Academic Supports for Students at Richard Montgomery High School
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CalculuswithApplications
Unit7AreaUndertheCurve
Area4RAMandNumInt(NotesandHomework)
1.
3
UseNUMINTtoestimatetheareaunder f ( x ) = x on[0,1].
2.
UseNUMINTtoestimatetheareaunder f ( x ) = cos x on [ 0, ] .
2
3. Giventheequation f ( x) = 2 x x on [ 0,2] :
(
CalculuswithApplications
Unit7AreaUndertheCurve
Area3RAMwithEquations(NotesandHomework)
2
1. Findtheapproximateareaunder f ( x ) = x on[0,5]usingLRAM5,RRAM5,and
MRAM5.
2
2. Findtheapproximateareaunder f ( x ) = 3 x x on[0,3]usingLRAM6,RRAM6,and
MRAM6.
3.
Warm up
A line has a slope of 2 and goes through the point (1,-3).
Write the equation of the line in
(a) Point-slope form
(b) Slope-intercept form
Exponentials Review
Objective: Students will be able to use the
properties of exponents to manipulate
expres
Warm Up
Solve.
(a) x 2 + 2 x 15 = 0
(b) x 2 + 2 x 13 = 0
Factoring and Zeros
Review
Objective: Students will be able to find the
zeros of a polynomial.
Factoring and Zeros Review
How do we interpret the solutions to the warm up?
Example 1
Solve.
x 2 + 2x
Warm up!
A certain drug leaves the body at a continuous rate of 12% per hour.
(a) Write a formula for the percent, A, of caffeine in the body t hours
after taking it.
(b) Using your calculator, sketch a graph the function from part (a).
(c) Use the graph
Warm up!
H
(a) What is the equation of the
persons height as a function
of their age?
(c) What is the meaning of the
slope?
Height of Person (in)
(b) What is the meaning of the
y-intercept?
60
50
40
30
20
10
2
4
6
8
Age in years
(d) During what intervals
Warm up!
A town has a population of 1000 people at time t = 0. In each of the
following cases, write a formula for the population, P, of the town as a
function of year t.
The population increases by 50 people a year.
The population increases by 5% each ye
Warm up!
(a) Given the exponential function
the graph.
x
y = 5 2 x fill in the table and sketch
y
y
0
1
2
3
x
(b) How will the graph change if
(i) the 5 is changed to 6?
(ii) the 5 is changed to 10?
(iii) the 2 is changed to 3?
(iv) the 2 is changed to 5?