if a set is compact set and the gradient of the function isnt equal to zero what does it mean

Q: What are the basic properties of limits of functions of two independent variables?

A: What are the basic properties of limits of functions of two independent variables?

Q: When the admission price for a baseball game was $18 per ticket, 36,000 tickets were sold. When the…

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Q: Sketch the graph of a smooth function ƒ and label a point P(a, ƒ(a)) on the curve. Draw the line…

A: The aim is to find the graph of a smooth function and represent the line which shows the linear…

Q: Describe two methods for optimizing a function z = f (x, y) subject to a constraint.

A: Optimization is the method to find the local minima or maxima of a function. If there are…

Q: Tell whether the enumerated function is linearly dependent or linearly independent using wronskian.

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Q: What is the minimum

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Q: What is the gradient of Y = x³ - 3x² + 4, when x = 1?

A: Gradient is the rate of fastest decrease at a particular point. In other words it is the derivative…

Q: what is the gradient of y=x3-3x2 +5 when x=1

A: Given y=x3-3x2 +5

Q: What does it mean for a function to be right-continuous at a point?

A: A function f is right continuous at a point c if it is defined on an interval [c, d] lying to the…

Q: Let f(x) = x³ + 3x2 + x + 3. Determine the points f where the tangent line is horizontal on

A: to find the points where the tangent line is horizontal we have to first derivate the function and…

Q: What is the analog of the Two-Path Test for functions of a single variable?

A: The two path for function is if f(x, y) approaches two different values as (x, y) approaches (a, b)…

Q: It is defined as the limit of the ratio of the change in a function to the corresponding change in…

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Q: Let f(x) be a differentiable function. Explain why it is possible that f'(c)=0 for a function but…

A: Let f(x) be a differentiable function.

Q: Suppose f is a linear function and that f (2)=7 and f (5)=7.1.  Then the slope of is postive   true…

A:

Q: Suppose that f(x, y) = 3x* + 3yª – 2ry Then the minimum is

A: Given, f(x,y)=3x4+3y4-2xy

Q: Is 6y-y^2 a convex function

A: Given:  Let fy=6y-y2  To Find: To check the given function for a convex function.

Q: FInd the equation of a linw whose gradient is 3/2 and which passes through the point P,where P…

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Q: When the admission price for a baseball game was $78 per ticket, 36,000 tickets were sold. When the…

A:

Q: Give two distinct linear functions ƒ and g that satisfy ƒ'(x) = g'(x); that is, the lines have equal…

A: It is given that fx and gx two distinct function.

Q: When is a function of two (three) independent variables continuous at a point in its domain? Give…

A: When is a function of two (three) independent variables continuousat a point in its domain? Give…

Q: What are the removable singularities of the functions ?

A: Topic:- function

Q: What does it mean for a function to be left-continuous at a point?

A: function to be left-continuous at a point?

Q: 4 3- 2. 1. -D2 -3- -4 4 A 7 B 1 C 3 5

A: Answer is given below

Q: a box with a square base and no top has a volume of 100cubic cm. If the material for the 4 sides…

A: Given that, the volume of the box is 100 cubic cm, the material cost for the 4 sides is 8 cents per…

Q: Suppose that f(a, b) is an absolute maximum of the function f (x, y). Must f (a, b) also be a local…

A: First of all, undrstand the difference between absolute maxima and local maxima.Let, z = f(x,y)…

Q: Define Wronskian of Linearly Dependent Functions?

A: We have to define the Wronskian of linearly dependent functions: Let f1 ,f2 ,...,fn be n real or…

Q: Differentiate the given function glu)- In (u+ Vuzti)

A: Differentiate using basic laws

Q: Differentiate the function.

A: we have bee given the equation  u=t23+2t3 it can be written as  u=t21/3+2t3

Q: Determine the point at which the function is not analytic iz² – 2z ƒ(z) = 3z + 1 - i

A:

Q: One of the following is a set of linearly dependent functions on the interval  (-∞,∞)

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Q: At what points are the functions continuous x+3 y =- 3x, Зх, y = y = (2x – 1)3 х-2 x2 -3x-10'

A: To find the points where following functions are continuous y=1x-2-3xy=x+3x2-3x-10y=2x-113

Q: One of the following is a set of linearly dependent functions on the interval (minus infinity,…

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Q: Determine the minimum value of the function y=x√x.

A: We apply ln on both sides and then find dy/dx

Q: Create a linear function over [2,4] that has an area of zero.

A: To create a linear function

Q: Which of the following is an example of a continuous variable?

A: Here use basic of continuous variable and discrete variables

Q: Suppose we form the composition of two linear functions f(x) and g(x) with slopes m1 and m2,…

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Q: One of the following is a set of linearly dependent functions on the

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Q: A function f defined on [a, b] always has an absolute maximum and absolute minimum on [a, b].…

A: False

Q: Analyze continuity of the function.

A: Before going to the continuity, we will be finding the domain of the given function. Note that the…

Q: Show that the function g(x)  =x| x has an inflection pointat (0, 0) but g"(0) does not exist

A: Given: The function g(x)= x |x| For x<0, |x|=-x, thus g(x)=x(-x)=-x2 Also for x≥0, |x|=x, thus…

Q: Find the gradient of the graph a) y = 6-3x where x = 5 )y= 12 + x-3x? where x = - 3

A: Find the gradient of the function

Q: prove two Function invezse each other fk)= (x-2)

A:

Q: If f : [0, 3] → R is continuous, must its range be a closed interval?  use the continuous map

A:

Q: Not every differentiable function is continuous

A: If a function is said to be differentiable at its domain then it must be continuous in its domain.…

Q: If is an inner-product function , then : Select one: a. equals one b. equals zero c. is greater…

A:

Q: It is defined as group of quantities as functions of one or more independent variables. *

A: Given that: Functions of one or more independent variables.

Q: What are Continuous Variables?

A: Continuous variables are numeric variables that have an infinite number of values between any two…

Q: {x+ 2x³,3+x, 1– x} on the interval [–1,1]

A: The given set of functions are: x+2x3,3+x,1-x and the interval is -1,1

Q: Let x and y be two positive numbers. If ry = 75 , find the minimum value of 3x +4y

A: The question mentions that, xy=75 Thus, y=75x Now, let the given function be, S=3x+4y…