MATH1013 Calculus I, 2013-14 Fall Week 02 First Tutorial ... machiang/1013/2013-14_Fall/... · Week…

Download MATH1013 Calculus I, 2013-14 Fall Week 02 First Tutorial ... machiang/1013/2013-14_Fall/... · Week…

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<ul><li><p>MATH1013 Calculus I, 2013-14 Fall</p><p>Week 02 First Tutorial Worksheet: Functions (Part I) (L10)</p><p>Name: ID No.: Tutorial Section:</p><p>Complete at least THREE questions from the following questions.</p><p>(Solution of this worksheet will be available at the course website after all the Friday tutorials)</p><p>1. (Demonstration) (page 10, Q. 21, Domain) A stone is thrown vertically upward from the ground ata speed of 40m/s at time t = 0. Its distance d (in meters) above the ground is approximated by thefunction f(t) = 40t 5t2. What is the domain of the function f(t)?</p><p>2. (Demonstration) (p. 11, Q. 69, interpreting secant line) Sketch the function of volume V of an idealgas in cm3 with V = 2p , where p is the pressure in atmosphere, at the end points of 0.5 p 2, a secantbetween the two points at p = 0.5 and p = 2, and interpret your answer as an average rate of change.</p><p>3. (Demonstration) (p. 11, Q. 83) Use the definition of absolute value to graph the function |x| |y| = 1.</p><p>4. (Demonstration) (p. 22, Q. 34) Graph the function</p><p>f(x) =</p><p>|x 1|x 1</p><p>, if x 6= 1;</p><p>0, if x = 1.</p><p>5. (Class work) (page 10, Q. 22) A stone is dropped off a bridge from a height of 20m above a river. If trepresents the elapsed time (in seconds) after the stone is released, then its distance d (in meters) abovethe river is approximated by the function f(t) = 20 5t2. What is the domain of the function f(t)?</p><p>Answer</p><p>6. (Class work) (p. 11, Q. 70, interpreting the slope of the secant line) The speed of a car prior to hardbraking can be estimated by the length of the skid mark. The skid mark function is given by S =</p><p>30`</p><p>in mile/hour, where ` is in feet. Sketch the function between 50 ` 150, and a secant between thetwo points at ` = 50 and ` = 150 and interpret its meaning.</p><p>Answer</p><p>1</p></li><li><p>7. (Class work) (p. 22, Q. 24) Graph the function</p><p>f(x) =</p><p>x2 x 2</p><p>x 2, if x 6= 2;</p><p>4, if x = 2.</p><p>Answer</p><p>8. (Class work) Use the definition of absolute value to graph the function |x| |2y| = 1.</p><p>Answer</p><p>9. (Class work) Graph the function</p><p>f(x) =</p><p>|2x + 1|2x + 1</p><p>, if x 6= 12 ;</p><p>0, if x = 12 .</p><p>Answer</p><p>10. (Class work) (p. 23, Q. 45) Given f(x) = x2, sketch the function g(x) = 6 f(x 2</p><p>3</p><p>)+ 1.</p><p>Answer</p><p>2</p></li></ul>