CALCULUS I
Dr. Nguyen Ngoc Hai
DEPARTMENT OF MATHEMATICS
INTERNATIONAL UNIVERSITY, VNU-HCM
April 19, 2010
Dr. Nguyen Ngoc Hai
CALCULUS I
References
Main textbook:
J. Steward, Calculus. Concepts and Co
Chapter 4. THE INTEGRAL
4.1
THE AREA PROBLEM
Problem:
Find the area of the region S under the curve y = f (x ) over
an interval a x b, where f (x ) 0 and f is continuous on
[a, b ].
This means that S
Chapter 2 DIFFERENTIATION
Contents
[1.] Tangent Lines and Their Slopes
[2.] Derivatives
[3.] Dierentiation Rules
[4.] Rates of Change in Natural and Social Sciences
[5.] Derivatives of Trigonometric F
Chapter 3. APPLICATIONS
OF DIFFERENTIATION
Contents
1. Related Rates
2. Extreme Values
3. The Mean Value Theorem. Shapes of Curves
4. Sketching the Graph of a Function
5. LHpitals Rule
o
6. Optimizati
Chapter 5. APPLICATIONS OF INTEGRATION
5.1
AREAS BETWEEN CURVES
5.1.1
AREA BETWEEN TWO CURVES
y = f (x ) AND y = g (x )
If f (x ) g (x ) 0 for x [a, b ], then the graph of f lies above
the graph of g
1.
lim x 3 f ( x )=3
means that as x approaches 3,
f (x)
gets closer to 3. It can
get infinitely close but not touch. So it can be
2.999999999999999999999999999999999 and be ok but it cannot be 3.
2.
1)
a. no limit
b. I am going to say no limit. I used 3 different calculators and got 3 different graphs.
2)
a. 2
b. 3
c. does not exist
d. does not exist
e. infinity
f. infinity
g. 1
x2
3) B(x)= x 2 +