10 Questions
| Total Attempts: 1148

Questions and Answers

- 1.Which of the following can be thought of as a special case of the Mean Value Theorem?
- A.
L'Hopital's rule

- B.
Intermediate Value Theorem

- C.
Rolle's Theorem

- D.
Extreme Value Theorem

- 2.How many REAL roots does the polynomial x to the fifth +12x-7 have?
- A.
3

- B.
0

- C.
1

- D.
2

- 3.What is the integral from 0 to Pi over 2 of (Sine of x divided by the sum of Sine of x and Cosine of x)?
- A.
Pi over 2

- B.
Pi over 6

- C.
Pi over 3

- D.
Pi over 4

- 4.How many roots (real or complex and counting multiple roots the number of times they occur) will a polynomial of degree n have?
- A.
We can't tell, we need more information to determine anything

- B.
At least n, but sometimes more

- C.
Exactly n

- D.
At most n, but sometimes less

- 5.True or False: If two infinitely differentiable functions match in their value and all their derivatives at a point, then the functions must be the same?
- A.
True

- B.
False

- 6.Are the following statements true or false: A. If a function is differentiable at 0, it is continuous there. B. If a function is differentiable at 0, its derivative is continuous there?
- A.
Neither are true

- B.
B is true, but not A

- C.
A is true, but not B

- D.
Both are true

- 7.What is the broadest definition of calculus?
- A.
The study of collections of data

- B.
The study of operations and applications

- C.
The study of change

- D.
The study of shape

- 8.What are the two main branches of calculus?
- A.
Differential and probability

- B.
Differential and integral

- C.
Integral and probability

- D.
Probability and trigonometry

- 9.Who is widely considered to be the father of calculus (or the father of differential and integral calculus)?
- A.
Both

- B.
Gottfried Wilhelm Leibniz

- C.
Sir Isaac Newton

- D.
Neither

- 10.When differentiating a function, what does the answer mean? In other words, what does the derivative of a function represent?
- A.
The rate of change of a function at a specific value

- B.
Both

- C.
The slope of the tangent line to a curve

- D.
Neither