In Exercises 47-52, use inductive reasoning to predict the next line in each sequence of computations. Then use a calculator or perform the arithmetic by hand to determine whether your conjecture is correct. 1 × 9 − 1 = 8 21 × 9 − 1 = 188 321 × 9 − 1 = 2888 4321 × 9 − 1 = 38 , 888
In Exercises 47-52, use inductive reasoning to predict the next line in each sequence of computations. Then use a calculator or perform the arithmetic by hand to determine whether your conjecture is correct. 1 × 9 − 1 = 8 21 × 9 − 1 = 188 321 × 9 − 1 = 2888 4321 × 9 − 1 = 38 , 888
Solution Summary: The author calculates the next line in the sequence of computation, which is 54,321times 9-1=488,888.
In Exercises 47-52, use inductive reasoning to predict the next line in each sequence of computations. Then use a calculator or perform the arithmetic by hand to determine whether your conjecture is correct.
1.3. The dots of Output 2 lie in pairs. Why? What property of esin(x) gives rise to
this behavior?
1.6. By manipulating Taylor series, determine the constant C for an error expansion
of (1.3) of the form wj−u' (xj) ~ Ch¼u (5) (x;), where u (5) denotes the fifth derivative.
Based on this value of C and on the formula for u(5) (x) with u(x) = esin(x), determine
the leading term in the expansion for w; - u'(x;) for u(x) = esin(x). (You will have
to find maxε[-T,T] |u(5) (x)| numerically.) Modify Program 1 so that it plots the
dashed line corresponding to this leading term rather than just N-4. This adjusted
dashed line should fit the data almost perfectly. Plot the difference between the two
on a log-log scale and verify that it shrinks at the rate O(h6).
4. Evaluate the following integrals. Show your work.
a)
-x
b) f₁²x²/2 + x² dx
c) fe³xdx
d) [2 cos(5x) dx
e) √
35x6
3+5x7
dx
3
g) reve
√ dt
h) fx (x-5) 10 dx
dt
1+12
Chapter 1 Solutions
Pearson eText for Thinking Mathematically -- Instant Access (Pearson+)
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Grade 12 and UG/ Introduction to logical statements and truth tables; Author: Dr Trefor Bazett;https://www.youtube.com/watch?v=q2eyZZK-OIk;License: Standard YouTube License, CC-BY