Difference between revisions of "2000 SMT/Calculus Problems"
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[[2000 SMT/Calculus Problems/Problem 10|Solution]] | [[2000 SMT/Calculus Problems/Problem 10|Solution]] | ||
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+ | ==See Also== | ||
+ | *[[Stanford Mathematics Tournament]] | ||
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+ | *[[Stanford Mathematics Tournament Problems|SMT Problems and Solutions]] | ||
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+ | *[[2000 SMT]] | ||
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+ | *[[2000 SMT/Calculus]] |
Latest revision as of 13:10, 21 January 2020
Contents
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?