1. An 8-foot-high camel is loping away from a streetlight. The camel is loping at 12 feet/second. The streetlight is 20 feet high. How fast is the camel's shadow growing? [2 marks] 2. A 1-inch high insect is crawling away from a candle. The insect is crawling at 10 inches/minute. The insect's shadow is growing at 2 inches/minute. How high is the candle? [2 marks] 3. A ladder is leaning against a wall. The ladder is 5 meters long. The top of the ladder is 3 meters above the ground. The top of the ladder is sliding down at 8 meters/second. a) How far is the bottom of the ladder from the wall? b) How fast is the bottom of the ladder sliding away from the wall? [2 marks] 4. A ladder is leaning against a wall. The ladder is 20 feet long. The top of the ladder is sliding down at 3 feet/second. The bottom of the ladder is sliding away from the wall at 4 feet/second. a) How high is the top of the ladder up the wall? b) How far is the bottom of the ladder from the wall? [3 marks]5. (5 marks) Evaluate the following indefinite integrals: (a) S(5x2 + 2x - 15) dx (b) s ( - - )dx (c) S ( #+ e3x) dx (d) S (sin(3x) - cos(2x))dx ( 4 -x3+x) dx (e) S 6. (8 marks) Evaluate the following definite integrals. Round your answers to one decimal place. (a) S'(e2x - 1) dx (b) S5, ( x3 + 3x2) dx (c) S V xz dx (d) " 3 sin(3x) dx 7. (3marks) A curve is given by the function: x4 + 2x2 a) What is the area under the curve between x = 1 and x = 4? b) What is the average value of the curve between x = 1 and x = 4? c) What is the volume of the solid generated when the area under the curve between x = 1 and x = 4 is rotated about the x axis