Calculus 1
Review Implicit Diff. and Related Rates (2)
Name
Block
Date
dy
and the equation of the tangent line at the given point.
dx
5x 2 y 3 5x 6y 18xy 3,1
1) Find
5x 2y 3 5x 6y 18xy
dy
dy
dy
56
18y 18x
dx
dx
dx
dy
dy
dy
5x 2 3y 2
6
18x
10xy 3 5 18y
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aft w
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2,9
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Calculus 1
WorksheeT - RecTilinear and ProjecTile MoTion
Name Kkg
DaTe
1) A parTicle is moving wiTh iTs posiTion defined by 5(2) 2 2T3 l2t1+18r +7 where T is in
seconds and s is in feeT.
a) WhaT are The parTicle's velociTy and acceleration funcTion
Calc1: Extra Practice with Related Rates
Name
Date
1) A tumor in an animals stomach is relatively spherical in shape. The radius of the tumor is growing
at a rate of 0.001 centimeters per day. What is the rate of change of the volume of the tumor when
the
Calculus 1
Worksheet Rectilinear and Projectile Motion (2)
Name
Date
Set up the steps required to solve the following problems.
(You cannot solve since there are no equations).
1. What is the acceleration when the velocity is 46 ft/sec?
v(t) = 46 (Set vel
Calculus 1
Review of Graphing and Applying Derivatives (B)
Name Key
Block
Date
1. Find the requested information, then sketch the graph using the information found.
f x x 3 x 2 x 3
f x 3x 2 2x 1
f x 6x 2
1
3
C. V.
1
, 1,
3
Inc.
1
,1
Dec.
3
1
3
C.
P,V,A Types of Possible Questions
1. Initial Position, Velocity and Acceleration
Plug zero in for x (or t)
Because you are talking about 0 seconds.
2. Max Height (for projectiles)
Set velocity equal to zero (this gives you time).
Because the velocity is g
Calculus I
Ms. Gemgnani
lgemgnani@cbsd.org
(267) 893-3000 x47130
General Policies and Expectations:
1.
Respect for yourself, other school members and property is expected.
2.
Be prepared for each day with your textbook, notebook, calculator and pencil(s).
Name - - - - - - Block - - - Date - - -
Calculus I
Review - Parent Graphs, Domain and Range and Piecewise (2)
Find the exact value of each of the following.
02.
1. cos n =
6
4.
n
=
4
Slll-
2. esc n =
2.
6
I2/z
7. S l l l - =
. 5n
6
10. sin n =
0
16. sin 2
Calculus 1
Assessment #3 Review
Name
Date
1) Use the limit definition of a derivative to find the derivative of f (x ) 2x 2 5 .
f (x h ) f (x )
h 0
h
2(x h )2 5 (2x 2 5)
lim
h 0
h
2
2(x 2xh h 2 ) 5 2x 2 5
lim
h 0
h
2
2x 4xh 2h 2 5 2x 2 5
lim
h 0
h
2
4xh 2
Calculus 1
Review: Domain, Range, Piecewise and Limits (ans)
Fill in the missing information for the following functions.
2x 2 3x 1
3x 2 6x
1) f x
2) f x
x 2
3x 2 x 4
2x 1 x 1
3x (x 2)
x 2
3x
Name
Block
Date
3) g x x 2 9
3x 4 x 1
2x 1
3x 4
Hole: (2,6
Calculus 1
The Chain Rule
Name _
The Chain Rule
The Chain Rule is a method used to find the derivative of a function that has other function(s) inside itself
(when you have the composition of functions).
Dx f g x f g x g x
1) y 4x 5 2x 2
2) y 6x 3 5x
3
Calculus I
Visual Examples
Continuity at a Point
Determine if the following functions are continuous. If the function has discontinuities
determine where it is discontinuous and the type of discontinuity. If the discontinuity is
removable, write a new equ
Calculus I
Deriving the Derivatives of Trig Functions
Name
Block
Date
Basic Trig Functions
Dx (sin x ) cos x
Derivatives of tan, sec, csc, cot
Dx (tan x )
Dx (csc x )
Dx (sec x )
Dx (cot x )
Dx (cos x ) sin x
Calculus 1
Derivatives of Trig Functions
d
Calculus 1
Notes: Product Rule
Product Rule;
Dx f x g x f x g x f x g x
Find the equation that determines the slope of the following equation (aka the derivative).
Then find the slope at the given value.
1. f x x 2 2 3x 3 x
x=2
2. f x 3x 2 4x 3 5
x = 1.5
Calculus 1
Power Rule Notes
Name _
Derivatives Slope of a Tangent
The expression found when determining the expression for the slope of a tangent ( mtan ) for a
function is called the derivative of the function. The derivative is used to find the
instanta
Calculus 1
Review Implicit Diff. and Related Rates
Name Key
Block
Date
1) Find dy dx and the equation of the tangent line for the given function and point.
3,2
3y 2y 2 xy 20
dy
dy
dy
3
4y
x
y 0
dx
dx
dx
dy
3 4y x y
dx
dy
y
dx 3 4y x
2) Find dy dx for 5x