(a)
The line that is tangent to the curve at a point.
(a)
Answer to Problem 19E
The required equation of the tangent line is
Explanation of Solution
Given information:
The curve:
The point =
Formula used:
Slope of a curve is:
The given curve is
Write the given definition using the above function as:
Substitute 1 for a in the above limit and simplify.
Simplify the above limit further.
So, the slope of the tangent line is 3 and the point is
To find the equation of the tangent, use point-slope formula of an equation of a line
Substitute 3 for m , 1 for
Hence, the required equation of the tangent line is
(b)
The line that is normal to the curve at a point.
(b)
Answer to Problem 19E
The required equation of the normal line is
Explanation of Solution
Given information:
The curve:
The point
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 1 for a in the above limit and simplify.
Simplify the above limit further.
So, the slope of the tangent line is 3 and the point is
It is known that the slope of a normal is the reciprocal of the slope of the tangent.
So, the slope of the required normal is,
To find the equation of the normal, use point-slope formula of an equation of a line
Substitute
Hence, the required equation of the normal line is
Chapter 3 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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