Unformatted text preview: MAT 2010 Term I, 10—11 LABS
(Sept21,2010) USING THE DIFFERENCE QUOTIENT AND THE IDEA 0F “LIMIT”TO FIND THE
SLOPE 0F TANGENT LINES OF CURVES PART I In class yesterday we determined for the problem about throwing an object of the top of a
building that 4 see. after the object was thrown it was only 4 it. above the ground and traveling at 88 ft/sec (60 mph). Let ﬁgure out how fast it’s going when it hits the ground. The function was s(t) = -l6t2 +40t +100. A. Find how long it take the object to hit the ground. Solve s(t) = 0. Call this value t*.
B. Set up and simplify the DQ S! t* + h)—sgt*[
h C. What is the value of the above formula when h approaches 0? This is the object’s
instantaneous velocity when it hits the ground in ft/sec. Convert this to mph. Does the obj ect’s
speed change much as between the time it is 4 it above the ground and when it hits the ground? PART II. In this case we will look at estimating slope of the tangent line of a function at t : 1 for some
different functions. Here is the DQ in this case. f1+h ‘fl
h Use the functions — A. ﬁ0=2€-5m+7
B. f(t) = (t+1)/(t — 5)
C. f(t) = t5 + 3t3 , 5t2 +2t -7 ...
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- Fall '10