First part of the small intestine, immediately beyond the stomach (8)

Daily solution for the Cryptic crossword No 29,122. The Guardian Cryptic Crosswords are very hard sometimes, with our help you will be able to finish the tricky definitions.
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Clues Answers
Defer turning up? Swell (3,3) PUTOFF
I’m backing competitions engaging student prodigies (8) MIRACLES
Finished tucking into drink, bowl turned upside-down? (6) CUPOLA
Game soldier from abroad occupying areas, offering defence (8) APOLOGIA
Equivalent figure in work to advance food additive (8,6) OPPOSITENUMBER
Government’s in better nick, providing digital coverage? (10) FINGERNAIL
Really? That’s half gone? It’s not true (4) MYTH
Shy about beginning to participate in reproduction (4) COPY
I start to raise it in allotment, producing annoyance (10) IRRITATION
Description of theatre and music person creating star, possibly (10,4) PERFORMINGARTS
Financial journalists and their boss recalled in unpleasantly sticky surroundings (4,4) CITYDESK
Meat served in American flight mostly spoken about (6) SALAMI
I utter a couple of names when pushing back Hindu beggar (8) SANNYASI
A second firm linked to motor-racing debacle (6) FIASCO
Large bra served up in purple (4) PUCE
Pinches trophy after taking up bowling like this (7) TOPSPIN
Almost half of Alcatraz united, enthralled by French bird man? (8) FALCONER
One held in jail around city — rough situation? (11) IMPRECISION
Disagree, dismissing first total (3-3) ALLOUT
Clearly article from Libération's fluently presented without opening line (7) LEGIBLY
Marine animal hunting curtailed after receiving text for you (3,6) SEAURCHIN
Dicks in orgasm possibly retaining utility (11) IGNORAMUSES
Female expert gets ready to leave external applications (4,5) FACEPACKS
I charge a French body of water to raise this seafood (8) CALAMARI
Joke about artist concealing sex — probably not a favourite of mine! (7) PURITAN
Seemingly unhappy career amongst those who got elected (2,5) INTEARS
Month in which daughter never turned up for start of week (6) MONDAY
Motor fuel going up, requiring investment of money (4) LIMO