Humanities Research Paper This is a research paper project about a topic of our choice. The student should employ the research, texts material and discussions in class. The topic I have chosen was: R

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Is continuous at x=2 Mathematically explain why or why not below:

QUESTION 3:

a) Evaluate:

b) Evaluate:

QUESTION 4:

Use the definition of derivative to find the derivative of

F(x) = 3x2 -5x

QUESTION 5:

Consider the following graphs of the functions f and g below . Beside each, sketch the graphs of f’(x) and g’(x) respectively. Consider finding the derivative at 3-5 distinctive (x,y) points.

QUESTION 6:

Differentiate the following.

a)

b)

QUESTION 7:

Find y’

QUESTION 8:

Find the equation of a passing through x = 10 if

QUESTION 9:

Find the x = c that satisfies the Mean Value Theorem for the function f(x) = x3 with endpoints x = 0 and x = 2.

QUESTION 10:

Suppose that you wanted to find the by using Newtons’ Method.

a) Define a function for Newton’s Method.

b) Show the method to find such what when Newton’s method is applied, .

QUESTION 11.

(More space on next page)

1. Find the critical points.

2. Find the intervals where increases.

3. Find the local minimum and maximum values on [-3,5].

4. Identify all inflection points.

5. Find the intervals of upward concavity.

6. Graph the function and label the critical and inflection points.

QUESTION 12:

Find two nonnegative numbers whose sum is 9 and so that the product of one number and the square of the other number is a maximum.

QUESTION 13:

a) Find the exact value of the integral:

B

b) Find each anti-derivative:

QUESTION 14: (10 points)

QUESTION 15: (10 points)

Draw the region R enclosed by the curves y =x and y =x2 which is rotated about the x-axis. Find the volume of the solid of the resulting solid.

QUESTION 16: (10 points)

In your own words, what is the main point of the study of Calculus?

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