Problem 1E: Given that limx2f(x)=4limx2g(x)=2limx2h(x)=0 find the limits that ex.ist. If the limit does not... Problem 2E: Tire graphs of f and g are given. Use them to evaluate each limit, if it exists. If the limit does... Problem 3E: Evaluate the limit and justify each step by indicating the appropriate Limit Law(s).... Problem 4E: Evaluate the limit and justify each step by indicating the appropriate Limit Law(s).... Problem 5E: Evaluate the limit and justify each step by indicating the appropriate Limit Law(s). limt2t422t23t+2 Problem 6E: Evaluate the limit and justify each step by indicating the appropriate Limit Law(s). limu2u4+3u+6 Problem 7E: Evaluate the limit and justify each step by indicating the appropriate Limit Law(s).... Problem 8E: Evaluate the limit and justify each step by indicating the appropriate Limit Law(s).... Problem 9E: Evaluate the limit and justify each step by indicating the appropriate Limit Law(s). limx22x2+13x2 Problem 10E: (a) What is wrong with the following equation? x2+x6x2=x+3 (b) In view of part (a). explain why the... Problem 11E: Evaluate the limit, if it exists. limx2x2+x5x5 Problem 12E: Evaluate the limit, if it exists. limx3x2+3xx2x12 Problem 13E: Evaluate the limit, if it exists. limx5x25x+6x5 Problem 14E: Evaluate the limit, if it exists. limx4x2+3xx2x12 Problem 15E: Evaluate the limit, if it exists. limt3t292t2+7t+3 Problem 16E: Evaluate the limit, if it exists. limx12x2+3x+1x22x3 Problem 17E: Evaluate the limit, if it exists. limh0(5+h)225h Problem 18E: Evaluate the limit, if it exists. limh0(2+h)38h Problem 19E: Evaluate the limit, if it exists. limx2x+2x3+8 Problem 20E: Evaluate the limit, if it exists. limt1t41t31 Problem 21E: Evaluate the limit, if it exists. limh09+h3h Problem 22E: Evaluate the limit, if it exists. limu24u+13u2 Problem 23E: Evaluate the limit, if it exists. limx31x13x3 Problem 24E: Evaluate the limit, if it exists. limh0(3+h)131h Problem 25E: Evaluate the limit, if it exists. limt01+t1tt Problem 26E: Evaluate the limit, if it exists. limt0(1t1t2+t) Problem 27E: Evaluate the limit, if it exists. limx164x16xx2 Problem 28E: Evaluate the limit, if it exists. limx2x24x+4x43x24 Problem 29E: Evaluate the limit, if it exists. limt0(1t1+t1t) Problem 30E: Evaluate the limit, if it exists. limx4x2+95x+4 Problem 31E: Evaluate the limit, if it exists. limh0(x+h)x3h Problem 32E: Evaluate the limit, if it exists. limh01(xh)21x2h Problem 33E: (a) Estimate the value of limx0x1+3x1 by graphing the function f(x)=x/(1+3x1). (b) Make a table of... Problem 34E: (a) Use a graph of f(x)=3+x3x to estimate the value of limx0f(x) to two decimal places. (b) Use a... Problem 35E: Use the Squeeze Theorem to show that limx0(x2cos20x)=0. Illustrate by graphing the functions f(x) =... Problem 36E: Use the Squeeze Theorem to show that limx0x3+x2sinx=0 Illustrate by graphing the functions f, q, and... Problem 37E: If 4x 9 f(x) x2 4x + 7 for x 0, find limx4f(x) Problem 38E: If 2x g(x) x4 x2 + 2 for all x, evaluate limx1g(x) Problem 39E: Prove that limx0x4cos2x=0. Problem 40E: Prove that limxxesin(/x)=0. Problem 41E: Find the limit, if it exists. If the limit does not exist, explain why. limx3(2x+x3) Problem 42E: Find the limit, if it exists. If the limit does not exist, explain why. limx62x+12x+6 Problem 43E: Find the limit, if it exists. If the limit does not exist, explain why. limx0.52x12x3x2 Problem 44E: Find the limit, if it exists. If the limit does not exist, explain why. limx22x2+x Problem 45E: Find the limit, if it exists. If the limit does not exist, explain why. limx(1x1x) Problem 46E: Find the limit, if it exists. If the limit does not exist, explain why. limx0+(1x1x) Problem 47E: The signum (or sign)function, denoted by sgn, is defined by sgnx={1ifx00ifx=01ifx0 (a) Sketch the... Problem 48E: Let g(x) =sgn(sinx). (a) Find each of the following limits or explain why it does not exist. (i)... Problem 49E: Let g(x)=x2+x6x2 (a) Find (i) limx2+g(x) (ii) limx2g(x) (b) Does limx2 g(x) exist'! (c) Sketch the... Problem 50E: Let f(x)={x2+1ifx1(x2)2ifx1 (a) Find limx0 f(x).and lim x0+ f(x) (b) Does limx0 f(x) exist? (c)... Problem 51E: Let B(t)={412tift2t+cift2 Find the value of c so that limt2B(t) exists. Problem 52E: l.et g(x)={xifx13ifx=12xif1x2x3ifx2 (a) Evaluate each of the following, if it exists. (i) limx1g(x)... Problem 53E: (a) If the symbol denotes the greatest integer function defined in Example I 0, evaluate (i)... Problem 54E: Let f(x)=cosx,x. (a) Sketch the graph of f. (b) Evaluate each limit, if it exists. (i) limx0f(x)... Problem 55E: If f(x)=x+x, show that lim x0 f(x) exists hut is not equal to f(2). Problem 56E: In the theory of relativity, the Lorentz contraction formula L=L01v2/c2 expresses the length L of an... Problem 57E: If p is a polynomial, Show that limxa p(x) = p(a) Problem 58E: If r is a rational function. use Exercise 57 to show that limxa r(x) = r(a) for every number a in... Problem 59E: If limx1f(x)8x1=10, find limx1f(x). Problem 60E: If limx0f(x)x2=5, find the following limits. (a) limx0f(x) (b) limx0f(x)x Problem 61E: If f(x)={x2ifxisrational0ifxisirrational prove that limx0f(x)=0. Problem 62E: Show by means of an example that limxa[f(x)+g(x)] may exist even though neither... Problem 63E: Show by means of an example that limxa[f(x)g(x)] may exist even though neither limxa f(x) nor limxa... Problem 64E: Evaluate limx26x23x1. Problem 65E: Is there a number a such that limx23x2+ax+a+3x2+x2 exists? If so, find the value of a and the value... Problem 66E format_list_bulleted