{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ws27 - WORKSHEET 27 Fall 1995 1 Below the graph of f(x = x2...

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

View Full Document Right Arrow Icon
WORKSHEET 27 - Fall 1995 1. Below, the graph of f ( x ) = x 2 is given. The line below the graph is the tangent line at x = 1. The lines above the graph connect the points (0 , 0), (1 , 1), and (2 , 4). 1 2 3 4 1 2 a) Find the area bounded by the tangent line, the x -axis, and the line x = 2. b) Find the area bounded by the two segments above the graph, the x -axis, and the line x = 0. the graph. c) Use your answers to a) and b) to venture a guess as to the area between the graph of f and the x -axis lying over the interval [0 , 2]. d) Find a function g such that g = f . What is g (2) g (0)? How close is this to your guess in part c)? Creepy, eh? There are several functions having x 2 as a derivative. What if you had chosen another? 2. Let f be a continuous function with f ( x ) > 0 for all x . Let A be the function such that A ( x ) equals the area between the graph of f and the x -axis on the interval [0 , x ]. a) Draw a picture of this for some value of x . Label A ( x ). For a small value of h , also indicate A ( x + h ) in your picture. What is A (0)?
Background image of page 1

Info iconThis 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 ]}