3 Suppose that e(x) and f(x) are differentiable on [0, 1] and that 0 < |e'(x)| < |f'(x)| for all x € (0, 1). Show that |e(x) – e(y)| < |f(x) – f(y)| for all æ, y E [0, 1].

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A: topic - integration

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A: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

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A: We will use properties of logarithm. lnan = n lna  ln(a.b) = lna + lnb

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A: if we want to fine any fuction has relative extrema then

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A: To show: For any constant k, ddxf(x)k = f'(x)k

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A: f(0)=2   and f'(x)≤3  for all x&gt;0 ⋯(i)integrate (i) w.r.to x ,we getf(x)≤3x+kput…

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A: We have to prove the given equation.

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A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Suppose that a continuous function g satisfies: g(x)dr = 30 and g(2x)dx = 3. 0. 2 Find r9(3x²)dx.

A: Suppose that a continuous function g satisfies: ∫03gxdx=30 and ∫06g2xdx=3. The, we have to find the…

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A: We need to find inverse function.

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A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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