Vertical tangent lines If a function f is continuous at a and lim x → a | f ′ ( x ) | = ∞ , then the curse y = f ( x ) has a vertical tangent line at a and the equation of the tangent line is x = a. If a is an endpoint of a domain, then the appropriate one-sided derivative (Exercises 31–32) is used. Use this information to answer the following questions. 36. Graph the following curves and determine the location of any vertical tangent lines. a. x 2 + y 2 = 9 b. x 2 + y 2 + 2 x = 0
Vertical tangent lines If a function f is continuous at a and lim x → a | f ′ ( x ) | = ∞ , then the curse y = f ( x ) has a vertical tangent line at a and the equation of the tangent line is x = a. If a is an endpoint of a domain, then the appropriate one-sided derivative (Exercises 31–32) is used. Use this information to answer the following questions. 36. Graph the following curves and determine the location of any vertical tangent lines. a. x 2 + y 2 = 9 b. x 2 + y 2 + 2 x = 0
Solution Summary: The author illustrates how the function x2+y 2=9 has a vertical tangent at x=3, and the derivative is infinite at these points.
Vertical tangent linesIf a function f is continuous at a and
lim
x
→
a
|
f
′
(
x
)
|
=
∞
, then the curse y = f(x) has a vertical tangent line at a and the equation of the tangent line is x = a. If a is an endpoint of a domain, then the appropriate one-sided derivative (Exercises 31–32) is used. Use this information to answer the following questions.
36. Graph the following curves and determine the location of any vertical tangent lines.
3) If a is a positive number, what is the value of the following double integral?
2a
Love Lv
2ay-y²
.x2 + y2 dady
16. Solve each of the following equations for x.
(a) 42x+1 = 64
(b) 27-3815
(c) 92. 27² = 3-1
(d) log x + log(x - 21) = 2
(e) 3 = 14
(f) 2x+1 = 51-2x
11. Find the composition fog and gof for the following functions.
2
(a) f(x) = 2x+5, g(x) = x²
2
(b) f(x) = x²+x, g(x) = √√x
1
(c) f(x) = -1/2)
9
9(x) =
х
=
-
X
Chapter 3 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Calculus: Early Transcendentals (3rd Edition)
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY