Ma 113 Functions And Inverse Functions, The Exponential Function And The Logarithm Worksheet Page 32
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11. Let f (x) = x
3x + 1, x
= 3. Apply Newton’s Method to f (x) and initial guess x
to calculate
1
1
x
, x
, x
.
2
3
4
2
12. Find the most general anti-derivative of f (x) = x
+ cos(2x + 1).
13. Find a function with f (x) = sin(2x), f (π) = 1, and f (0) = 2.
14. Consider the region bounded by the graph of f (x) = 1/x, the x-axis, and the lines x = 1 and x = 2.
Find L
, the left endpoint approximation of this area with 3 subdivisions.
3
20
10
2
15. We know
a = n
+ 2n for n = 1, 2, . . . . Find
(4a + 1). Find
a .
=1
=1
=5
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