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1. Which of the following is a necessary and sufficient condition for a function, f, to be continuous at the point c = 4? O lim f (I) does not exist. O lim f (z) = f(4). O f is defined on an open interval that contains a = 4. O lim f (z) exists. 2. Consider the function: f(z) 12 - 1 - 1 Which of the conditions of continuity are not met by f (x) at x = 1? O f (1) must be defined. O lim f(z) must exist. O lim f(x) = f(1). 3. Let f (z) = 12 - 9 I - 3 Is f (I) continuous at I = 3? O No, f (I) is not continuous at I = 3. Yes, f (z) is continuous at I = 3. 4. Suppose f(I) = 12 - 4x+3 12 - 51 + 6 Which statement describes the continuity of f (I) at a = 3? O f is continuous at I = 3. O f has a removable discontinuity at I = 3. Of has a jump (nonremovable) discontinuity at a = 3. f has an infinite discontinuity at i = 3. 5. Suppose f (I)= I+ 7, 1>0 Which statement describes the continuity of f at a = 0? O f is continuous at I = 0. O f has a removable discontinuity at I = 0. O f has a jump (nonremovable) discontinuity at I = 0. O f has an infinite discontinuity at a = 0. 6. Let f (i) = = + 2 for # -2 and f (I) = 1 for I = -2. Explain why the function is discontinuous at -2. Of(-2) is not defined O f(-2) is defined, but lim, f(I) does not exist. O f(-2) and lim, f (i) are both defined, but lim, f(z) # f(-2). O lim f (z) and lim, f (z) are both defined, but lim f(z) + lim f(I) 7. Let f(x) = sin(z) if z > T/4. Explain why the function is continuous on (-0o, co). O f is continuous on (-00, oo) because both sin(I) and cos(I) are continuous on (-00, oo), and the sum of continuous functions is continuous. f is continuous on (-oo, oo) because both sin(z) and cos(z) are continuous on (-00, oo), and the composition of continuous functions is continuous. f is continuous on (-00, oo) because both sin(I) and cos(I) are continuous on (-0o, oo), and sin(I) = cos(z) when I = TT /4. O f is continuous on (-00, oo) because both sin(z) and cos(z) are continuous on (-00, oo), and sin(z) 4 Find the values of m and b that make f (I) differentiable. O m = 8,b= -28 O m =8,b= -16 O m = 4,b= -12 O m = 4,b=0 9. Find the derivative of the function using the definition of derivative. g(t) = Preview will appear here... Enter math expression here 10. Find the derivative of the function using the definition of the derivative. k(I) =1-12 Enter the expression for the derivative only, not k'(x) =. Preview will appear here... Enter math expression here. Find the horizontal asymptote(s) of 3x + 4x 212 - 1 Select all of the options below that are horizontal asymptotes. No horizontal asymptote exists Dy= 2 Oy=0 . Find the horizontal asymptote(s) of f(z) - 212 +2 select all of the options below that are horizontal asymptotes Oy=0 O y= O f(z) has no horizontal asymptotes. 3. Find the horizontal asymptote(s) of f(z) = 3x + 2. Select all of the options below that are horizontal asymptotes. Of(z) has no horizontal asymptote. Oy=2 Dy=3 . Find the limit. If the limit is not a whole number, enter it as a decimal. Enter "+infinity" for +0o and "-infinity" for -00. Enter "DNE" if the limit does not exist and is not infinite. Do not use any spaces in your answer. t-tvt 18 2+3/2 + 2t - 5 Enter answer here . Find the limit. If the limit is not a whole number, enter it as a decimal. Enter "+infinity" for +00 and "-infinity" for -00. Enter "DNE" if the limit does not exist and is not infinite. Do not use any spaces in your answer. lim Vil + 1 Enter answer here S. Find the limit. mit is not a whole number, enter it as a decim. is not infinite. Do not use any spaces in your answer. lim ez + cos (2) Enter answer here 7. The function g(I) is graphed below. Find lim 9(z). If the limit is not a whole number, enter it as a decimal. Enter use any spaces in your answer. 8. The function g(I) is graphed below. Find lim g(z). If the limit is not a whole number, enter it as a decimal. Enter "+infinity" for too an use any spaces in your answer. Enter answer here . The function g(I) is graphed below. Find all vertical asymptotes of g. Oy= -1 The function has no vertical asymptotes. O y=2 O z = -1 O z=0 Dy=0 0 1 = 10. The function g(I) is graphed below. Find all horizontal asymptotes of g. O z =2 O y = 2 O z=0 O z=-1 D y=0 O y= -1 The function has no horizontal asymptotes.1. Suppose that lim f (x) = 32, lim g(x) = 68, and lim h(I) = 10. z-+a I-+a Then lim f(z) + g(I) h(I) is equal to which of the following? O 1 The limit is undefined. The limit cannot be determined from the given function. Of(a) + g(a) h(a) 2. Gary is simplifying the expression for a function f (I). What is wrong with his work? f(I) = 12 - 5x + 6 3x - 6 f(z) = 2-2)(2-3) 3x - 6 (I - 2)(1 -3) 3(I - 2) Therefore, Gary concludes, f (I) = I - 3 3 He factored incorrectly. There is nothing wrong with his work. The factors of (I - 2) cannot be canceled from the fraction. Gary has to note that I cannot equal 2 using his simplified expression. 3. f(I) = (212 - 4x - 8)6 Find lim f(I). Enter answer here 4. Evaluate the limit, if it exists. If your answer is not a whole number, enter it as a decimal. If the limit does not exist, enter "DNE" lim vu4 + 3u + 6 12 Enter answer here 5. Evaluate the limit, if it exists. If your answer is not a whole number, enter it as a decimal. If the limit does not exist, enter "DNE" 2x + 12 2 6 1 + 6 Enter answer here 6. True or False? If -12 + 4x - 3