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Tangents
Veolcity
Limits & Rationalizing
More Limits
Continuity
Limits &
Rationalizing
More Limits
Continuity
Velocity
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CATEGORY 1 - $100
Calculate the slope of the tangent to each curve at the given point or value of x.
f (x) = x2+ 3x - 5 , (-3, -5)
CATEGORY 1 - $200
Calculate the slope of the tangent to each curve at the given point or value of x.
y = 4 , (6, 1)
x-2
CATEGORY 1 - $300
Calculate the equation of the tangent to each curve at the given point or value of x.
CATEGORY 1 - $400
Find the coordinates of the point on the curve f (x)= 3x2 - 4x where thetangent is parallel to the line y=8x
CATEGORY 1 - $500
Show that, at the points of intersection of the quadratic functions y= x2and
y= 0.5- x2 the tangents to the functions are perpendicular.
CATEGORY 2 - $100
The function describes s(t) = 6t2 + 6t the distance (in kilometres) that a car has travelled after a time (in hours), for
0 <= t <=6. find the velocity when t=2.
CATEGORY 2 - $200
Consider the function f(t) = 7t2 + 14t where t is measured in seconds and f(t) is measured in metres. Now, find the instantaneous velocity when t=1.
CATEGORY 2 - $300
CATEGORY 2 - $400
CATEGORY 2 - $500
A manufacturer of basketballs finds that the profit from the sale of x basketballs per week is given by the function P (x) =180x-2x2, where P is measured in dollars. What is the rate of change of profit between the
time of selling 20 basketballs and 60 basketballs?
CATEGORY 3 - $100
Rationalize each denominator.
a) b)
CATEGORY 3 - $200
CATEGORY 3 - $300
Evaluate the limit. If the limit does not exist, explain why.
CATEGORY 3 - $400
Find the indicated limit, if it exists.
CATEGORY 3 - $500
CATEGORY 4 - $100
Evaluate the following limits
CATEGORY 4 - $200
Evaluate the following limits
CATEGORY 4 - $300
Evaluate the following limits
CATEGORY 4 - $400
Evaluate the following limits
CATEGORY 4 - $500
CATEGORY 5 - $100
Determine all values of x for which each function is continuous.
CATEGORY 5 - $200
Find the value(s) of x at which the following functions are discontinuous, and state the type of discontinuity.
CATEGORY 5 - $300
Find the value(s) of x at which the following functions are discontinuous, and state the type of discontinuity.
CATEGORY 5 - $400
CATEGORY 5 - $500
Answer
-3
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Answer
-9
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Answer
Y=1/6 x +1/6
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Answer
(2, 4)
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Answer
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Answer
30 km/h
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Answer
28 m/s
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Answer
22 m/s
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Answer
48 m/s
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Answer
$20/basketball
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Answer
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Answer
a. 2
b. 2
c. -1
d. DNE
e. 1
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Answer
a. 90
b. DNE
c. 1
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Answer
DNE
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Answer
m=1, b=-1/3
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Answer
2√5
5
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Answer
-1
6
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0
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0
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Answer
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Answer
a. all real numbers
b. x >= 4 and x ≠ 0
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Answer
VA: x = 4
Infinite discontinuity
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Answer
x = 4, x =-4
Open Hole discontinuity
x =-1
Jump discontinuity
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Answer
k = 2
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Answer
a =1, b=0
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FINAL CATEGORY
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FINAL CATEGORY
INSERT FINAL QUESTION (ANSWER) HERE
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FINAL CATEGORY
WHAT OR WHO IS THE FINAL ANSWER?
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END OF GAME
Daily Doubles and
usage notes follow...
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