2 *3 X3 6. Consider a function y = f(x) such that lim f(x) = 2, lim f(x) = 2, and f(3) = -1. Explain whether each statement is true or false. a) y=f(x) is continuous at x = 3. b) The limit of f(x) as x approaches 3 does not exist. c) The value of the left-hand limit is 2. d) The value of the right-hand limit is -1. e) When x = 3, the y-value of the function...
1. Determine whether the statement is true or false. If false, explain why and correct the statement (T/FIf)exists, then lim ()f) o( T / F ) If f is continuous, then lim f(x) = f(r) (TFo)-L, then lim f(x)- lim F(x) "( T / F ) If lim -f(x)s lim. f(x) L, then lim f(x)s 1. "(T/F) lim. In x -oo . (T/F) lim0 ·(T / F ) The derivative f' (a) is the instantaneous rate of change of y...
1. Find lim f(x) and lim f(x) for each of the following. Assign oo or - where appropriate: (a) f(z)=42 -2 (b) f(x)= 3r-2 (e) f(1)--5rt6 (x - 2)2 2. Find each of the f limits, assigning oo or-o where appropriate x+2z-1 (b)lm 3r-2 3 r-2 (c) li 42+1 (k) im (2r V4r2-8r 3) 15r-2 3. Find the horizontal and vertical asymptotes of each of the following functions 4. Sketch the graph of each of the following functions and determine,...
Use the graph to answer these questions. 10- a. Find lim f(x) and lim f(x). x-4 X-4 b. Find lim f(x) c. Find f(4) d. Is f(x) continuous at x = 4? Why or why not? y = f(x) 0 10
3. Given that lim f(x) = 4 and lim f(x) = -4, what is true about lim f(x)? x-1 4. Given that lim f(x) = 1, lim f(x) = 1, and f(-3) = 1, what is true about lim f(x)? 5. Given that lim f(x) = 0, lim f(x) = 0, and f(2) = 3, what is true about limf(x)? X-3 X-3 X-2
Use the graph to find the following imits. 6- a. lim f(x)b. lim f(x) x-3 4 2 a. Find f(x) or state that it doesn't exist. Select the correct choice below and fill in any answer boxes lim x→-3 in your choice. -4 -2 OA. f(x)= lim (Type an integer.) O B. The limit does not exist. b. Find lim f(x) or state that it doesn't exist. Select the correct choice below and fill in any answer boxes x→-1 in...
Use the graph below to determine whether the statements about the function y=f(x) are true or false. Ay 10- 8- 6 -10 -8 -6 -4 -2 2 8 10 True or false; lim f(x)= 9. X-3+ O True O False True or false: lim f(x) = 3. X-0- O True O False True or false: lim f(x) = lim f(x). X-0 X0- O True False True or false: lim f(x) exists. x0 0 True 0 False True or false: lim...
funct (b) Use the graph of f(x) to answer the questions that follow: 10+ i. lim f(x) lim /(x) = lim f(x) = f(-2) - ii. Is f(x) continuous at -2? Explain briefly. $(2) = iii. lim (3) - lim f(x) = lim /(r) - iv. Is (1) continuous at : = 2? Explain briefly wolle v. List all intervals on which f(x) is continuous
Sketch the graph of f(x) given the following: lim f(x) = 2 f(-1) =1 f(1) =1 lim f(x) = DNE 1--1 -> A function f is continuous at a number a if lim y(x) = f(a) ca requires the following 3 things:
True or False If f is differentiable everywhere and f^′(x)<0 for all x, then lim x→∞ f(x)= −∞