need help, with these questions

Name: Full solutions are required. Answer in the spaces provided. 1. Determine the following limit exactly. Show all work. 2. The value of a $1000 investment earning 6% compounded annually is given by V = 1000(106)", where n is the number of years the money remains invested. a) What is the average rate of change of value for the first 3 years of the investment? b) How fast the investment is growing at ten years. 3. Match each given function to its derivative below. Give one reason for each choice. Sketch the unmatched derivative. 11) iii) C A) Page 5 of 11 Name: 3 4. Determine and simplify the derivative of f (x) : 1 2 7 X from first principles. 5. A piece of string 100cm long is to be cut into two pieces. One piece will be bent into a circle and the other will be bent into a square. Where should the string be cut in order to minimize the total area of the two figures. Verify that your answer is indeed a minimum. (Answer to two decimal places) Page 6 of 11 Name: 6. Examine the graph of the function y = AX and its derivative. Assume each y-intercept crosses at the line on the graph paper. [5] a) Which is the function? How do you know? b) What is the scale on the y-axis? c) What is the equation of the tangent at x = 0? d) What is the value of A? Explain. 7. A plane travels 300 km at (a bearing of) 1200 then travels 250 km at 200, Give a single vector for the direct route ight. Page 7 of 11 Name: 8. A 100 kg weight is held from the ceiling by two cables, as shown. If the system is perfectly balanced, determine the tension (One decimal place) in each cable. \"WW I 9. Find the scalar equation of the plane that contains the point (2, 1, 5) as well as the line + t. Page 8 of 11 \fName: 11. Analyze the function y =- * +1 (x - 1)2 , under the headings: Domain, Intercepts, Asymptotes, Increasing/Decreasing, Maximum/Minimum, Concavity and Points of Inflection. Then sketch the curve. Page 10 of 11