{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Assignment 2 Solutions - 1 F x lim x → 1 x 2 − 1 | x...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
MAT 1330, Fall 2010 Assignment 2 Due Wednesday October 6, 8:30am at the beginning of class. Late assignments will not be accepted; nor will unstapled assignments. Instructor (circle one): Frithjof Lutscher Angelika Welte Aziz Khanchi Robert Smith? DGD (circle one): 1 2 3 4 Student Name Student Number By signing below, you declare that this work was your own and that you have not copied from any other individual or other source. Signature Question 1. Find lim x 0 x 3 + cos 5 x 10 , 000 . Answer: 1 10000 Give one sequence to support your claim. Five terms are enough. x n f ( x n ) 0.5 0.124920 0.1 0.001088 0.05 0.000222 0.01 0.000101 Question 2. Does the limit lim t 0 t 1 1 + t exist? Answer: Yes Justify your answer in at most two lines without using sequences of numerical values for x . Answer: lim t 0 t 1 1 + t = lim t 0 t 1 1 + t × 1 + 1 + t 1 + 1 + t = lim t 0 t (1 + 1 + t ) 1 (1 + t ) = lim t 0 t (1 + 1 + t ) t = lim t 0 (1 + 1 + t ) = 2 . 1
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Question 3. Let F ( x ) = x 2 1 | x 1 | . a) Find lim
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 + F ( x ). lim x → 1 + x 2 − 1 | x − 1 | = lim x → 1 + x 2 − 1 x − 1 = lim x → 1 + ( x − 1)( x + 1) x − 1 = lim x → 1 + ( x + 1) = 2. b) Find lim x → 1-F ( x ). lim x → 1-x 2 − 1 | x − 1 | = lim x → 1-x 2 − 1 − ( x − 1) = lim x → 1-( x − 1)( x + 1) − ( x − 1) = lim x → 1-− ( x + 1) = − 2 . . c) Does lim x → 1 F ( x ) exist? Answer: No Justify your answer: lim x → 1 + F ( x ) ± = lim x → 1-F ( x ) = ⇒ The limit at 1 does not exist. Question 4. Consider the function f ( x ) = 3 x . Use the de±nition of the derivative to compute f ± (3). Answer: f ± (3) = lim h → f (3 + h ) − f (3) h = lim h → 3 3+ h − 1 h = lim h → 3 − (3+ h ) 3+ h h = lim h → − h h (3 + h ) = lim h → − 1 3 + h = − 1 3 . 2...
View Full Document

{[ snackBarMessage ]}

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