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
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
The line y = L is called a
horizontal asymptoteof the curve y = f(x) if either:
MAT 145Monday, August 31, 2015
Sketch the graph of by finding its intercepts and its limits as and as .