Calculus 1501A/B- Midterm Exam Guide - Comprehensive Notes for the exam ( 113 pages long!)

Y Ethics Cases I Et le wri , Lecture Notes- l ㈢ LetureChapter . My PittHorne-B Mail. CNRT@ u/res/pitt/athanas/optimization-3.problem?symb CALCULUS 1 - HOCKE Connor] willson ▼ (Student -section: 30731) Contents Grades Course Contents PROBLEM SET 10» optimization-3 Me An open box is to be constructed so that the length of the base is 4 times larger than the square foot and the cost to construct the four sides is 1 dollars per square foot, determin would minimize the cost of construction. The values for the dimension of the base are: The height of the box is: Submit Answer Tries 0/8 Type here to search DOLL

Algebra Consider the matrices A= (1 0 2 0 3 4 5 6 0) B= (0 3 4 1 0 2 50 60 0) (a) Using the correspondence between elementary matrices and elementary row operations, find a matrix C such that CA = B. (b) Using the expressions for the inverses of elementary matrices from the lecture notes, and the rule for inverses of products of matrices, find the inverse matrix of C (c) Check your answer by computing directly that C^-B = A. Calculus (a) what is the value of are sin(sin(pi))? Show your reasoning. (b) A ball is dropped from a height of 30 m. If we neglect air resistance and apply Newton's second law, the height of the ball above the ground after t seconds is given by y(t)=30 - y^t^2/2, for t elementof [0, t] where g is the gravitational acceleration, which we take to be 9.8 m/s/s, and t_f > 0 is the time at which the ball hits the ground. Find the inverse function t(y) and use this to determine t_f.

Please read the directions for each problem carefully. You may work together and receive help on this exam; however, each student must turn in his or her own exam. This exam is due by 11:30am on Monday November 27th. Late exams will not be accepted. If you are unable to attend class on Monday November 27th, you must scan and email the exam to me by 11:30am (11 points) Given the function f(x) =- (a) Find the domain of the function in interval notation. (x-1)2 x2+1 I. Answer (in interval notation):0o o (b) Find the intercepts of the function. All work must be shown. Write your answers as ordered pairs. o Answer(s) (written as ordered pairs): L101-10.1) (c) Find the equations of any asymptotes. All work must be shown. L91 C110) Answer(s) (written as equations) (d) Find the critical numbers. All work must be shown