In this exercise we investigate the curve et – 1 y = f(x) ez +1 (a) Explain why –1< f(x) < 1 for all real numbers x. (b) Find lim f(x) and lim f(x). (c) Find f'(x) and explain why the function f is increasing.

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A: given that the function f(x) is a function with the following properties: a) f(-1)=2, f(1)=1 and…

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A: Since you have asked multiple sub parts in a single request so we will be answering only first three…

Q: 62²(2³-128) (³+64)³ Consider the function f and its derivatives f(x)=3+64 f'(x)= -2(³-32) (+64)2…

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Q: Use the limit definition of the derivative to show that the derivative does not exist at x = a for…

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Q: In the above space, draw the graph of a function with ALL of the following properties: (a) f(0) =…

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A: Let

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Q: (a) Let h(x) = f(x)/g(x). Find h'(1). (b) Let h(x) = g(f(x)). Find h'(-1).

A: Definition used -           Quotient rule of derivative -…

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Q: Shown below are six statements about functions. Match each statement to one of the functions shown…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: