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.

Q: If f(x) = (1+%) 3 ) 6x *", find lim f(x).

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Q: I feel confident about one of my answers but not sure. Can you help me solve number 1 a-c. Thanks

A: a)Given function is f(x)=x^2+3By defintion , f'(x) can be evaluated as

Q: Consider the piece wise function – x² + 16 x 4 VI

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Q: (x)- f(1) lim f(x) = 2 , where x-1 х-1

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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: