The limit of f (x, y) : as (x,y) approaches (0,0): %3D O Infinity O Doesn't exist Exists and equal to 0

Q: Q2 (A) At what points f(x, y, z) in which the function f(x, y, z) = -√x²+y² is Z- continuous?

A:

Q: Use the linear approximation to f (x, y) = √x/y at (9, 4) to estimate √9.1/3.9.

A: f(x,y)=xy at (9,4) to estimate 9.13.9

Q: Find the local minimum value of f(x,y) 4x2 + 3y2+ 2x + 2y + 4. Give your answer correct to two…

A: The given function is f(x,y)=4x2+3y2+2x+2y+4

Q: Sx, ifx 1 f(x) = Show that f is R- integrable.

A: R- integrable function

Q: Let f (x, y) = xy2 + 5. Evaluate df/dy at (x, y) = (2, -1) and interpret your result.

A: Given: f (x, y) = xy2 + 5.

Q: Use the limit definition of partial derivatives to find f(x, y) and f (x, y). F(x, y) = x² – 5xy +…

A: on using the definition of limit of partial derivative we will get

Q: Find all points (x, y) where f(x, y) has a possible relative maximum or minimum.

A: We have to find the critical points for the function f(x,y)=-x2+2y2+6x-8y+5.

Q: Find positive numbers x and y, whose sum is 75, such that xy2 is maximized.

A: Positive numbers x and y,x+y=75xy2 is maximized

Q: Use the Linear Approximation to f(x, y) = x/y at (9, 4) to estimate 9.1/3.9.

A:

Q: Q2: f(x. y)- x/y over the region in the first quad- rant bounded by the lines y x,y 2x,x 1,x-2

A:

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: Find the absolute maximum and absolute minimum values of the function f(x, y) 2x3 + 3xy + 2y %3D…

A: We have to find the absolute maximum and absolute minimum values of the function fx,y=2x3+3xy+2y3…

Q: A function f : R? → R is given by f(x,y) = y² + 2x² – x²y. Find and classify its critical points.

A:

Q: \+etari), find f.. S, and f.- xyz 3. If f(x,y,z)= hn 2

A: We have to find fx , fy , fz.

Q: Find the absolute maximum of f(x,y) = 7x²y² + 5y² + 9x² bounded by y = x, y = 0 and x = 2.

A:

Q: I. Use the limit of the rates as Ax approaches zero. Ar 1. y = Ax + B 2. y = 2x2 – 3x +5 3. y = x3

A: "Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Suppose that f(x, y) : at which {(x, y) | 0 < x < 4, – x < ys va}. 1+ x D

A: Consider a given function:  The objective is to evaluate the following double integral of fx, y…

Q: 교꾸가고 (a, y) + (0,0) (x, y) = (0,0) f(x, y) = x2+y2 is discontinuous at (0,0).

A:

Q: of For the function below, use the limit definition of partial derivative to compute and at ôx…

A:

Q: Use the limit definition of partial derivatives to find f,(x, y) and f, fy(x, y). f(x, y) = x2 – 6xy…

A: Using partial derivative,

Q: Find the local minimum value of f(x, y) = 4+ xl+yl1 11æy. -

A:

Q: A cafe estimates a monthly profit (in thousand pesos) of P(x, y) = 27 – x² – y? + 6y if they open a…

A:

Q: d) The function +(xy)-r*r2y) exp G 18xy is homogencous in of degree X and

A: The given function is: f(x,y)=(x2+2y)e2xy+8xy...(1) The function f(x,y) is said to be homogeneous…

Q: Find A and B so that f(x, y) = x2 + Ax + y² + B has a local minimum at the point (4, 0), with…

A: Given function of two variables is f(x,y)=x2+Ax+y2+B it has local minimum point at (4,0) and minima…

Q: Find the limit of function f (x, y)D. at the point (0,0) through the path x=y². а. О b. 1 8 d. does…

A:

Q: Define the function f: R? → R by f (x, y) = 2xy² – y² – 2x². a) Find the critical points of f. b)…

