Explanation Given: y = ln x a t x = 1 Formula used: The equation of the tangent line is calculated by y − y 1 = m ( x − x 1 ) Calculation: The equation of the tangent line is calculated as y − y 1 = m ( x − x 1 ) Slope, m = d y d x Differentiate the function y = ln x with respect to x We know that d y d x ( ln x ) = 1 x d y To determine (b) To calculate: The approximate values of ln(1.1) and ln(2) To determine (c) To explain: Whether the approximated values are greater or smaller than the actual values using the graph and say whether the same will occur for ln(0.9) and ln(0.5)

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 3.2, Problem 57P

To determine

(a)

To find:

The equation of the tangent line to the given function.

To determine

(b)

To calculate:

The approximate values of ln(1.1) and ln(2)

To determine

(c)

To explain:

Whether the approximated values are greater or smaller than the actual values using the graph and say whether the same will occur for ln(0.9) and ln(0.5)

Expert Solution & Answer

Chapter 3 Solutions

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(a) To find: The equation of the tangent line to the given function.

Solution Summary: The author explains that the equation of the tangent line is x-1.

Concept explainers

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(a) To find: The equation of the tangent line to the given function.

(b) To calculate: The approximate values of ln(1.1) and ln(2)

(c) To explain: Whether the approximated values are greater or smaller than the actual values using the graph and say whether the same will occur for ln(0.9) and ln(0.5)

Chapter 3 Solutions

(a)

To find:

The equation of the tangent line to the given function.

(b)

To calculate:

The approximate values of ln(1.1) and ln(2)

(c)

To explain:

Whether the approximated values are greater or smaller than the actual values using the graph and say whether the same will occur for ln(0.9) and ln(0.5)