6. Assume f(x) is a continuous function on [0, 1], prove that 3x € (0, 1) s.t. f(x) < 1/x. (hint: should NOT use IVT for 1/x on [0, 1] since 1/x is not defined at 0)

Q: 9. How should f(0,0) be defined so that f(x,y) - (x + y)² (X+s x² + y² is continuous at (0, 0)?

A: The given function is: fx,y=x+y2x2+y2 is continuous at 0,0 To define f0,0

Q: Use the Second Fundamental Theorem of Calculus to find F'(x). • L₁ VE 4 + 4 dt Vt Step 1 F(x) = Note…

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Q: 6. Does there exist a continuous function on the interval [0, 2] such that f(0) = 0, f(2) = 7, and…

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Q: 3. For m₁ and m₂ numbers, with m₁ { Prove that the function f:R → R is continuous but not…

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Q: Show that a continuous function f : [0, 1] → Z is a constant function.

A: Consider a function .We need to show that a continuous function  is a constant function.We know…

Q: Explain why or why not Determine whether the following statements are true and give an explanation…

A: We have to determine whether the given statements are true or not: a.  ∫fx f'x dx=12fx2+Cb.  ∫fxn…

Q: 10. (True/False) For any continuous function f(x, y), we have fry = fyr.

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Q: 9 f:(-0,0) U (0, ∞) → (∞,0) U (0, ∞0). Where f(x) х Show that f(x) is continuous at x=3 with the…

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Q: 15. Let f(x, y) = 22 if (x, y) ‡ (0,0), and f(0,0) = 0. Is ƒ continuous at (0,0)? x+y

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Q: 3. Define f(x) so that S(2) = {ap(). f(x) = 0, |피 1 (a) Explain why the function f(x) must be…

A: As per our guidelines we can answer only 3 subparts. please ask others seperately.

Q: rence quotlent ic 10t1 'function beIow f(x) =4x2-Loxti IMmify your answer .h..

A: f(x) = 4 x2- 6x + 1   Difference quotient = f(x+h) -f(x)h   f(x+h) =4(x+h)2 -6(x+h)+1 f(x+h) =…