3. Describe the domain and range (i.e., comment on whether the domain and range are bounded/unbounded and open/closed) of the function f(x,y) = /In (x2 + y²).

Q: 5. Determine the minimum value of f(x) 3x on the interval [-1,1] %3D

A: Let's find.

Q: 1. Find and sketch the domain of the function f(x, y)= In ツー1 Vアーx

A: As per our company guidelines we are supposed to answer only one question at a time. Kindly repost…

Q: What is the global maximum of the function, x2 f(æ): 3 on the interval[-2, 2] ? 3 2

A:

Q: Find the global maximum of f(x) = x(4−2x) over the interval (−∞,∞)

A: Given:The function is f(x) = x(4-2x) .The interval is (−∞, ∞).

Q: Say if the following statement is true or false: If a function f is twice differentiable at the…

A: If c is a critical point of the function, then  f'c=0. To check whether the critical point…

Q: Consider the function f(x,y,z) = (x+y+z)° on the domain R’. (b) Is f a quasi-concave function? If ƒ…

A: Given: Function f(x, y, z)=x+y+z3 on the domain ℝ3. To determine: Whether the given function is…

Q: 4. Use the graph of y = f(x), at right, to determine whether f possesses extrema on the interval (a,…

A:

Q: 1. Determine and sketch the domain of the function f(r,y) = e2/Vy¬I, What is the range of f?

A: So, given function is    f(x, y) = e-x/y-1     here,  y should strictly be above 1    and then it…

Q: Show that the limit of the function f(x,y)= (0,0). (x+y)² x² + y² is indeterminate at

A: Limit of the function

Q: Define the function f(x, v) = 4x³-x³y-4y5 3x5-3y5 at the origin so that it becomes continuous there.

A: A function is said to be continuous at (a,b) if the the value of function at (a,b) is equal to…

Q: Use limits to determine if f(x) = is continuous at z = -2. (z+2)²

A: Given that  f(x)= 1(x+2)2 is continuous at x = -2

Q: Let f(x) xe^-x/2 Find the absolute maximum of the value of f on the interval [0,6]

A:

Q: Let f(x) = x³ - 3x². Find the absolute minimum value of f(x) on the interval [1, 4].

A: The given function,  f(x)=x3-3x2 on the interval 1,4

Q: Let f be the function defined byf (z) = 3z2 -z. What is the absolute minimum value of f on the…

A: Topic = Application of Derivative  The absolute minimum value of f is 0.

Q: calculate the are between the curves f(x)=x^2 and g(x)=x^3 on the interval [-1,1]

A: Given,

Q: Describe the domain of the function f(x, y) = In(4 – z – y). O {x.y):y<-x+4}

A: Given: fx,y=ln4-x-y Objective of the given problem is to find the domain of the given function. The…

Q: Find the global maximum and global minimum of f(x)=x√x in the interval [2,3].

A:

Q: Find the absolute extrema of the function on the closed interval.                      g(x) = 6x2/(x…

A: Given    g(x)=6x2x-2 ;  -2,1

Q: How do I solve this?

A: Global maxima or minima of f(x) in [a, b] is basically the greatest or least value of f(x) in [a,…

Q: 4. Use the graph of y = f(x), at right, to determine whether f possesses extrema on the interval (a,…

A:

Q: Let f(x) = x -[r] and f :[1,5) →[0,1). What is the discontinuously type of f(x) at the point x = 3?

A:

Q: 5. (a) Consider the function f : C → R, f(2) = (z + z)². Write down the %3D domain, codomain and…

A: The domain is C, the set of all complex numbers. The codomain is R, the set of all real numbers.

Q: Let f(x) be maximum and g(x) be minimum of {x|×|, x² |x} then

A:

Q: Show that the limit of the function f(x,y) = at (0,0) does not exist. (x+y)² x² + y²

A: Limit of a Function: Like a single-variable function, a multi-variable function can also have limit.…

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: Consider the function f(x) = 2x3 - 3x2-12x+c, where c is some ne location of the absolute maximum…

A:

Q: Locate the absolute extrema of the function on the closed interval. f(t) = ₂, [3,5]

A:

Q: Let f (x, y) = 4-y² In(y–z²) %3D Draw a picture of the domain of this function.

A: x,y ∈R2

Q: Suppose that u(x) is a differentiable function such that

A:

Q: 1. Give an example of a function f : R –→ R that is continuous and bounded but does not achieve…

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

Q: Determine the maximum value of f (x) = 5x – e5x [T:3] on the interval [-1,1] %3D

A:

Q: Determine the set of points at which the function is continuous. F(x, y) - х-у 1 + x² + y2

A:

Q: Find and sketch the domain of the function f (x, y) = In(9 – x² – 9y²).

A: The given function,  f(x,y)=ln9-x2-9y2

Q: Find the limit of the function f(x) = x²esin(1/x) as x approaches to zero.

A: To find limit of function f(x)=x2esin(1/x) as x approaches to 0. (Using Squeeze theorem)

Q: Use the intermediate value theorem to show that f(x) = e-x2− x has at least one root in the interval…

A:

Q: Use limits to determine if f(x) = is continuous at x = 1. z-2

A:

Q: Give an example of a derivable function f (x) with f ′ (- 4) = -3

A:

Q: Locate the absolute extrema of the function on the closed interval. In x, [1,4] 7x g(x) = minimum…

A:

Q: 4|x| – 3 pour x 1, x² – 4 f2(x) + V2 + x², || ||

A: Given that, f1x=4x-3x≤1-3xx2-4x&gt;1f2x=1+2+x2 To determine set of points which they are derivable…

Q: Any function f defined on R should have a relative extremum.   True or False

A: In the question we have to find whether the statement is true or not.

Q: Find the absolute extrema of the function on the closed interval. f(x) = x3 - 12x, [0,6]

A:

Q: Use the intermediate value theorem to show that f(x) = (e^−x^2)−x has at least one root in the…

A:

Q: Use the intermediate value theorem to show that f(x) = e −x 2 − x has at least one root in the…

A:

Q: what is the absolute maximum/minimum of: f(x)=xln(x/4) on [0.2,4]

A: Given, function is

Q: Describe the domain and range of the function. f(x, y) = In(xy-1) Dor

A:

Q: Q1// Find and sketch the Domain of f(x,y) In (x' y)

A:

Q: Let f(x, y) = -e2"-y + In(3x – y). Find the domain of this function.

A:

Q: ) Use the Intermediate Value Theorem to show that there is one such that f"(a) = 0. point x = a

A: As per our guidelines we are supposed to answer only first 3 subparts of the question. Kindly repost…

Q: Suppose that f is a function with f(2) &gt; 0 and f1(2) = 0. If f is a local minimum of f, what do…

A: It is supposed that f is a function with

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.