Concept explainers
(a)
To show: The inequality
(a)

Explanation of Solution
Definition used:
Natural logarithmic function:
It is defined as
Geometrically the natural logarithmic function can be interpreted as the area under the curve
Calculation:
The given inequality is
Geometrically, the function
Use online graphing calculator and sketch the graph of the curve as shown below in Figure 1.
From Figure 1, the area under the curve
The area of the rectangle BCDE is computed below.
The area of the trapezoid ABCD is
Comparing these two areas with the function
Thus, it is clear that
(b)
To estimate: The function
(b)

Answer to Problem 1E
The estimated value of
Explanation of Solution
Definition used:
Midpoint rule:
It is defined as
Here,
Calculation:
The equation of the curve is
Given that
From part (a), the function
Then,
Use the definition of midpoint rule to estimate the value of
On further simplification,
Thus the estimated value of
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Chapter G Solutions
CALCULUS: EARLY TRANS. (LL)W/WEBASSIGN
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- Find the derivative of the function. g'(t) = 9t g(t) = In(t) (9ln(t) - 1) [In(t)] 2 × Need Help? Read It Watch Itarrow_forwardFind the accumulated amount A, if the principal P is invested at an interest rate of r per year for t years. (Round your answer to the nearest cent.) P = $3800, r = 4%, t = 10, compounded semiannually A = $ 5645.60 × Need Help? Read It SUBMIT ANSWER [3.33/6.66 Points] DETAILS MY NOTES REVIOUS ANSWERS ASK YOUR TEACHER TANAPCALC10 5.3.001.EP. PRACTICE ANOTHER Consider the following where the principal P is invested at an interest rate of r per year for t years. P = $3,100, r = 4%, t = 10, compounded semiannually Determine m, the number of conversion periods per year. 2 Find the accumulated amount A (in dollars). (Round your answer to the nearest cent.) A = $ 4604.44arrow_forwardForce with 800 N and 400 N are acting on a machine part at 30° and 60°, respectively with a positive x axis, Draw the diagram representing this situationarrow_forward
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