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

Explanation of Solution
Definition used:
The natural logarithmic function is the function defined by
If
Calculation:
The given inequality is
Here,
By using the above mentioned definition,
Use online graphing calculator, graph of the curve
From Figure 1, it is observed that the area is larger than the area of rectangle BCDE and smaller than the area of trapezoid ABCD.
The area of the rectangle BCDE is calculated as follows.
The area of the trapezoid ABCD is calculated as follows.
It is known that the value of
The decimal value of the fraction
By comparing the above values with
Hence proved.
(b)
To show: The function
(b)

Answer to Problem 1E
The estimated value of
Explanation of Solution
Definition used:
Midpoint Rule:
Midpoint rule can be defined as
Where,
Natural logarithmic:
The natural logarithmic function is the function defined by
Calculation:
It is known that the equation of the curve is
Here,
From definition of natural logarithmic, the function
Here,
Find
Estimate the value of
Further simplification,
Therefore, the estimated value of
Want to see more full solutions like this?
Chapter C Solutions
Essential Calculus: Early Transcendentals
- Graph y=log2(x+3) 10+ 9 8 7- 6 5 4 3 3 2 1 10 -9 -8 -7 -6 -5 -4 -3-2-1 1 2 3 4 5 6 7 8 7 8 9 10 -1 -2 -3 -4 -5 -6 -7- -8 -9 -10 Clear All Drawarrow_forwardWrite an equation for the graph below. +10+ 9 10 -9 -8 -7 -6 -5 -4 -3-2-1 8 7 6 5 4 3 2 1 1 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 f(x) = 9 -9 -10-arrow_forward3. Solve the inequality and give your answer in interval notation. Be sure to show all your work, and write neatly so your work is easy to follow. (4 points) 2|3x+12 ≥ 18arrow_forward
- - 2. In words, interpret the inequality |x8|> 7 the same way I did in the videos. Note: the words "absolute value" should not appear in your answer! (2 points)arrow_forwardFind the tangential and normal components of the acceleration vector for the curve (t) = (2t, -3t5,-3+4) at the point t = 1 ā(1) = T + N Give your answers to two decimal placesarrow_forwardA gun is fired with muzzle velocity 1152 feet per second at a target 4150 feet away. Find the minimum angle of elevation necessary to hit the target. Assume the initial height of the bullet is 0 feet, neglect air resistance, and give your answer in degrees.arrow_forward
- "Use the Opposite Method to solve the following differential equation:" 4'"""" + 34" + 34 + 4 = xarrow_forwardFor the curve defined by (t) = (e cos(t), et sin(t)) find the unit tangent vector, unit normal vector, normal acceleration, and tangential acceleration at πT t = 3 П I(3) 丌_3_3 N (1) ат aN || = = =arrow_forwardFind the velocity vector for the position vector (t) = (sin(9+), 9t10, e¯7). x component = y component = Z component =arrow_forward
- In the xy-plane, an angle 0, in standard position, has a measure of the following is true? T. Which of 3 A The slope of the terminal ray of the angle is 1. B The slope of the terminal ray of the angle is 1. C D 3 The slope of the terminal ray of the angle is ✓ 2 The slope of the terminal ray of the angle is √3.arrow_forwardy'''-3y''+4y=e^2x Find particular solutionarrow_forward1 -1- Ο Graph of f y = + y = 1 + 1/2 ·2· x Graph of g y = 1- 플 The figure gives the graphs of the functions f and g in the xy-plane. The function of is given by f(x) = tan¹ x. Which of the following defines g(x)? A tan 1 x + 1 B - tan 1 x + П 2 C tan-1 (2/2) + 1 D tan-1 (2/2) + 1/1arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning




