(a)
To find: the counter examples to the given statements.
(a)
Answer to Problem 40E
Here, the curve is the case for a parabola and not an ellipse.
Explanation of Solution
Given:
Calculation:
The given statement is false. The following example shows this:
Let
Now,
This is the case for a parabola, and not an ellipse.
Conclusion:
Hence, the curve is the case for a parabola and not an ellipse.
(b)
To find: the counter examples to the given statements.
(b)
Answer to Problem 40E
Here, the curve is the case for a parabola and not an hyperbola.
Explanation of Solution
Given:
Calculation:
Let
Now,
This is the case for a parabola, and not a hyperbola.
Conclusion:
Hence, the curve is the case for a parabola and not an hyperbola.
(c)
To find: the counter examples to the given statements.
(c)
Answer to Problem 40E
Here, the curve is definitely a hyperbola.
Explanation of Solution
Given:
Calculation:
The given statement is true.
Given that
Now,
Since
Conclusion:
Hence, the curve is definitely a hyperbola.
Chapter A5 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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