Calculus: 3 ~ Limit Theorems - The University of Utah · PDF file3B Limit Theorems 4...
6
3B Limit Theorems 1 Calculus: 3 ~ Limit Theorems f(x)=x 2 g(x)=4-2x
Transcript of Calculus: 3 ~ Limit Theorems - The University of Utah · PDF file3B Limit Theorems 4...
![Page 1: Calculus: 3 ~ Limit Theorems - The University of Utah · PDF file3B Limit Theorems 4 Substitution Theorem If f(x) is a polynomial or a rational function, then assuming f(c) is defined.](https://reader034.fdocuments.us/reader034/viewer/2022052419/5a78467d7f8b9a1b688e9b92/html5/thumbnails/1.jpg)
3B Limit Theorems
1
Calculus: 3 ~ Limit Theorems
f(x)=x2
g(x)=4-2x
![Page 2: Calculus: 3 ~ Limit Theorems - The University of Utah · PDF file3B Limit Theorems 4 Substitution Theorem If f(x) is a polynomial or a rational function, then assuming f(c) is defined.](https://reader034.fdocuments.us/reader034/viewer/2022052419/5a78467d7f8b9a1b688e9b92/html5/thumbnails/2.jpg)
3B Limit Theorems
2
Limit Theorems is a positive integer.
is a real number
have limits as x → c
![Page 3: Calculus: 3 ~ Limit Theorems - The University of Utah · PDF file3B Limit Theorems 4 Substitution Theorem If f(x) is a polynomial or a rational function, then assuming f(c) is defined.](https://reader034.fdocuments.us/reader034/viewer/2022052419/5a78467d7f8b9a1b688e9b92/html5/thumbnails/3.jpg)
3B Limit Theorems
3
EX 1
EX 2
EX 3If
find
![Page 4: Calculus: 3 ~ Limit Theorems - The University of Utah · PDF file3B Limit Theorems 4 Substitution Theorem If f(x) is a polynomial or a rational function, then assuming f(c) is defined.](https://reader034.fdocuments.us/reader034/viewer/2022052419/5a78467d7f8b9a1b688e9b92/html5/thumbnails/4.jpg)
3B Limit Theorems
4
Substitution Theorem
If f(x) is a polynomial or a rational function, then
assuming f(c) is defined.
Ex 4
Ex 5
![Page 5: Calculus: 3 ~ Limit Theorems - The University of Utah · PDF file3B Limit Theorems 4 Substitution Theorem If f(x) is a polynomial or a rational function, then assuming f(c) is defined.](https://reader034.fdocuments.us/reader034/viewer/2022052419/5a78467d7f8b9a1b688e9b92/html5/thumbnails/5.jpg)
3B Limit Theorems
5
EX 6 Hint: rationalize the numerator.
![Page 6: Calculus: 3 ~ Limit Theorems - The University of Utah · PDF file3B Limit Theorems 4 Substitution Theorem If f(x) is a polynomial or a rational function, then assuming f(c) is defined.](https://reader034.fdocuments.us/reader034/viewer/2022052419/5a78467d7f8b9a1b688e9b92/html5/thumbnails/6.jpg)
3B Limit Theorems
6
f(x)=x2
g(x)=4-2xf(x) - g(x) =x2+2x-4