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# [et f be a real- -valued function defined on (_o, such that | f (x) Isler - 1| for all x in (-o, 0 ). Compute the value of f (0) and determine whether f is continuo...

## Question

###### [et f be a real- -valued function defined on (_o, such that | f (x) Isler - 1| for all x in (-o, 0 ). Compute the value of f (0) and determine whether f is continuous at 0. 8 marks)Let fbe a real-valued function that is continuous o [0, 1] and differentiable on (0, 1)and let g be a function defined on [0, 1] by g (x) =f (x) - (Y) x Iff(0) = 0,f ()-and f (1) = 0,show that there exists â‚¬ in (Y, 1) such that g (c) = 0.(6 marks)(ii) determine whether the equation g (x') 0 has any real root in

[et f be a real- -valued function defined on (_o, such that | f (x) Isler - 1| for all x in (-o, 0 ). Compute the value of f (0) and determine whether f is continuous at 0. 8 marks) Let fbe a real-valued function that is continuous o [0, 1] and differentiable on (0, 1) and let g be a function defined on [0, 1] by g (x) =f (x) - (Y) x Iff(0) = 0,f ()- and f (1) = 0, show that there exists â‚¬ in (Y, 1) such that g (c) = 0. (6 marks) (ii) determine whether the equation g (x') 0 has any real root in (0,1). Justify your answer: (6 marks)  #### Similar Solved Questions

##### 1 8 3V Ul U V 1 V { Ju 1 1 1 " L L ] | ] 1 1 [ I JlE 1J U ; [ 1 1 ]
1 8 3V Ul U V 1 V { Ju 1 1 1 " L L ] | ] 1 1 [ I JlE 1 J U ; [ 1 1 ]...
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(I 1 #id Lelzug i0 S. Ttc? #u2l; 6-'c8 @ j...
##### Concciltaton_ (D) increase the BrOs- concentration 20. The oxidation number of carbon changes from this redox reaction: ZMnO;-(aq) + 3C,0,-(aq) + 4OH-(aq) 2MnOs(s) 6CO} ; (aq) 2H,O() (A) +3t0+4 (B) +3t0+6 (C) +4t0+3 +6t0+4 21. The reaction Zn(s) Ni?*(aq) Zn?t(aq) Ni(s) occurs in the galvanic cell shown. Which statement is true?2NaSORZn metalmetalNiztZn2+SO?SO}(A) Electrons flow to the Ni electrode: Na" ions flow toward the Zn electrode. Electrons flow to the Ni electrode: Nat ions flo
concciltaton_ (D) increase the BrOs- concentration 20. The oxidation number of carbon changes from this redox reaction: ZMnO;-(aq) + 3C,0,-(aq) + 4OH-(aq) 2MnOs(s) 6CO} ; (aq) 2H,O() (A) +3t0+4 (B) +3t0+6 (C) +4t0+3 +6t0+4 21. The reaction Zn(s) Ni?*(aq) Zn?t(aq) Ni(s) occurs in the galvanic c...
##### (f any) at which total revenue maximizod domand function, find a. E, and the values of For Ihe folloving0.29 P=600 â‚¬ Find the elasticity of demand (E) In terms ol qE(q) =b. Find the values of q (If any) at which total revenue maximized. Select the correct cholce below; and If necessary fill in theRavenue maximized at q= (Typo un Intoger or & simplifiod Iraction ) 0 B No valuab ol maximizo rovonuo
(f any) at which total revenue maximizod domand function, find a. E, and the values of For Ihe folloving 0.29 P=600 â‚¬ Find the elasticity of demand (E) In terms ol q E(q) = b. Find the values of q (If any) at which total revenue maximized. Select the correct cholce below; and If necessary fill...
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##### Determine the number of combinations (subsets) of the follcwing 10 objects takemie a0 a timelThele arecombinations pfi1o objects taken 6 at a time
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##### A tank contains 100 kg of salt and 2000 of water. solution of a concentration 0.025 kg of salt per liter enters rank at the rate 10 Llmin: The solution is mixed and drains from the tank at the same rate.Let y be the number of kg of salt in the tank after minutes:Write the differential equation for this situationdz y(0)PreviewPreview
A tank contains 100 kg of salt and 2000 of water. solution of a concentration 0.025 kg of salt per liter enters rank at the rate 10 Llmin: The solution is mixed and drains from the tank at the same rate. Let y be the number of kg of salt in the tank after minutes: Write the differential equation for...
##### Define the relation on Rx (R| {0}) as follows: For all (1,1). (&w) â‚¬ Rx (R| {0H) (2,4) ~ (W) ~TW #v:Is this An equivalance relation?
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##### Thue or FbeA and B ate not null veclxs If Ax B =0 and Ahen A an & ar Parall_ 2vedo v: vit ~jj- Vk i SolenoiJal In 4hele dimenswn (Jv)f8x+ ( Jvz) / 8y (Jv,Y 2 = 0The vecdex from p ( 0 ,-') 40 A (5,3,2) i -4,4,3)Ip AErImpl; es Jhot A -RaI 8 pF "m plies sticdhat 4" = &?
Thue or Fbe A and B ate not null veclxs If Ax B =0 and Ahen A an & ar Parall_ 2 vedo v: vit ~jj- Vk i SolenoiJal In 4hele dimenswn (Jv)f8x+ ( Jvz) / 8y (Jv,Y 2 = 0 The vecdex from p ( 0 ,-') 40 A (5,3,2) i -4,4,3) Ip AEr Impl; es Jhot A -R aI 8 pF "m plies sticdhat 4" = &?...
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##### Determine the magnitude and direction of the force between two parallel wires 20 m long and 6.0 an apart, each @rying 25 A in the sarme direction.Seled one: a.0.04 N Attraqionb.292 Mauractve00.04 H repulsive 4.292M reduistve
Determine the magnitude and direction of the force between two parallel wires 20 m long and 6.0 an apart, each @rying 25 A in the sarme direction. Seled one: a.0.04 N Attraqion b.292 Mauractve 00.04 H repulsive 4.292M reduistve...
##### A person with normal eye looks through magnifier at an object: A virtual, upright image forms 50 cm from the lens The lens has focal length of 10 cm What is the angular magnification (M)?hint; the near point for normal eye is 25 cm: The eye is close to the lens and this particular image is not at maximum magnification:3.0infinite3.54.02.5
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##### 6. Kz[Cr(C204131.3H20 7 . [RezClg] 2-
6. Kz[Cr(C204131.3H20 7 . [RezClg] 2-...
##### 9-12, write the inequality in the form $a < x < b$.$$|3 x-4|<2$$
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2 9 )" Cos 2 dz ~T...