Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Practice Exam 4 - Fall 2004 - Calculus I | MAT 124, Exams of Calculus

Material Type: Exam; Class: Calculus I; Subject: MAT Mathematics; University: Eastern Kentucky University; Term: Fall 2004;

Typology: Exams

Pre 2010

Uploaded on 08/19/2009

koofers-user-6li
koofers-user-6li 🇺🇸

10 documents

1 / 2

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
MAT 124 Jones - Fall 2004
Calculus I
Exam 4
Place all solutions neatly on a separate sheet of paper; solutions written on the exam may not be
graded. Show all work for partial credit! Clearly write ID# - no names - on each sheet of paper
you turn in to be graded.
1. Differentiate the following functions:
(a)
(b)
(c)
(d)
2. A catenary is the curve formed by a homogeneous flexible cable hanging from two
points under its own weight. If the lowest point of the catenary is the point (0,a), it can
be shown that an equation of it is . Show that a catenary is
concave upward at at each of its points. (That is, show that for all x.)
3. A ladder 25 feet long is leaning against a vertical wall. If the bottom of the ladder is
pulled horizontally away from the wall at a rate of 3 ft/sec, how fast is the top of the
ladder sliding down the wall when the bottom of the ladder is 15 feet from the wall?
4. (a) Find the absolute extrema for on .
(b) Find the absolute extrema for on .
pf2

Partial preview of the text

Download Practice Exam 4 - Fall 2004 - Calculus I | MAT 124 and more Exams Calculus in PDF only on Docsity!

MAT 124 Jones - Fall 2004 Calculus I Exam 4

Place all solutions neatly on a separate sheet of paper; solutions written on the exam may not be graded. Show all work for partial credit! Clearly write ID# - no names - on each sheet of paper you turn in to be graded.

  1. Differentiate the following functions:

(a)

(b)

(c) (d)

  1. A catenary is the curve formed by a homogeneous flexible cable hanging from two points under its own weight. If the lowest point of the catenary is the point (0, a ), it can be shown that an equation of it is. Show that a catenary is

concave upward at at each of its points. (That is, show that for all x .)

  1. A ladder 25 feet long is leaning against a vertical wall. If the bottom of the ladder is pulled horizontally away from the wall at a rate of 3 ft/sec, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 15 feet from the wall?
  2. (a) Find the absolute extrema for on.

(b) Find the absolute extrema for on.

  1. Evaluate the following limits:

(a)

(b)

(c)

(d)

  1. A dairy farmer plans to fence in a rectangular pasture adjacent to a river. The pasture must contain 180,000 square meters in order to provide enough grass for the herd. What dimensions would require the least amount of fencing if no fencing is needed along the river?
  2. Evaluate the following “most general antiderivatives”:

(a)

(b)

(c)

(d)

(e)

(f)