A:

Q: Identify the removable discontinuity. x² – 1 f(x) : X- 1 (х, у) %3D Additional Materials

A: A removable discontinuity is one at which the limit of the function exists but does not equal the…

Q: Fínd a differentiable curve y(x) that minimizes J = +

A: The objective is to find the differentiable curve yx that minimizes J=∫01y'x2+c2yx2dx if y0=0 and…

Q: Find f, (x,y) and fy (x.y), and explain why f(x,y) has no local extrema. f(x.y) = 8x + 3y + 4. fy…

A: It is partial derivative

Q: Use the definition of partial derivatives as limits to find f(x, y) and fy(x, y). f(x, y) = 6xy2 -…

A: Consider the function: fx,y=6xy2-6x3y To calculate partial derivatives with respect to “x” using the…

Q: Find the average vale ot f(x)=Dx²e-2x overthe interval [-1,1]

A:

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

A:

Q: Find the absolute maximum and minimum values off on D, where f(x, y) = x – 2xy+2y and D={(x,…

A:

Q: Find absolute maxima and minima of the function f(x, y) = x² + y² on the closed triangular plate…

A:

Q: Find the absolute maximum of f(x,y) = 3x2y2 + 2y2 + 2x2 bounded by y = x, y = 0 and x = 5.

A:

Q: lim, f(x)= 0, then | f(x)dx diverges

A: Statement:  limx→∞ f(x)≠0,  then ∫1∞ f(x) dx   diverges.

Q: Find the absolute maximum and minimum values of D(x,y)=x²-xy + y² + 1 On the closed triangular plate…

A: Here I am using basic calculus we and also use short method.

Q: Find a simple closed curve C with counterclockwise orien- tation that maximizes the value of f t* dx…

A: Given an integral. We need to find the C that maximises the value of the integration.  Let's start.

Q: Find the maximum value of f on the region shown, subject to the constraint g (x, y) = c . At what…

A: a. The maximum value of f is 4. The point at which the maximum occurs is (0, 4).

Q: Find the absolute extrema of the function f(x,y) = xy - x - 3y on the triangular region with…

A:

Q: maximize f(x,y)=xy subject to the contraint 6x+y=18  the last question is what is the maximum valye…

A: max . fx,y=xyS.t 6x+y = 18     6x+y=18⇒ 6x+y-18=0∴ gx,y=6x+y-18=0    Fx,y,L=fx,y-L g x,y⇒…

Q: Let f(r, y) 3ry? when (x, y) + (0,0) and f(0,0) = 0. g²+2y! At which points is f continuous?

A: The given function is: This function is continuous at a point if at that point limit exists and the…

Q: If f(x, y) is continuous, then it must have an absolute maximum in the region x? + y² < 1. True…

A: Given: f(x,y) is continuous Region R is an open circle centre at origin and radius 1 ie x2+y2 &lt; 1…

Q: Use the limit definition of partial derivatives to find fx(x, y) and fy(x, y). f(x, y) = x2 − 5xy +…

A: We need to find partial derivative.

Q: what is the maximum of the function g(x,y) = (x2 + y - 11)2 + (x + y2 - 7)2 over the region 0 ≤ x ≤…

A: The given function gx, y=x2+y-112+x+y2-72 over the region 0≤x≤5 and 0≤y≤5. The required partial…

Q: Find the values of x, y and z that correspond to the critical point of the function f(x, y) 4x? – 4x…

A:

Q: If y(x) is a solution of y' = (y+1)(50 – y) with y(0) = 0, what is the limit of y(x) as x approaches…

A: Given: yx is a solution of y'=y+150-y. Also, y0=0. To find the limit of yx as x→+∞. As, y'=y+150-y.…

Q: Find the absolute maxima and minima of the function on the given domain. 6) f(x, y) = 6x + 5y on the…

A: f(x,y) = 6x+5yfx(x,y) = 6     fy(x,y) = 5  (Hence No critical points of the function itself)Lets…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.