Calc Chapter 1.docx

2 Pages
74 Views
Unlock Document

Department
Mathematics
Course
MATH 1502
Professor
Bernucci
Semester
Summer

Description
Chapter 1: Misc topics Section 4.1 Indeterminate form – meaningless expression that describes the behavior of a function near a point or as it approaches infinity Ex) 0/0, ∞/∞, 0 * ∞, ∞ - ∞, 0^0, 1^∞, ∞^0 L’Hopital’s Rule: Suppose f(a) = g(a) = 0 and f, g are differentiable on an open interval containing a. Suppose g’(x) is not equal to 0 on this interval (x is not equal to a) Then lim xa f(x)/g(x) = lim xa f’(x)/g’(x) Remarks: 1) differentiate numerator and denominator separately(not quotient rule) 2)keep applying the rule as long as 0/0 remains 3)Be smart ex lim x0 = x^2/x = lim x0 2x/1 = 0 4)everything’s the same for 1 sided limits Ex lim x0+ (zero from the right) x-sin(x)/x^3 = lim x0+ 1-cos(x) =lim x0+ -sin(x)/6x = lim x-> 0+ -cos(x)/6 = 1/6 L’Hopital’s rule works the same for ∞/∞ as it does for 0/0 Ex) lim x∞ ln(x)/(2√x) = lim x∞ (1/x)/(1/√x) = lim x∞ (√x)/x = lim x∞ 1/√x = 0 Sometimes you need to exponentiate Ex) limx0+ = (ln(x) – ln(sin(x)) = lim x+ ln(x/sin(x)) =
More Less

Related notes for MATH 1502

Log In


OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.


Submit