Problem 1E: In Exercises 13, find the limit. limx03x2x2 Problem 2E: In Exercises 13, find the limit. limx03x2x Problem 3E: In Exercises 13, find the limit. limx03x2x4 Problem 4E: For Exercises 423, use algebra to simplify the expression and find the limit. limx3x23xx3 Problem 5E: For Exercises 423, use algebra to simplify the expression and find the limit. limt0t4+t22t39t2 Problem 6E: For Exercises 423, use algebra to simplify the expression and find the limit. limt0x33xx2x+3 Problem 7E: For Exercises 423, use algebra to simplify the expression and find the limit. limx4x+42x2+5x12 Problem 8E: For Exercises 423, use algebra to simplify the expression and find the limit. limy1y25y+4y1 Problem 9E: For Exercises 423, use algebra to simplify the expression and find the limit. limx1x2+2x3x23x+2 Problem 10E: For Exercises 423, use algebra to simplify the expression and find the limit. limt22t2+3t2t2+5t+6 Problem 11E: For Exercises 423, use algebra to simplify the expression and find the limit. limx3x29x2+x12 Problem 12E: For Exercises 423, use algebra to simplify the expression and find the limit. limy12y2+y13y2+2y1 Problem 13E: For Exercises 423, use algebra to simplify the expression and find the limit. limh0(3+h)29h Problem 14E: For Exercises 423, use algebra to simplify the expression and find the limit. limx3(x+5)24x29 Problem 15E: For Exercises 423, use algebra to simplify the expression and find the limit. limx35x215x49 Problem 16E: For Exercises 423, use algebra to simplify the expression and find the limit. limx22/x1x2 Problem 17E: For Exercises 423, use algebra to simplify the expression and find the limit. limt31/t1/3t3 Problem 18E: For Exercises 423, use algebra to simplify the expression and find the limit. limt01/(t+1)1t Problem 19E: For Exercises 423, use algebra to simplify the expression and find the limit. limh01/(4+h)1/4h Problem 20E: For Exercises 423, use algebra to simplify the expression and find the limit. limz0z1z1 Problem 21E: For Exercises 423, use algebra to simplify the expression and find the limit. limh09+h3h Problem 22E: For Exercises 423, use algebra to simplify the expression and find the limit. limx04x12x1 Problem 23E: For Exercises 423, use algebra to simplify the expression and find the limit. limh0(1+h)41h Problem 24E: In Exercises 2426, for the given constant c and functions f(x) and g(x), answer the following: (a)... Problem 25E: In Exercises 2426, for the given constant c and functions f(x) and g(x), answer the following: (a)... Problem 26E: In Exercises 2426, for the given constant c and functions f(x) and g(x), answer the following: (a)... Problem 27E: In Exercises 2734, use algebra to evaluate the limit. limz5z2+2z+12z3z2+9 Problem 28E: In Exercises 2734, use algebra to evaluate the limit. limxx+7x2113x22x Problem 29E: In Exercises 2734, use algebra to evaluate the limit. limt4et+3et5et+2e Problem 30E: In Exercises 2734, use algebra to evaluate the limit. limx2x+13x1 Problem 31E: In Exercises 2734, use algebra to evaluate the limit. limx23x+23x+3 Problem 32E: In Exercises 2734, use algebra to evaluate the limit. limxxex Problem 33E: In Exercises 2734, use algebra to evaluate the limit. limt(4et)(7et) Problem 34E: In Exercises 2734, use algebra to evaluate the limit. limtt2sint Problem 35E: Find limx1f(x) if, for all x, 4x + 6 f(x) x2 2x + 7. Problem 36E: Find limx0f(x) if, for all x, 4 cos(2x) f(x) 3x2 + 4. Problem 37E: Find limxf(x) if, for x 0, 4x25x2f(x)4x6+3x6 Problem 38E: In Problems 3849, find all values for the constant k such that the limit exists. limx4x2k2x4 Problem 39E: In Problems 3849, find all values for the constant k such that the limit exists. limx1x2kx+4x1 Problem 40E: In Problems 3849, find all values for the constant k such that the limit exists. limx2x2+4x+kx+2 Problem 41E: In Problems 3849, find all values for the constant k such that the limit exists. limx5x2kx+5x22x15 Problem 42E: In Problems 3849, find all values for the constant k such that the limit exists. limx0ek+2x8ex1 Problem 43E: In Problems 3849, find all values for the constant k such that the limit exists. limx1k240x9lnx