Pep Guardiola's team dropped out of the Champions League qualification places after losing four of the nine top-flight matches they played during December and January.
Three successive wins across two competitions have brightened the mood however, with Jesus making significant contributions in each match.
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The Brazil striker, whose move from Palmeiras was completed during the mid-season transfer window, has scored three times in his two Premier League starts, and got both goals as Swansea were defeated 2-1 at Eastlands last Sunday.
In the last few days, team-mates Fernandinho and Yaya Toure have both warned against getting too carried away with the 19-year-old's excellent start, yet some pundits have asked if this might be the beginning of the end for Sergio Aguero at City.
Aguero has made only brief substitute appearances in each of the club's last two matches, and suggested after the Swansea match that he was unsure about his future, although City moved swiftly to indicate that they had no plans to sell a striker who is under contract until 2020.
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It has been a difficult season for the Argentina international, who has missed seven City matches through suspension, had missed four penalties for club and country by the middle of October.
Aguero has also lost his starting place in the national team of late too and may have to settle for a place on the bench at Bournemouth.
With City in fifth place, behind fourth placed Liverpool on goal difference, Guardiola has other selection issues to consider.
Claudio Bravo, the first choice, has not played well in recent weeks and was dropped after a 2-2 draw at home to Tottenham on January 21.
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Willy Caballero, the back-up, has played in the three matches since, all of which City have won.
Despite those selection dilemmas, Guardiola is more content with the way his team are playing now than a month ago, when a 4-0 defeat at Everton prompted him to declare City were out of the Premier League title race.
Nonetheless, the manager respects a Bournemouth side who have beaten Liverpool this season - and should have beaten Arsenal, instead drawing 3-3 after being three goals up.
"In the last two years, it is outstanding what Bournemouth have done," Guardiola said. "They are so aggressive. They are an honest team.
"They play for the spectators in that they want to do something. They are fast guys to use the counter attack. I know what happened against Liverpool and Arsenal, the big teams. It will be tough."
Bournemouth are comfortably placed in 14th, six points clear of the relegation places.
But Eddie Howe's side are yet to taste victory in 2017 however and know they risk being dragged downwards if that trend persists.
The Cherries will look to Jack Wilshere, the on-loan Arsenal midfielder, for inspiration against City.
Wilshere joined Bournemouth for regular football after a succession of injury-hit seasons with the Gunners and inevitably speculation has begun about a permanent switch.
"We would love that to happen," Howe said. "I can't rate Jack any higher as a footballer or a person, and how he's come into the team and what he has delivered for us.
"But there has been no discussion with Arsenal. As I see it Jack is on loan for the season, then we'll look at it - and Jack will look at it - from that point."
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