Q#11. The graph of y=f(x)=x^2 + 2x is shown in the graph.

i) Find the slope of the secant line joining (2, f(2)) and (4, f(4)).
ii) Find the slope of the secant line joining (2, f(2) and (2+h, f(2+h))
_____ + _____ h

Q#12. Suppose an object moves along the y axis so that its locations is y=f(x)=x^2+3x at time x(y is in meters and x is in seconds).
i) Find the average velocity (the average rate of change of y with respect to x) for x from 3 to 4.

Q#13. A ball dropped from a balloon falls y=16x^2 feet in x seconds suppose a ballon is 1296 feet above the ground when the ball is dropped.
i) After how many seconds does the ball hit the ground?

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Consider the function f(x)= sqrt(7x+6)
We will take steps to find the tangent line to the graph of f at the general point (x,f(x)), and use it to find a tangent line with a specific property.
(a) For any point (x,f(x)) on the graph of f, let (x+h,f(x+h)) be another point on the graph of f, where h [cannot]= 0 . The slope

Please see the attached file for the fully formatted problems.
1. Let . Tabulate the change of over the intervals (i) , (ii) , (iii) , (iv) , (v) . Graph together with the secantline passing through and .
Estimate how quickly is changing at .

Compute by double false position, to three decimal places, the root of: x^3 - 36x + 72 =0 that lies between 2 and 3.
* He gave us the following formula to use when using double false position:
x(subscript 2)y(sub1)-x(sub1)y(sub2)/y(sub1)- y(sub2)
I couldn't figure out how to get subscripts to show up!
PLEASE SHOW EACH S

Let f(x) = x^2 - x - 3
(a) Find the Newton-Raphson formula pk = g(pk-1).
(b) Start with p0=1.6 and find p1,p2 and p3.
(c) Start with p0=0.0 and find p1,p2, p3 and p4. What do you conjecture about this sequence.

** Please see the attached file for the complete solution response **
2) The limit of f(x) = (sin x)/x as X approaches 0 is 1
a) Let (x, sin x) be a point on the graph of g near (0,0), and write a formula for the slope of the secantlinejoining (x, sin x) and (0,0). Evaluate this formula at x = 0.1 and x = 0.01. Then

See attached.
1) Consider . Find all values, c, in the interval [0,1] such that the slope of the tangent line to the graph of f at c is parallel to the secantline through the points (0, f(0)) and (1, f(1)).
2) Use a graphing calculator to graph the function .
a) Adjust the viewing window and use the zoom and trace fea

Please respond with a Microsoft Word document with the answers written in standard text. Thank you.
Series of Various Calculour Questions Attached.
You do not need to show your work for this one because I would simply like to compare your answers with mine so that I am sure that I did everything correct on mine. Please ju

Parabola in the figure is given by: f (x) 0.5x^2 - x + 1.5
Consider the straight lines given by: y = 0.5x + b
The figure is plotted three straight lines with three different b-values, namely, 1.0, -1 ie.
y = 0.5x +1
y = 0.5x
y = 0.5x -1
a) Calculate for b = 1.5 coordinate the set for each of the intersections betw