{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

StudySheetTest2_10 - Study Sheet for Test 2 Honors Calculus...

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

View Full Document Right Arrow Icon
Study Sheet for Test 2 Honors Calculus Keesling Test on 10/27/10 1. Suppose that f is an increasing function on the interval [ a , b ] . Subdivide [ a , b ] into n equal subintervals. Let S n ( f , a , b ) be the upper sum and let S n ( f , a , b ) be the lower sum. Show that S n ( f , a , b ) ! S n ( f , a , b ) = ( f ( b ) ! f ( a )) " ( b ! a ) n . Use this to show that lim n !" S n ( f , a , b ) # S n ( f , a , b ) $ % & ' = 0 . 2. Suppose that F ( x ) and G ( x ) are differentiable functions such that ! F ( x ) " ! G ( x ) on an interval. Show that there is a constant C such that F ( x ) ! G ( x ) + C . 3. Suppose that f ( x ) is a continuous function and that F ( x ) = f ( t ) dt a x ! . Show that ! F ( x ) " f ( x ) . 4. Suppose that f ( x ) is a continuous function and that G ( x ) is a differentiable function having the property that ! G ( x ) " f ( x ) on the interval [ a , b ] . Show that f ( x ) dx a b ! = G ( b ) " G ( a ) . 5. Determine the following integrals. Be able to use the following methods and combinations of them to determine the integrals: Substitution or Integration by Parts. (a) tan x dx ! (b) sin 2 x dx ! (c) cos 6 x dx !
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
Image of page 2
This is the end of the preview. Sign up to access the rest of the 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