1. Find the derivative dy/dx for the following functions

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1. Find the derivative dy/dx for the following functions: 2. A popular search engine is targeting European countries where the number of online households is expected to grow at a steady rate. Data was taken over time, and it was found that the number of online houses (in millions) projected can be modeled by the following function: The year is 2004 when. Address the following: a. What was the projected number of online households at the beginning of 2005? b. How fast was the projected number of online households increasing at the beginning of 2005? 3. Light is absorbed when it passes through a glass window. If r% of the light is absorbed by a glass with a thickness w, then the percent of light that is absorbed by a piece of glass with a thickness nw for any natural number n is modeled by the following function: a. Show that A is an increasing function of n if 0 < r < 100. b. Sketch the graph of A when r = 10. c. Evaluate limn∞ A(n), and interpret the results.

Individual Project

1. Find the derivative
dy/dx
for the following functions:

2. A popular search engine is targeting European countries where the number of online households is expected to grow at a steady rate. Data was taken over time, and it was found that the number of online houses (in millions) projected can be modeled by the following function:

The year is 2004 when. Address the following:

a. What was the projected number of online households at the beginning of 2005?

b. How fast was the projected number of online households increasing at the beginning of 2005?

3. Light is absorbed when it passes through a glass window. If
r%
of the light is absorbed by a glass with a thickness
w
, then the percent of light that is absorbed by a piece of glass with a thickness
nw
for any natural number
n
is modeled by the following function:

a. Show that A is an increasing function of n if 0 < r < 100.

b. Sketch the graph of
A
when
r = 10.

c. Evaluate limn∞ A(n), and interpret the results.

4.

What are the different type of critical values of a continuous function on the interval (a,b).

Provide an example on the stationary value.