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This problem has been solved! (a) How many n th-order partial derivatives does a function of two variables have? (b) If these partial derivatives are all continuous, how many of them can be distinct? (c) Answer the question in part (a) for a function of five variables. This is the best answer based on feedback and ratings.

(b) If these partial derivatives are all continuous, how many of them can be distinct? (c) Answer the question in part (a) for a function of five variables.

(b) (5 pts) If these partial derivatives are all continuous, how many of them can be distinct? Your answer should be a formula in terms of n. (c) (5 pts) Repeat parts (a) and (b) for h(x, y, Question: 4. Consider a function g(,y). (a) (5 pts) For n a counting number, how many nth-order partial deriva- tives does g have?

18.05.2018 · Show activity on this post. The theorem says that for f to be differentiable, partial derivatives of f exist and are continuous. For example, let f ( x, y) = x 2 + 2 x y + y 2. Let ( a, b) ∈ R 2. Then, I know that partial derivatives exist and f x ( a, b) = 2 a + b, and f y ( a, b) = a + 2 b. In order to test the continuity,

77E. 78E. 79E. (a) How many n th-order partial derivatives does a function of two variables have? (b) If these partial derivatives are all continuous, how many of them can be distinct? Step-by-step solution. Step 1 of 4. (A) For a function f of two variables the second order partial derivatives are.

If these partial derivatives are all continuous, how many of them can be distinct? Solution. Counting mixed partials as different, we get 2 kor n for 2 or n variables, respectively. If they are all continuous, then for the case of 2 variables, we only care how many times we take derivative with respect to x, which could be any integer

5.Assume f and all of its rst, second and third partial derivatives are continuous. How many possible third partials are there? How many can be distinct? 6. Optional: How many nth-order partial derivatives does a function of two variables have? If they’re all continuous, how many of them can be distinct?

Problem 98E. (a) How many n th-order partial derivatives does a function of two variables have? (b) If these partial derivatives are all continuous, how many of them can be distinct? (c) Answer the question in part (a) for a function of three variables. Chapter 14.3, Problem 98E is solved.

12.01.2021 · So we have to to the end party here is just to to the end, um, part B, it says, Um, well, if these parts derivatives are all continuous, how many of them can be distinct or that would be then, um, that would be m plus one.

2" (b) If these partial derivatives are all continuous, how many of them can be distinct? 2" (c) Answer the question in part (a) for a function of three ...

78E. 79E. (a) How many n th-order partial derivatives does a function of two variables have? (b) If these partial derivatives are all continuous, how many of them can be distinct? Step-by-step solution. Step 1 of 4. (A) For a function f of two variables the …

If these partial deriva- tives are all continuous, how many of them can be distinct? Solution For each of the successive partial derivatives ...

(b) If these partial derivatives are all continuous, how many of them can be distinct? (c) Answer the question in part (a) for a function of three variables ...

How about n variables? If these partial derivatives are all continuous, how many of them can be distinct? Solution. Counting mixed partials as ...

These approximations require f to be a 'nice' function. A sufficient condition is that all partial derivatives up to order four are continuous in a disc that ...

If these partial derivatives are all continuous, how many of them can be distinct? Solution. Counting mixed partials as different, we get 2 kor n for 2 or n variables, respectively. If they are all continuous, then for the case of 2 variables, we only care how many times we take derivative with respect to x, which could be any integer

So we have to to the end party here is just to to the end, um, part B, it says, Um, well, if these parts derivatives are all continuous, how many of them can be distinct or that would be then, um, that would be m plus one.

This is the problem of distributing n balls over k bins, which can be solved using the stars and bars approach; the result is.

... solutions and your answer to the following textbook question: If these partial derivatives are all continuous, how many of them can be distinct?.

So in order to understand the general solution here, let's start with some simple cases, some simple cases. So if N is equal to one, then there are only two possibilities here. We either have, well, the partial derivative with respect to X. So if some X or the powerful derivative with respect to Y f sub y. Um, if n equals two, well, then there are four possibilities.