January Regional
_
Calculus Individual Test
For all questions, NOTA is defined as None of the above answers is correct.
1) Suppose that there is a continuous function
such that
and
. Which
theorem guarantees that
has at least one zero? (Note: V and T stan
JANUARY REGIONAL
CALCULUS TEAM ROUND
QUESTION 1:
Let
be the line that is normal to
at the -intercept of
.
Let
be the line that is tangent to
at the -intercept of
.
Let
be the slant asymptote of the function
.
What is the area of the triangle bound by the
January Regional
Question #1
(
A.
Calculus Team
)
B.
C.
D.
Find
.
January Regional
Question #1
(
A.
B.
C.
D.
Find
.
)
Calculus Team
January Regional
Question #2
Calculus Team
A. The slope of ( )
B.
( ( )|
C.
( ) for ( )
at
for ( )
(
)
D. The slope of ( )
January Regional
Precalculus Individual
Note that answer choice E) NOTA indicates none of the above answer choices are correct.
denotes the magnitude of , and the inverse trigonometric functions have their
,
traditional ranges. Work quickly, yet carefull
January Regional
Pre-Calculus Individual
The abbreviation NOTA denotes none of these answer. Assume radians unless degrees is implied.
All arc functions are restricted to their traditional ranges.
1. Which of the following numbers are in the domain of
A.
JANUARY REGIONAL
CALCULUS INDIVIDUAL TEST
The choice e) NOTA denotes None of the Above.
1) Let f ( x ) = sin ( x ). Compute f ' ( ).
a) 1
b) 0
c) 1
d)
e) NOTA
2) Let f ( x ) = sin ( x ). Find
a)
b)
c)
d)
e)
sin ( x )
cos ( x )
sin ( x )
cos ( x )
NOTA
3
January Regional
Let
Pre-Calculus Team: Question #1
Let
Let
Let
Find
January Regional
Let
Let
Let
Let
Find
Pre-Calculus Team: Question #1
January Regional
Given
,
Let be the degree of the equation.
Let be the sum of roots.
Let be the product of roots.
Let
JANUARY REGIONAL
CALCULUS INDIVIDUAL TEST
The choice e) NOTA denotes None of the Above
1. The points and lie on the curve
such that an equilateral triangle is formed by
the line tangent to , the line tangent to , and the -axis. What is the area of this tr