Concept explainers
(a)
The lines that are tangent to the curve at
(a)
Answer to Problem 20E
The required equation of the tangent line is
Explanation of Solution
Given information:
The curve:
Formula used:
Slope of a curve is:
The given curve is
Write the given definition using the above function as:
Substitute 4 for a in the above limit and simplify.
Substitute 4 for x in the above limit and simplify.
Also, substitute 4 for x in the curve
So, the slope of the tangent line is
To find the equation of the tangent, use point-slope formula of an equation of a line
Substitute
Hence, the required equation of the tangent line is
(b)
The lines that are normal to the curve at
(b)
Answer to Problem 20E
The required equation of the tangent line is
Explanation of Solution
Given information:
The curve:
Formula used:
Point-slope form of the equation of a line:
Slope of a curve is:
The given curve is
Write the given definition using the above function as:
Substitute 4 for a in the above limit and simplify.
Substitute 4 for x in the above limit and simplify.
Also, substitute 4 for x in the curve
So, the slope of the tangent line is
It is known that the slope of a normal line is the negative reciprocal to the slope of the tangent line.
So, the slope of the normal line is
To find the equation of the tangent, use point-slope formula of an equation of a line
Substitute
Hence, the required equation of the tangent line is
Chapter 3 Solutions
Calculus: Graphical, Numerical, Algebraic
Additional Math Textbook Solutions
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
University Calculus: Early Transcendentals (4th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
University Calculus: Early Transcendentals (3rd Edition)
Calculus & Its Applications (14th Edition)
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