2000 SMT/Calculus Problems
Contents
[hide]Problem 1
Find the slope of the tangent at the point of inflection of .
Problem 2
Karen is attempting to climb a rope that is not securely fastened. If she pulls herself up feet at once, then the rope slips feet down. How many feet at a time must she pull herself up to climb with as few pulls as possible?
Problem 3
A rectangle of length and height 4 is bisected by the x-axis and is in the first and fourth quadrants, with the leftmost edge on the y-axis. The graph of = divides the area of the square in half. What is C?
Problem 4
For what value of does achieve its minimum?
Problem 5
For let . Find a closed form expression (a closed form expression is one not involving summation)for f.
Problem 6
A hallway of width 6 feet meets a hallway of width feet at right angles. Find the length of the longest pipe that can be carried horizontally around this corner.
Problem 7
An envelope of a set of lines is a curve tangent to all of them. What is the envelope of the family of lines y = , with ranging over the positive real numbers?
Problem 8
Find
Problem 9
Let If , find .
Problem 10
A mirror is constructed in the shape of equals for , and for . A ray of light enters at (10,1) with slope 1. How many times does it bounce before leaving?