a.
To graph: The secant line to the given function at base point
a.
Explanation of Solution
Given:
The given function is
Method used:
The function and the secant line is plotted using graphic calculator.
Calculations and Graph:
The given function is
The coordinates of base point say, P are
The point at distance
The graph of the function and the secant is shown in Figure (a)
b.
To graph: The secant line to the given function at base point
b.
Explanation of Solution
Given:
The given function is
Method used:
The function and the secant line is plotted using graphic calculator.
Calculations and Graph:
The given function is
The coordinates of base point say, P are
The point at distance
The graph of the function and the secant is shown in Figure (b).
c.
To graph: The secant line to the given function at base point
c.
Explanation of Solution
Given:
The given function is
Method used:
The function and the secant line is plotted using graphic calculator.
Calculations and Graph:
The given function is
The coordinates of base point say, P are
The point at distance
The graph of the function and the secant is shown in Figure (c). We see the secant line tends to tangent line at point P .
d.
To graph: The secant line to the given function at base point
d.
Explanation of Solution
Given:
The given function is
Method used:
The function and the secant line is plotted using graphic calculator.
Calculations and Graph:
The given function is
The coordinates of base point say, P are
The point at distance
The graph of the function and the secant is shown in Figure (d).
We see the secant line tends to tangent line at point P .
e.
To graph: The secant line to the given function at base point
e.
Explanation of Solution
Given:
The given function is
Method used:
The function and the secant line is plotted using graphic calculator.
Calculations and Graph:
The given function is
The coordinates of base point say, P are
The point at distance
The graph of the function and the secant is shown in Figure (e).
We observe that points
Here, the slope of the tangent by definition is
And from the formula as the tangent line is the limiting case of secant line
Thus, the slope of the tangent line is 25.
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Chapter 2 Solutions
Modeling the Dynamics of Life: Calculus and Probability for Life Scientists
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