Problem 44E: In Problems 3849, find all values for the constant k such that the limit exists. limxx2+3x+54x+1+xk Problem 45E: In Problems 3849, find all values for the constant k such that the limit exists. limxe2x5ekx+3 Problem 46E: In Problems 3849, find all values for the constant k such that the limit exists. limxx36xk+3 Problem 47E: In Problems 3849, find all values for the constant k such that the limit exists. limxekx+11e5x3 Problem 48E: In Problems 3849, find all values for the constant k such that the limit exists. limx3kx+632x+4 Problem 49E: In Problems 3849, find all values for the constant k such that the limit exists. limx3kx+632x+4 Problem 50E: In Problems 5055, use the indicated new variable to evaluate the limit. limy4y2y4,lett=y Problem 51E: In Problems 5055, use the indicated new variable to evaluate the limit. limx9xx6x3,lett=x Problem 52E: In Problems 5055, use the indicated new variable to evaluate the limit. limh01+h1h,lett=1+h Problem 53E: In Problems 5055, use the indicated new variable to evaluate the limit. limx1x13x1,lett=x3 Problem 54E: In Problems 5055, use the indicated new variable to evaluate the limit. limx0e3xe2xex1,lett=ex Problem 55E: In Problems 5055, use the indicated new variable to evaluate the limit. limx2e3x15e3x+ex+1,lett=ex Problem 56E: Use the Squeeze Theorem to prove limxsinxx=0. Problem 57E: Use the Squeeze Theorem to prove limx1x+ex=0. Problem 58E: In Problems 5861, use the Squeeze Theorem to calculate the limit. limxcos2x2x+1 Problem 59E: In Problems 5861, use the Squeeze Theorem to calculate the limit. limx0x4sin(1/x) Problem 60E: In Problems 5861, use the Squeeze Theorem to calculate the limit. limxxx3+1 Problem 61E: In Problems 5861, use the Squeeze Theorem to calculate the limit. limx1x+2cos2x Problem 62E: Let limxf(x)=0 and limxg(x)=0. Give possible formulas for f(x) and g(x) if... Problem 63E: In Problems 6366, for the given constant c and function f(x), find a function g(x) that has a hole... Problem 64E: In Problems 6366, for the given constant c and function f(x), find a function g(x) that has a hole... Problem 65E: In Problems 6366, for the given constant c and function f(x), find a function g(x) that has a hole... Problem 66E: In Problems 6366, for the given constant c and function f(x), find a function g(x) that has a hole... Problem 67E: In Problems 6772, for the given m and n, evaluate limx1f(x) or explain why it does not exist, where... Problem 68E: In Problems 6772, for the given m and n, evaluate limx1f(x) or explain why it does not exist, where... Problem 69E: In Problems 6772, for the given m and n, evaluate limx1f(x) or explain why it does not exist, where... Problem 70E: In Problems 6772, for the given m and n, evaluate limx1f(x) or explain why it does not exist, where... Problem 71E: In Problems 6772, for the given m and n, evaluate limx1f(x) or explain why it does not exist, where... Problem 72E: In Problems 6772, for the given m and n, evaluate limx1f(x) or explain why it does not exist, where... Problem 73E: For any f(x), where 1xf(x)1x, find values of c, and L for which the Squeeze Theorem can be applied. Problem 74E: In Problems 7475, explain what is wrong with the statement. If f(x)=x21x+1andg(x)=x1,thenf=g. Problem 75E: In Problems 7475, explain what is wrong with the statement. If f(1) = 0 and g(1) = 1, then... Problem 76E: Are the statements in Problems 7683 true or false? Explain. If b(x)f(x)a(x) and... Problem 77E: Are the statements in Problems 7683 true or false? Explain. If 0f(x)a(x) and limx0a(x)=0, then... Problem 78E: Are the statements in Problems 7683 true or false? Explain. If b(x)f(x)a(x) and limx0b(x)=limx0f(x),... Problem 79E: Are the statements in Problems 7683 true or false? Explain. If limx0g(x)=0thenlimx0f(x)g(x)=. Problem 80E: Are the statements in Problems 7683 true or false? Explain. If... Problem 81E: Are the statements in Problems 7683 true or false? Explain. If... Problem 82E: Are the statements in Problems 7683 true or false? Explain. If... Problem 83E: Are the statements in Problems 7683 true or false? Explain. If... format_list_bulleted