1. Let h: R→ R be some twice-differentiable function. Define f(x, y) = h() for all x 0. Show that 8² f 20²f əyəx Əy² x202 f + 2xy მ2 +y² = 0.

Q: 3. Suppose that f is a differentiable function of one variable. If we define u(x, y) = x² f(y + In…

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Q: Assume that is differentiable on a ≤ x ≤ b and that f (b) < f (a). Show that f' is negative at some…

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Q: On what domain is the function f(x) = 3 + V5x – 20 continuous?

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Q: 1. Let h : R → R be some twice-differentiable function. Define f(x,y) =h() for all x ≠ 0. Show that…

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Q: Verify that the function ƒ(x) = x4 is concave up for x &gt; 0and for x &lt; 0. Is x = 0 an…

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Q: 10. Let F(x, y) = 1 + v4 – y². (a) Evaluate F(3, 1). (b) Find and sketch the domain of F. (c) Find…

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Q: 3. Let z = yg(x2 - y²) be a differentiable function. Show that z(x,y) satisfies 1 дz 10z 7 - + - = х…

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Q: Determine whether the following function continuous at point (1, 1). Justify your answer. (x²-xy if…

A: Here we have to determine whether the given function is continuous or not.

Q: Suppose f is a differentiable function of x and y, and g(r, s) = f(2r - s, s² - 7r). Use the table…

A: ​gr​(7,6)=−50gs​(7,6)=93​Explanation:Step 1:​Given a Table of values of f,g and fx​,fy​​​To find:…

Q: (-) = { 2*. x 2 Find the values of a and b so that f will be differentiable at x = 2.

A: Given function is fx=7x2        ,x≤2ax+b    ,x&gt;2. By continuity, 722=a2+b74=2a+b2a+b=28     ...1…

Q: Check that the equation x³ + y³ + 2³ = x + y + z implicitly defines at least one differentiable…

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Q: The interval in which the function f(x) = 2x – 12x is decreasing is O a. (-0,0) O b. (-0,-4) O c.…

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Q: Let f(x) = x° – 2, -1< x < 3 The domain ofƒ¯is the interval [A, B]| where A = and B =

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Q: Let the function f:R-->R be twice differentiable and suppose that f(x)≤0 and f''(x)≥0 for all x.…

A: It is given that, the function f:R--&gt;R be twice differentiable and suppose that f(x)≤0 and…

Q: Let fbe adifferentiable function satisfying the condition. f(x) for all x, y (+0) ERand f(y)#0. f(y)…

A: Let f be differentiable function satisfying the condition Given f(xy)=f(x)f(y)put…

Q: Draw the level curves for the function f(x,y) = x2-y. Show five level curves within the limits…

A: We shall use MATLAB to solve the above problem.We are using computer code so that it will be very…

Q: Let f(2)=u+iv be an analytic function. Given that u=v² show that f(z) is a constant.

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Q: Show that f(x)= |x| is not differentiable at x = 0.

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Q: Let f(x, y) ƒ(2, 1) = = 150 - 2x² - 4y2. Evaluate f(2, 1). Give answer in exact form. 138

A: given  f(x,y)=150-2x2-4y2for  f(2,1) , put x=2  and y=1 in f(x,y)

Q: 2. Let f(x) be a function with domain (00, -00) and f'(x) = 2x3+3x²-36r. Find the intervals where…

A: Step 1:Step 2: Step 3: Step 4: