Please solve question 6, doing surds
1 answer:
See the attached diagram, it has all the information you need.
(a) If the green radii are all 1, then the orange diameters are all 2 + √2, so that the orange radii are (2 + √2)/2 = 1 + √2/2.
This is because we can join the radii of two adjacent green circles to form the sides of a square with side length equal to twice the radius - i.e. the diameter - of the green circles. The diagonal of any square occurs in a ratio to the side length of √2 to 1. Then we get the diameter of an orange circle by summing this diagonal length and two green radii, and hence the radius by dividing this by 2.
(b) We get the blue diameter in the same way. It has length (2 + √2) (1 + √2/2) = 3 + 2√2, so that the blue radius is (3 + 2√2)/2 = 3/2 + √2.
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<h2>Part 1.</h2>
Answer:
The limit of the difference quotient is simply the derivative, so we can express this as follows:
So our function is:
Taking the derivative, we have:
So the correct option is:
Answer:
The equation of the line that passes through the same point can be found as:
Where , so we need to find
. Plug in that x-value in the function we have:
And the slope is:
Then, the equation of the line is:
Answer: Shown below
As you can see below, the graph of the function of is continuous. This is so because we have plotted a polynomial function whose domain is the set of all real numbers. So the function is defined at the point
, so the derivative exists at this point, hence we can calculate a tangent line there. In conclusion, we get the graph shown below. The blue line is the tangent line while the red curve is the graph of