{"paper":{"id":"site-4934","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"rozszerzona","variant":null,"exam_pdf":null,"key_pdf":null,"question_count":3,"source_label":"Matematyka · Zbiory zadań (rozszerzona)","subject_label":"Matematyka","category_label":"Zbiory zadań"},"questions":[{"id":"site-4934/zad/5502","paper_id":"site-4934","number":"5502","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"rozszerzona","text":"Rozwiązanie zadania. Prosta dana równaniem y = 1/2x + 3/2 jest prostopadła do stycznej do wykresu funkcji f(x) = x^4 - 3x^3 + x^2 + x + 5 w punkcie A. (-1,6) B. (0,5) C. (1,5) D. (2,3).","answer":null,"answer_text":null,"solution":null,"image":"img/site/4934/zad-5502.svg","solution_image":"img/site/4934/rozw-5502.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (rozszerzona)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4934/zad/6681","paper_id":"site-4934","number":"6681","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"rozszerzona","text":"Funkcja f jest określona wzorem f(x) = {x² + 3/ x-1} dla każdej liczby rzeczywistej x≠1. Wyznacz równanie stycznej do wykresu tej funkcji w punkcie P=(-3,-3).","answer":null,"answer_text":null,"solution":null,"image":"img/site/4934/zad-6681.svg","solution_image":"img/site/4934/rozw-6681.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (rozszerzona)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4934/zad/7229","paper_id":"site-4934","number":"7229","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"rozszerzona","text":"Dana jest parabola o równaniu y=x^2+1 i leżący na niej punkt A o współrzędnej x równej 3. Wyznacz równanie stycznej do tej paraboli w punkcie A.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4934/zad-7229.svg","solution_image":"img/site/4934/rozw-7229.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (rozszerzona)","subject_label":"Matematyka","category_label":"Zbiory zadań"}]}