1.4 The Limit of a Function handout.pdf - HW page 38 4-13(1.4 The Limit of a Function The nota)on lim Defini2on of a Limit L f x = L Limits and Their

1.4 The Limit of a Function handout.pdf - HW page 38...

This preview shows page 1 - 2 out of 5 pages.

The nota)on is read “ the limit of f(x) , as x approaches a , equals L ” and means that the value of f(x) can be made arbitrarily close to L by choosing x to be sufficiently close to a (but not equal to a ) . L x f a x = ) ( lim a ( ) y f x = L NOTE: “Approaching” (NOT the same as “Equal”) can get very, very, very close but not equal. Defini2on of a Limit (1.4) The Limit of a Function HW: page 38: 4 -13 Limits and Their Existence We say that the number L is the limit of a func)on y = f(x) as x approaches the value of ‘a’, wriDen as , if and . Otherwise, does not exist. L x f a x = ) ( lim L x f a x = ) ( lim L x f a x = + ) ( lim L x f a x = ) ( lim A limit exists if and only if both the left-hand limit and the right-hand limit exist and are equal in value . -10 -8 -6 -4 -2 2 4 6 8 10 -10 -8 -6 -4 -2 2 4 6 8 10 x f(x) a) a) f (2) = und lim x 2 f ( x ) = 4 since lim x 2 + f ( x ) = 4 and lim x 2 f ( x ) = 4 b) b) x y 0 2 2 1 1 f (3) = 4 lim x 3 f ( x ) = 4 since lim x 3 + f ( x ) = 4 and lim x 3 f ( x ) = 4 We write this as: The answer can be found graphically, algebraically, and analy)cally .
Image of page 1

Subscribe to view the full document.

Image of page 2
  • Summer '14
  • JasonBrown

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes