Let f : R → (0, +∞) be differentiable. Suppose that f' has no zero. If lim→0 f(x) = %3D 0, then lim,-o (csc f(x))f(æ) is 0 (b) is 1 (c) does not exist (d) None of them a

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A: The given function is f:ℝ2→ℝ defined as: fx,y=y2-x2y4+x2if x,y≠0,01if x,y=0,0 Claim: The given…

Q: Let f(r) = In r Find and simplify f"(x).

A: Please refer the attached image for complete solution. THANK YOU.

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Q: Suppose f: (0,00) → (0, ∞) and g: (0, ∞o) → (0, ∞o) are continuous functions. True or false: If g…

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Q: 1. Let f : (−1,1) → R, f(x) = (1+x³)-³. Compute g' : (0, 1) → R where (a) g(x) = X X f. (b) g(x) =…

A: Answers along with explanations are provided in the image. Explanation:

Q: 3. Find and sketch the domains of f(x, y) = xy and g(x, y) = xy In(9-x² - 9y²)*

A: The given functions are,

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A: Bartleby Guideline : ''Since you have posted a question with multiple sub parts , we will provide…

Q: 31. Assume that f is continuous and 2x S f ₁ f(t) d² = 4 + x²" dt (a) Determine f(0). (b) Find the…

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Q: f(x,y) = x=y - 2xy? + 3xy +4 %3D

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Q: Show that f : ℝ → ℝ, f(x) = 5x − 3 is a bijective function.

A: The given function is f:ℝ→ℝ defined by fx=5x-3. We say that a function f is bijective if it is both…