6. Let f(x) = x2/3. (a) Then fis uniformly continuous on [-1,1]. Why? (b) Show that there does not exist a constant M such that |F(x) – f(x')|

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A:

Q: 6.(a) Show that (f.g) = f f(x)g(x)dx satisfies the axioms of an inner product on C[a, b], the space…

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Q: 3. Let f be continuous on [-1, 4] and differentiable on (-1,4). If f(-1) = –1 and f(4) = 4, then the…

A:

Q: Sketch the graph of f(x) if ...f'(x)>0 on (2,4) and f'(x)<0 on (−∞, 2) ∪ (4, ∞),f''(x)>0 on…

A: Here we suppose that the given function is continuous on the given intervals and differentiable on…

Q: ƒ(0) = 0, and ƒ'(−2) = f'(1) = ƒ'(9) = 0 ● lim f(x) = 0 and lim f(x) x →∞ x→6 • f'(x) 0 on (-2, 1)…

A:

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

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A: Increasing/Decreasing Functions: The derivative of a function used to determine whether the function…

Q: 9 Prove that if m(x) is differentiable on (-∞, 0) and its derivative m'(x) is bounded then m is…

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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: Which of the following is a graph of a functionf that satisfies the following conditions: • f'(x) 0…

A: d2dx2fx >0  on  -∞,-1  Thus, the minima lies in region x =  -∞,-1    Thus, only graphs C and D…

Q: Q2 1 Point Assume that f : [0, 1] → R is differentiable, that ƒ'(0) = 1 and ƒ'(1) = 2. Which, if…

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A: Solution is in next step

Q: Consider f, a function such as f(2) = 1, f'(2) = 2, f''(2) = 3 and f'''(2) = 4 and that verifies:…

A: Given: f(2)=1, f'(2)=2, f''(2)=3 and f'''(2)=4 To find: Error bound in the approximation of f1.

Q: Suppose f(z) is defined on all of C, is differentiable at z = a, and satisfies f(a) = a. Show that…

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Q: Exercise 1: For the following properties, give an example of a functionf that is continuous…

A: given condition:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.