PRACTICE MIDTERM FOR MATHS1101

Notes

PRACTICE MIDTERM FOR MATHS1101 i PRACTICE MIDTERM FOR MATHS1101 1 1 (20 pts). Concept explanation (1) (5 pts) Let f p x q be a function. Let a be a real number. What’s the meaning of lim x Ñ a f p x q “ `8 . (2) (5 pts) Let f p x q be a function. Let L be a real number. What’s the meaning of lim x Ñ`8 f p x q “ L. (3) (5 pts) Let f p x q and g p x q be two functions. Let a be a real number. State the product rule of limits lim x Ñ a f p x q g p x q . (4) (5 pts) Let f p x q and g p x q be two functions. State the product rule for the derivative p f p x q g p x qq 1 . 2 PRACTICE MIDTERM FOR MATHS1101 2 (20 pts). Calculations. (1) (5 pts) lim x Ñ 3 x 3 ́ 3 x ` 10. (2) (5 pts) lim t Ñ 0 sin p t q 2 t . (3) (5 pts) Let f p x q “ 3 a 1 ` tan p x q . What’s f 1 p 0 q ? (4) (5 pts) Let g p x q “ e sin p x q ` cos p e x q . What’s g 1 p x q ? PRACTICE MIDTERM FOR MATHS1101 3 3 (20 pts) True or false. (1) (5 pts) If f and g are two differentiable functions. Then p f ̋ g q 1 p x q “ g 1 p f p x qq ̈ f 1 p x q . (2) (5 pts) If f p x q “ 10 x . Then f 1 p x q “ x 10 x ́ 1...