Download 4 Questions on Calculus II - Exam 2 | MATH 141 and more Exams Calculus in PDF only on Docsity! October 15, 2004 MATH 141 โ TEST 2 (7.1 โ 8.3) [Pilachowski] Follow directions carefully: โข Use exactly ONE answer sheet per question (use the back of the sheet if needed). โข Put your name, your TA's name and the question number on EACH page. โข No books, notebooks, calculators, cell phones or other electronic devices. โข Put a BOX around the final answer to a question. โข Show enough work that we can follow your thinking. You must show all appropriate work in order to receive full credit for an answer. Answers should always be in simplest form. โข Before handing in your test: on your first answer sheet only, please copy the pledge and sign. 1. a. (10 points) Let and Let [a, b] be the largest interval containing 0 such that f has an inverse function on this interval. Find a and b. (Show all your steps.) ( ) 3163 +โ= xxxf 1โf b. (5 points) Determine whether f is increasing or decreasing on this interval. State how you know. c. (5 points) Determine whether f has a point of inflection on this interval. State how you know. d. (6 points) Find . (Show all your steps.) ( ) ( )31 โฒโf 2. (12 points each) Find the following limits. Possible answers are a calculated numeric value, ,, โโโ or DNE (does not exist). You must show all your steps in order to receive full credit. a. 2 1 0 tanlim x x x โ +โ b. xx x 2 0 loglim+โ 3. a. (10 points) Solve for the general, explicit function: โ โ โโ โ โ โ=โฒ 22 1 yey x . (Show all your steps.) b. (15 points) Evaluate . (Show your steps and give a numeric answer in simplest form.) โซ 3 1 2 ln dxxx c. (4 extra points) Given the linear first order differential equation xxyy coscos =+โฒ , state the integrating factor ( )xSe . 4. a. (10 points) Find . (Show all your steps.) โซ dxxx 2sec2tan 33 b. (15 points) Evaluate โซ โ โ 2 2 24 dxx . (Show all your steps.) Math 141, Sections 02**, T Pilachowski, Fall 2004
