monday, august 31, 2015mat 145. monday, august 31, 2015mat 145
TRANSCRIPT
Calculus I (MAT 145)Dr. Day Monday August 31,
2015 Continue to Formalize and Extend the Idea of Limits
(2.2-2.4, 2.6)
Assignments
Monday, August 31, 2015
MAT 145
MAT 145
Approachment
Monday, August 31, 2015
As the values of some set of inputs tend to get closer and closer to a number, the corresponding list of outputs get closer and closer to some number.
MAT 145
Transitioning from . . .
Approachment
Monday, August 31, 2015
As the values of some set of inputs tend to get closer and closer to a number, the corresponding list of outputs get closer and closer to some number.… to …
an equivalent
mathematical representation
MAT 145Monday, August 31, 2015
This says that the values of f(x) tend to
get closer and closer to the number L as
x gets closer and closer to the number a
(from either side of a) but x ≠ a.
The concept of . . . LIMIT!
MAT 145Monday, August 31, 2015
MAT 145Monday, August 31, 2015
LIMIT LAWS!Suppose that c is a constant and the limits
and exist.
1. The limit of a sum is the sum of the limits.
2. The limit of a difference is the difference of the limits.
3. The limit of a constant multiplied by a function is the product of the constant and the limit of the function.
4. The limit of a product is the product of the limits.
MAT 145Monday, August 31, 2015
MORE LIMIT LAWS!
5. The limit of a quotient is the quotient of the limits, provided the denominator limit is not 0.
6. The limit of a function raised to a power n is the nth power of the limit of the function.
7. The limit of a constant function is that constant.
8. The limit of y = x as x approaches a is just the value a.
MAT 145Monday, August 31, 2015
MORE LIMIT LAWS!
9. The limit of a power function as the base approaches a constant is that constant power function.
11. The limit of an nth-root function is the nth root of the limit of the function.
8. The limit of the nth-root of x as x approaches a is just the nth root of a.
MAT 145Monday, August 31, 2015
MAT 145Monday, August 31, 2015
MAT 145Monday, August 31, 2015
MAT 145Monday, August 31, 2015
MAT 145Monday, August 31, 2015
MAT 145Monday, August 31, 2015
MAT 145Monday, August 31, 2015
The line y = L is called a
horizontal asymptoteof the curve y = f(x) if either:
MAT 145Monday, August 31, 2015
MAT 145Monday, August 31, 2015
MAT 145Monday, August 31, 2015
MAT 145Monday, August 31, 2015
MAT 145Monday, August 31, 2015
Sketch the graph of by finding its intercepts and its limits as and as .
MAT 145
Assignments WebAssign : Chapter 2 (limits) due throughout this
week WebAssign Quiz #4 : Open now, due Tuesday at
midnight, two submissions
Wrapping It Up
Monday, August 31, 2015