r, y) : %3D f,(x, y) =

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Q: f (x, y, 2) = In (x² + y? + ²) ve df x = cost, y = sint, z = tise dt It%=D1

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Q: Find fr and fy- pry S(27, y) = /" 2e" dt %3D f.(r, y) = | f„(x, y) = | %3D

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Q: UNIVERSIT b) Given z = f (x – y, 2x – 2y, 3x – 3y). Show that - dz dz + = 0. dy

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

A: Given that, s=x2+y2

Q: 3r²y Determine if ƒ is continuous at (0,0) where f(r, y) = { r4 + 2y2 (x, y) + (0,0) (1, y) = (0,0)

A: for f(x) to be continuous at (0,0) limx→0+,y→0+f(x,y)=limx→0-,y→0-f(x,y)= f(0,0)

Q: Aşağıdaki alıştırmalarda, f., fy ve fiyi bulun. 23. f(x, y, z) = 1 + xy² – 2z2 25. f(x, y, z) = x -…

A:

Q: bounded by Y=x3, V=1x i rotare about X=1

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Q: valuate S S Se(3 – 4x)dV, whe e xy-plane defined by 0 < x s

A: To find: ∫∫∫E(3-4x) dV

Q: over the open surface S given by the upper part (only) of the intersection of ti of the function z =…

A: Introduction: Stokes Theorem (also known as Generalized Stokes Theorem) is a statement about the…

Q: uppose that F(x, y, z) = 0 defines z as a function of x and y and F is differentiable. "rove that dy…

A: Given F(x,y,z)=0

Q: Suppose f(x, y) =                             ((xy2) / (x2 + y4)), for (x, y) ≠ (0, 0)…

A: The given function is,

Q: valuate S. F · ds, where F(x, y, z) = (z, x, y) and c(t) = (t, t², t³), 0 < t < 1.

A: F(x,y,z)=(z,x,y)

Q: What is the value of the line integral ∫ AB y dx + x dy, if x = 3*t, y = 4*t + 4 and 0 ≤ t ≤ 1?

A: I am solving this in step 2

Q: If x, y, and z are lengths of the edges of a rectangular box, the common length of the box’s…

A: Given If x, y, and z are lengths of the edges of a rectangular box

Q: Find the extrema of the function f (x, y) =x² + y² + x²y + 4 in the domain D={(X, Y), 1X1 <1, iyi <…

A: See the attachment

Q: Groph of f(x)= (x² Is there a Is f differentiable at X=o? Justify %3D sharp Corner at X=O ?

A: Consider the given graph. fx=x2+0.0001 Now, draw the graph.

Q: { 2+y? if(x, y) # (0,0) if(x, y) = (0,0) xy 1. Given that f(x,y) Is f(x, y) continuous at (0,0)?…

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Q: Compute fe F d where F (x, y) = x² + y). (2xy + x, Hint: Is F conservative?

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Q: DNE.) +2+ f defined on |-1,3] maximum (x, y) = minimum (x, y) = Need Helo?

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Q: f(r, y, z) = byz In(4ry) %3D fz = fy = た=

A: Given:

Q: True or False: For an IVP dy/dx = f(x,y); y(a)=b, if f(x,y) is not continuous near (a,b), then its…

A:

Q: 0, x? < y < 2x² 1, otherwise. Show that f.(0, 0) and f (0, 0) exist, but ƒ is not differentiable at…

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Q: If u(x,y) and v(x,y) are differentiable, than, is it necessary that f(z)=u(x,y)+iv(x,y) is also…

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: Let z = In(x² + y²) be a differentiable function of x and y, where x = sin t, y = cos t. dz when t =…

A:

Q: Solve dy = ytan t, dt using separation of variables given the inital condition y(0) = 15. Assume the…

A:

Q: The maximum rate of change of the function f (x, y, z) = x lIn(yz) at (1;2;-) is equal to: O 3 None…

A: We have to find the maximum rate of change of the function f(x,y,z)= x ln(yz) at (1,2,1/2).

Q: Find fz and fy- f(x, y) = Te“ dt f„(x, y) %3D S,(x, y) =| %3D

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Q: Find fr and fy- f (x, y) = 4etlo dt f#(x, y) f„(x, y) =|

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

A: Differentiablility: A function z=f(x, y) is said to be differentiable in its domain D if the partial…

Q: ||| V3(x² + y²)dV, where V is bounded by y = 2x² + 2z² and y = 8.

A:

Q: Find fr and fy. f (x, y) = 4e" dt f(x, y) = f,(x, y) =

A: A detailed solution is given below.

Q: fze [sin(3x)]-m(x, y, z), where m(x, y, z) = Part C. yz-1 %3D

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Q: he The product of linear integration is where c t $ (2xy – x²) dx + (x + y²)dy, x = y? 30 y = x? ,…

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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: (a, b), f (x, 42. Show that ifJ (2, Y) is differentiable at then the function of one variable J (2,…

A: Definition (Differentiability of two variable function): A real valued function f(x,y) is said to be…

Q: At what points (x,y,z) in space are the functions continuous? a. h(x,y,z) = In (2z2 – x² – 3y³ – 4)…

A: we want to find the domain of given  function

Q: 4. Given f(x, y) = arctan(x + 2y). Find the local linear approximation of f at (1,0) and use it to…

A:

Q: Find fr and fy- f(x, y) = fetlo dt f.(r, y) = fy(x, y)

A:

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: 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: 2s+3 13. F(s) = s2–5

A:

Q: (a) Show that y = x* is concave upwards at the origin and y= e* is everywhere concave upwards.

A:

Q: Find fr and fy- f(x, y) = ets dt %3D f (x, y) = %3D fy(r, y) =

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.