Birla Institute of Technology & Science, Pilani  Hyderabad
Calculus I
MA 101

Spring 2015
Calculus  I
(MA 101)
M.Thamban Nair
Department of Mathematics
Indian Institute of Technology
December 2001
Contents
Preface
6
1 Sequence and Series of Real Numbers
1.1
1.2
1
Sequence of Real Numbers . . . . . . . . . . . . . . . .
1
1.1.1
Convergence and
Birla Institute of Technology & Science, Pilani  Hyderabad
Calculus I
MA 101

Spring 2015
2
Limit, Continuity and Differentiability
of Functions
In this chapter we shall study limit and continuity of real valued functions defined
on certain sets.
2.1
Limit of a Function
Suppose f is a real valued function defined on a subset D of R. We are goi
Birla Institute of Technology & Science, Pilani  Hyderabad
Calculus I
MA 101

Spring 2015
DEPARTMENT OF MATHEMATICS
IIT MADRAS
MA1010: Calculus I : Functions of one variable1
Problem Sheet V
1. Let f be a bounded function on [a, b]. Prove that, if there is a partition P of [a, b]
such that L(P, f ) = U (P, f ), then f is a constant function.
2
Birla Institute of Technology & Science, Pilani  Hyderabad
Calculus I
MA 101

Spring 2015
Production Examples
On each example worksheet, read the comments at the bottom of the sheet, then
click Tools Solver. to examine the decision variables, constraints, and objective.
To find the optimal solution, click the Solve button.
One of the areas whe
Birla Institute of Technology & Science, Pilani  Hyderabad
Calculus I
MA 101

Spring 2015
Name: _ Date: _ Due: Sunday, October 9th, 11:59p
Ch 17, 88 pts.
Instructions:
1. Answer the following questions on this sheet only. That is, do not answer on a separate
paper. Do not give me the graphs on a separate sheet (like a spreadsheet).
2. Submit
Birla Institute of Technology & Science, Pilani  Hyderabad
Calculus I
MA 101

Spring 2015
DEPARTMENT OF MATHEMATICS
IIT MADRAS
MA1020: CalculusII: Functions of Several Variables
Problem sheet  2
(1) A function f of two variables is said to be homogeneous of degree n if it satisfies
the following equation:
f (x, y) = n f (x, y) for all real ,
Birla Institute of Technology & Science, Pilani  Hyderabad
Calculus I
MA 101

Spring 2015
1. [15 points] Awesome Swords manufactures two types of swords: knight
and magical. The following information about the production process is
available:
Number produced
Machine hours
Knight
120,000
Magical
75,000
95,000
25,000
7,000
35,000
Inspection hour
Birla Institute of Technology & Science, Pilani  Hyderabad
Calculus I
MA 101

Spring 2015
Problem2
The manager of the Radford Credit Union (RCU) wants to determine how many parttime tellers to employ to cover the peak demand time in its lobby from 11 am to 2 pm.
RCU currently has 3 fulltime tellers, but during this peak demand time customers
Birla Institute of Technology & Science, Pilani  Hyderabad
Calculus I
MA 101

Spring 2015
QSO 320 Milestone Four Business Scenario
As a business analyst, you have been asked by management to examine the data collected and analyzed
in the previous modules. The objective is for you to help management decide on the right mix of wine
bottles to se
Birla Institute of Technology & Science, Pilani  Hyderabad
Calculus I
MA 101

Spring 2015
A. The XYZ Corporation is considering plant expansion to enable it to begin production
of a new military helicopter. The companys CEO must decide whether to order a
medium or a large scale expansion.
Demand for the new military helicopter is uncertain be
Birla Institute of Technology & Science, Pilani  Hyderabad
Calculus I
MA 101

Spring 2015
Solutions of Some Problems from Assignment SheetI
M.T.Nair
Department of Mathematics, IIT Madras
August 29, 2013
1. Suppose an a.
(b) Suppose a > 0. To show that that there exists k N such that an  > a/2 for
all n k.
We have
an  = a (a an ) a
Birla Institute of Technology & Science, Pilani  Hyderabad
Calculus I
MA 101

Spring 2015
BLTD CorporationCapital Budgeting Case
Corporate FinanceMoeller
BLTD Corporation is a drug manufacturing company that emphasizes developing new
drugs. They have been working on a series of related methods to help people cope with
anxiety. Currently they
Birla Institute of Technology & Science, Pilani  Hyderabad
Calculus I
MA 101

Spring 2015
I am creating a game called Name that Dog. The game will work as follows: An ASCII image of a
dog will appear on the screen and the player will be asked to name what breed of dog it is. The
player will win when they guess all five breeds correctly, the pl
Birla Institute of Technology & Science, Pilani  Hyderabad
Calculus I
MA 101

Spring 2015
E1.1
2
H2.2
Discussion on features of the each language.
Evaluation of programming language based on Objectoriented
abstraction, Imperative programming and Web development.
Stance taken and justification
PartA Max Marks
Designing a state diagram to reco
Birla Institute of Technology & Science, Pilani  Hyderabad
Calculus I
MA 101

Spring 2015
Below is the information for two microscopes, Model A and
Model B
Model A This microscope comes with four objectives
10X, 20X, 40X and 60X. The ocular is rated at 5X. The
minimal distance between two points that can be
distinguished as separate from each
Birla Institute of Technology & Science, Pilani  Hyderabad
Calculus I
MA 101

Spring 2015
a) For the beam shown below derive the equations of shear force and bending moment
using dV/dx=w and dM/dx=V for regions AB and BC. Then draw them on Shear
force and bending moment diagrams (in your SFD and BMD, you should also indicate
the place of zero
Birla Institute of Technology & Science, Pilani  Hyderabad
Calculus I
MA 101

Spring 2015
Investments and Security Analysis common stock pricing
1. (20) ABC Inc. expects earnings over the next year of $4 and has a dividend payout
ratio of 50 percent, a beta of 2, growth in dividends of 8%, and an ROE of 16%. One
way to get an estimate of a com
Birla Institute of Technology & Science, Pilani  Hyderabad
Calculus I
MA 101

Spring 2015
Extra Credit Problem (10 points)
Cavitation
ME 111 Fluid Mechanics
Dr. Paul Kutler
Fall 2016, Section 2
Name: _
During class, Dr. Kutler demonstrated how cavitation can break the bottom off
a beer bottle. The beer bottle was filled with water to the base