WORKSHEET 9 - Fall 19951. Recall that sin2(x)+cos2(x) = 1. Write an expression for each trig function squared in terms of one ofthe other trig functions.a) sin2(x)b)cos2(x)c)tan2(x)d)cot2(x)e)sec2(x)f)csc2(x)2. Compute the limits.a) limx→0sin22xx2d) limx→01+cot23x4x2b) limx→01−cos 3xx2e)limx→π/6[1−sec(x+π3)](x−π6)2c) limx→0x1−secxf)limx→2cosx2x−π3. For each of the following, de±ne a function satisfying the conditions. Graph your function.a)g(x) is a rational function which is de±ned for allxexceptx=1,2.b) limx→0f(x)doesnotexistand|f(x)|<2 for allx.c)f(x) is discontinuous at every point.4. Sketch graphs of the following functions, determine the points of discontinuity, and state whether it’s aremovable or nonremovable (i.e. essential) discontinuity.a)f(x)=x2−1x+1b)f(xx2,x<−2−2=−2x,−2<x≤02,0<x<23x,2≤xc)f(x|x+2|.5.a) Computeg0(1), whereg(xx+f(x)x−f(x),f(1) = 4, andf0(1) = 2.b) Supposef(xxf0(x) for allxin the domain off(x). What can we say about the functiong(x)?6. Suppose thatfis di²erentiable at
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This note was uploaded on 04/11/2011 for the course MATH 1400 taught by Professor Grether during the Spring '08 term at North Texas.