Test 2 - Math 161 Fall 2013 Test 2 Study Sheet 1 The graphs of F(x and G(x are given below Find the following If a value doesnt exist write DNE(a G(2(b

# Test 2 - Math 161 Fall 2013 Test 2 Study Sheet 1 The graphs...

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Math 161 Fall 2013 Test 2 Study Sheet 1. The graphs ofF(x) andG(x) are given below. Find the following. If a value doesn’texist, write DNE.(a)G(2)(b)F0(5)(c) limx4G(x)(d) Allx-values whereFis not differentiable2. Find the derivative of each function. Do not simplify:(a)f(x) = secx-2xx2+ 4(b)g(x) = 3x18-10x1.9(c)y= 3 cos(5t)t4+ 23. Using the information in the graphs in problem 1, find the derivatives below. If theydon’t exist, say DNE.(a) IfH(x) =GF(x), findH0(7).(b) IfS(x) =F(x)G(x), findS0(4).4. Find the equation of the tangent line to the graph of 2x+xy= 7 at the point (-7,-1).5.(a) Give thedefinitionof the derivative of a functionf(x). (Your definition shouldbe the limit of something.)(b) Use the definition to show that the derivative off(x) = 3x2isf(x) = 6x.6. SupposeM(t) is a function giving the mass (in kilograms) of an ice block,tminutesafter removing it from a freezer and placing it in the sun. What doesM(t) represent?WillM(t) be positive or negative? What are the units ofM(t)?7. Pick a related rates problem from the handout on section 2.8, or from the book insection 2.8, and do it. 1
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