Concept explainers
(a) A table of values of a function g is given. Use Simpson’s Rule to estimate
x | g(x) |
0.0 | 12.1 |
0.2 | 11.6 |
0.4 | 11.3 |
0.6 | 11.1 |
0.8 | 11.7 |
1.0 | 12.2 |
1.2 | 12.6 |
1.4 | 13.0 |
1.6 | 13.2 |
(b) If
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Chapter 7 Solutions
Single Variable Calculus
- (a) To obtain the graph of g(x)=2x1 , we start with the graph of f(x)=2x and shift it _____________ (upward/ downward) 1 unit. (b) To obtain the graph of h(x)=2x1 , we start with the graph of f(x)=2xand shift it to the (left/right) 1unit.arrow_forwardDecay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.arrow_forward
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