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Calculus 1 Quiz Questions and Instructions from Prof. Brick, Exercises of Calculus

Instructions and questions from a series of calculus quizzes given by prof. Brick during the fall ’00 semester. The quizzes cover various topics in calculus, including limits, derivatives, and integrals. Students are asked to print their names, discuss their reasons for taking the course, and estimate slopes of tangent lines. Some questions require the use of calculus concepts to find formulas, limits, and tangent lines.

Typology: Exercises

2012/2013

Uploaded on 03/31/2013

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Prof. S. Brick Math 125
Fall ’00 section 51
Calculus 1; Quiz 0
1. Print your name. You must print it legibly. Also mention your year in
school and your probable major.
2. Why are you taking this course ? Will you be taking other math or statistics
courses ?
3. What, when, where, and from whom was the last math course you took ?
4. What is Calculus ? Why do we study it ?
5. How many hours per week do you plan to put into this class ? What will
you do if you start having difficulties with the material ?
6. Why are you taking a night course ? Are you aware that they are often
more demanding on the student ?
7. What grade do you honestly expect to get from this class ? Why ?
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Prof. S. Brick Math 125 Fall ’00 section 51

Calculus 1; Quiz 0

  1. Print your name. You must print it legibly. Also mention your year in school and your probable major.
  2. Why are you taking this course? Will you be taking other math or statistics courses?
  3. What, when, where, and fromwhomwas the last math course you took?
  4. What is Calculus? Why do we study it?
  5. How many hours per week do you plan to put into this class? What will you do if you start having difficulties with the material?
  6. Why are you taking a night course? Are you aware that they are often more demanding on the student?
  7. What grade do you honestly expect to get fromthis class? Why?

Fall ’00 section 51

  1. Print your name:
  2. How is the graph of y = π − f (x +
  1. obtained from that of y = f (x).
  1. A piece of wire ten inches long is to be cut in two to form a circle and a square. Find a formula for the total area enclosed by these two regions (as a function of a single variable).
  2. For what value of k is the graph of f (x) =

2 x

(^2) + k, if x ≤ 1, x, if x > 1,

a single continuous

curve? Sketch the graph.

Fall ’00 section 51

  1. Print your name:
  2. Draw the graph of a function y = f (x) which is defined and non-zero for all x, with lim x→−∞ f (x) = −∞, lim x→ 3 f (x) = +∞, and lim x→+∞ f (x) = 0
  3. Find lim x→−∞

3 x^2 − 5 x^3 + 7 8 x^3 + 19

. Show your work.

  1. Suppose f (x) =

x. Using f ′(x) =

x

, find the tangent line to y = f (x) at x = 4.

Fall ’00 section 51

  1. Print your name:
  2. Using the definition, find

d dx

3 x^2 + 5x

  1. Use the derivative to approximate
  1. Graph a function whose derivative is always positive but whose derivative is also always decreasing.

Fall ’00 section 51

  1. Print your name:

No Calculators allowed.

  1. Let P (t) be the price of a stock listed on the New York Stock Exchange, where P is in dollars per share and t is in days (with t = 0 being the 1/1/00). What are the units of P ′(t)? What does P ′(286) < 0 and P ′′(286) > 0 say about the stock?
  2. Find a formula for

dy dx

given that x^2 + y^2 = e−x/y^.

  1. Find the line tangent to xy^2 − 3 x^2 y = sin(3x^2 − y) at (1, 3)

Fall ’00 section 51

  1. Print your name:

No Calculators allowed for exercises 1 and 2.

  1. Find the derivative of y = ln(5x^2 + 10) + arctan(1 + x^3 )
  2. Find the derivative of y = (3x^2 + 1)x+
  3. The radius of a circular silicon wafer is estimated to be 0.14 cm with a possible maximum error of ± 0 .003 cm. Estimate the error and relative error that may result from using this measurement to calculate the area of the circular region.

Fall ’00 section 51

  1. Print your name:
  2. Find lim x→ 0

ex^ − x − 1 x^2

  1. A 50 foot straight section of fencing is to be completed into a rectangular garden using 120 feet of new fencing. How should it be done to yield maximum area?
  2. Suppose C(x) = 100 + 8x + x^2 is the cost function for producing widgets. Find the marginal and average cost. What production level minimizes aveage cost?