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Suppose that f is a function with lim f(x)=b (where b is a constant). Which of the following must be true? Select all that apply. The graph of f will never cross the line y=b. . The graph of f crosses the line y= b at most once. The line y =b is a horizontal asymptote of f. f has a vertical asymptote at x =b . The values of f get infinitely large as x approaches b . n / ( - ) =6. lim f(x) =b . x= =00In x Where does the function / (x) = have a vertical asymptote? X+5 O At 1=-5. O At x=1. ON XEO. O At XEe. Of has no vertical asymptotes.Let f(x) = x2 Which of the following is true? lim f(x) + lim f(x) x-0 x+07 lim f(x) = co X-0 O lim f(x) = 0 x-0 O lim f(x) = =00 X+0 O lim f(x) = f(0) x-05x Which lines are horizontal asymptotes of y= V9x2+4 Choose all that apply. V= 0 VComplete the following sentence: The equation of the tangent line to the curve y=2vx+1 at *= = 15 YEmix+b , where m= and bu (You answers should be integers or reduced fractions.)In a controlled experiment, yeast cells are grown and the number C of yeast cells present after / hours is calculated. It is found that C()= +1+1 . At what rate (In number of cells per hour) is the number of cells changing at 1=10-hours? ( Your answer should be an integer.)For each statement, explain why it must be true, or use an example to show that it can be false. . If y= f(x) has a horizontal tangent line at x = 1 then y=g(x) , where a(x)= /(x-1)+1 , has a horizontal tangent line at x=2. . A tangent line always has exactly one point in common with the graph of the function.Suppose the curve y= / (x) has a tangent line y=4x-5 at x=1 . Consider the function g(x)=2/(x)+x+1. What is the slope of the tangent line to g() at x=1 ? (Your answer should be an integer.)For which value(s) of a does the curve y= x tax +2 have a horizontal tangent line at x=1 ? Show your work. Do not use any differentiation rules