If f(x) is continuous false 2. Assume that f(t) is continuous on [1,5] and that f(1) = 20, f(5) = 100. Determine statements is always true, never true, or sometimes true. (a) f(c) = 3 has a solution with c € [1, 5]. Never Truz Sometimes true (b) f(c) = 75 has a solution with c E [1,5]. Always true (e) f(c) = 50 has no solution with c E [1, 5]. Never true (d) f(c) = 30 has exactly one solution with c E [1,5]. Sometimes true 3. Use the IVT to show that f(x) = x³ + x takes on the value 9 for some x in [1, 2]. 4. Show that cos x = x has a solution in the interval [0, 1]. Hint: Show that f(x) = x - cosa ha 5. Use the IVT to find an interval of length containing a root of f(x) = x³ + 2x +1. 6. Prove using the IVT. (i) √c+√c+2=3 has a solution. (ii) 2 = bx has a solution if b> 2. (iii) 2 + 3 = 4* has a solution. (iv) tan x= x has infinitely many solutions. 7. Find an interval of length in [1, 2] containing a root of the equation x7 + 3x - 10 = 0 Holy Cross 8. Evaluate lim 818 9. Evaluate lim H-X sin x I x² + x 3-x 10. Evaluate lim x²-x 818 12. Evaluate lim 11. Evaluate lim √x²+x-x H48 1+3x x+∞ √√2x²+x