7. Show that the function r(0) =0+ sin2 -8 has exactly one zero in the interval (- ∞,00). Rolle's Theorem states that for a function f(x) that is continuous at every point over the closed interval [a,b] and differentiable at every point of its interior (a,b), if f(a)=f(b), then there is at least one number c in (a,b) at which f (c) = 0. Find the derivative of r(0) =0 + sin2 3-8. r'(0) = Can the derivative of r(0) be zero in the interval (- 0,00)? O Yes O No in the interval (- 00,00). According to Rolle's Theorem, since the derivative of r(0) is never zero in the interval (- 0,00), there cannot be two points e= a and 0=b for which r(a) =r(b) in this interval. In other words, the function r(0) has (1) Which theorem can be used to determine whether a function has any zeros in a given closed interval? O A. Mean value theorem O B. Extreme value theorem OC. Intermediate value theorem To apply this theorem, evaluate the function r(0) =0+ sin -8 at each endpoint of the interval [-37,31]. г(- Зл) 3D (Type an exact answer, using n as needed.) (Type an exact answer, using n as needed.) г(Зл) 3D Ө According to the intermediate value theorem, r(0) =0+ sin 2 -8 has (2) in the interval [-37,37]. If r(e) has at least one zero in the interval [- 3n,37], and this interval is fully contained within the interval (- 00,00), then r(0) has at least one zero in the interval (- 0,00). Ө Thus, since the intermediate value theorem shows that r(0) =0+ sin23 -8 has at least one zero in the interval (- 0,00) and Rolle's Theorem shows that r(0) has at most one zero in this interval, the function r(0) has exactly one zero in the interval (-o,00). (1) o at least one zero o no zeroes O exactly one zero o at most one zero (2) o exactly one zero o at least one zero o no zeroes
7. Show that the function r(0) =0+ sin2 -8 has exactly one zero in the interval (- ∞,00). Rolle's Theorem states that for a function f(x) that is continuous at every point over the closed interval [a,b] and differentiable at every point of its interior (a,b), if f(a)=f(b), then there is at least one number c in (a,b) at which f (c) = 0. Find the derivative of r(0) =0 + sin2 3-8. r'(0) = Can the derivative of r(0) be zero in the interval (- 0,00)? O Yes O No in the interval (- 00,00). According to Rolle's Theorem, since the derivative of r(0) is never zero in the interval (- 0,00), there cannot be two points e= a and 0=b for which r(a) =r(b) in this interval. In other words, the function r(0) has (1) Which theorem can be used to determine whether a function has any zeros in a given closed interval? O A. Mean value theorem O B. Extreme value theorem OC. Intermediate value theorem To apply this theorem, evaluate the function r(0) =0+ sin -8 at each endpoint of the interval [-37,31]. г(- Зл) 3D (Type an exact answer, using n as needed.) (Type an exact answer, using n as needed.) г(Зл) 3D Ө According to the intermediate value theorem, r(0) =0+ sin 2 -8 has (2) in the interval [-37,37]. If r(e) has at least one zero in the interval [- 3n,37], and this interval is fully contained within the interval (- 00,00), then r(0) has at least one zero in the interval (- 0,00). Ө Thus, since the intermediate value theorem shows that r(0) =0+ sin23 -8 has at least one zero in the interval (- 0,00) and Rolle's Theorem shows that r(0) has at most one zero in this interval, the function r(0) has exactly one zero in the interval (-o,00). (1) o at least one zero o no zeroes O exactly one zero o at most one zero (2) o exactly one zero o at least one zero o no zeroes
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![7.
Show that the function r(0) =0+ sin2
-8 has exactly one zero in the interval (- ∞,00).
Rolle's Theorem states that for a function f(x) that is continuous at every point over the closed interval [a,b] and differentiable at every point of its interior (a,b), if f(a)=f(b), then there is at least one number c in (a,b) at which f (c) = 0.
Find the derivative of r(0) =0 + sin2
3-8.
r'(0) =
Can the derivative of r(0) be zero in the interval (- 0,00)?
O Yes
O No
in the interval (- 00,00).
According to Rolle's Theorem, since the derivative of r(0) is never zero in the interval (- 0,00), there cannot be two points e= a and 0=b for which r(a) =r(b) in this interval. In other words, the function r(0) has (1)
Which theorem can be used to determine whether a function has any zeros in a given closed interval?
O A. Mean value theorem
O B. Extreme value theorem
OC. Intermediate value theorem
To apply this theorem, evaluate the function r(0) =0+ sin
-8 at each endpoint of the interval [-37,31].
г(- Зл) 3D
(Type an exact answer, using n as needed.)
(Type an exact answer, using n as needed.)
г(Зл) 3D
Ө
According to the intermediate value theorem, r(0) =0+ sin 2
-8 has (2)
in the interval [-37,37].
If r(e) has at least one zero in the interval [- 3n,37], and this interval is fully contained within the interval (- 00,00), then r(0) has at least one zero in the interval (- 0,00).
Ө
Thus, since the intermediate value theorem shows that r(0) =0+ sin23
-8 has at least one zero in the interval (- 0,00) and Rolle's Theorem shows that r(0) has at most one zero in this interval, the function r(0) has exactly one zero in the interval (-o,00).
(1) o at least one zero
o no zeroes
O exactly one zero
o at most one zero
(2) o exactly one zero
o at least one zero
o no zeroes](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9321e6ee-9aa3-4080-82c3-086b2b0cdde0%2F8fc58cb0-c098-4f83-a59c-3e0e46296a9e%2Fvohae6p.png&w=3840&q=75)
Transcribed Image Text:7.
Show that the function r(0) =0+ sin2
-8 has exactly one zero in the interval (- ∞,00).
Rolle's Theorem states that for a function f(x) that is continuous at every point over the closed interval [a,b] and differentiable at every point of its interior (a,b), if f(a)=f(b), then there is at least one number c in (a,b) at which f (c) = 0.
Find the derivative of r(0) =0 + sin2
3-8.
r'(0) =
Can the derivative of r(0) be zero in the interval (- 0,00)?
O Yes
O No
in the interval (- 00,00).
According to Rolle's Theorem, since the derivative of r(0) is never zero in the interval (- 0,00), there cannot be two points e= a and 0=b for which r(a) =r(b) in this interval. In other words, the function r(0) has (1)
Which theorem can be used to determine whether a function has any zeros in a given closed interval?
O A. Mean value theorem
O B. Extreme value theorem
OC. Intermediate value theorem
To apply this theorem, evaluate the function r(0) =0+ sin
-8 at each endpoint of the interval [-37,31].
г(- Зл) 3D
(Type an exact answer, using n as needed.)
(Type an exact answer, using n as needed.)
г(Зл) 3D
Ө
According to the intermediate value theorem, r(0) =0+ sin 2
-8 has (2)
in the interval [-37,37].
If r(e) has at least one zero in the interval [- 3n,37], and this interval is fully contained within the interval (- 00,00), then r(0) has at least one zero in the interval (- 0,00).
Ө
Thus, since the intermediate value theorem shows that r(0) =0+ sin23
-8 has at least one zero in the interval (- 0,00) and Rolle's Theorem shows that r(0) has at most one zero in this interval, the function r(0) has exactly one zero in the interval (-o,00).
(1) o at least one zero
o no zeroes
O exactly one zero
o at most one zero
(2) o exactly one zero
o at least one zero
o no zeroes
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