Exerise: Letf:K⊂Rn→Rbe a continuous function. Let&be a compact set \[ \begin{array}{l} M=\{x \in x: f(x) \text { ise } \\ \text { max of } f \\ \text { on } k\} \\ \end{array} \] Show:M is compact.   please do not provide solution in image format thank you!

Q: Suppose  f ( 200 , 300 ) = 1000and ∂ f ∂ x ( 200 , 300 ) = 12 and ∂ f ∂ y ( 200 , 300 ) = 10.…

A: Given, f(200,300)=1000 ∂f∂x(200,300)=12∂f∂y(200,300)=10

Q: Provide an example of a function which is continuous on all of R and differentiable on all of R…

A: The function is y=x+4 (shown in the figure above)

Q: Suppose f is a function defined and continuous on the open interval (a, b). Suppose g is a function…

A: Given that: f is a function defined and continuous on the open interval (a, b).g is a function…

Q: Which of the following mappings A: R^2->R is a linear functional? (a) (a,b) -> lal + lbl. (b)…

A: Step 1:A linear functional is a linear map from a vector space to its underlying field. Formally,…

Q: Consider a function f:C⟶C, defined by f(z)=7z^2. Then which of the following is true? Check all…

A:

Q: How are the continuous extensions often found?

A:

Q: The linear mapping A:R^2[x] -> R^2x2 is defined by the rule Ap= [p(0);p(1);p(-1);p(0)]. Then the…

A: Step 1:A:R2[X]→R2∗2  Defined by  A(p(x))=[p(0)p(−1)​p(1)p(0)​] Step 2: let kernel K is the kernel of…

Q: Find the arc length from (0,8) clockwise to (7. √15) along the circle x² + y2 = 64. (Round your…

A: Solution:Given circle: we have to find the arc length from clockwise to along the circle

Q: Giveanexampleofafunctionf :R→Randapointx0 ∈Rsuchthatx0 is a stationary point but it is neither a…

A:

Q: Every function defined on a closed interval [a, b] must have a global maximum and a global minimum…

A: Find your answer below

Q: Find the domain and the range of the functions and describe it as regions in relevant spaces as well…

A: The objective is to evaluate the domain and range of x+116-x2-y22-z2. To find the domain and range…

Q: Consider the function f(x)=x³-2-x+2 that has exactly one root. Which of the following intervals…

A:

Q: What is the least upper bound of the real interval (2, 6)?

A: