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Answer: option 3
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"Mx Letf: R-> R be a differentiable function and f(15)-2. Then the value of lim x...
It is known that f :(0,2) + R is a differentiable function such that \f'(x) < 5 for all x € (0,2). Now let bn := f(2 – †) for all n € N. Prove that this is a Cauchy sequence.
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...
2. Let f: R R be a continuous function. Suppose that f is differentiable on R\{0} and that there exists an L e R such that lim,of,(z) = L. Prove that f is differentiable at 1-0 with f,(0) = L. (Hint: Use the definition of derivative and then use mean value theorem) 2. Let f: R R be a continuous function. Suppose that f is differentiable on R\{0} and that there exists an L e R such that lim,of,(z) =...
It is known that f :(0,2) + R is a differentiable function such that \f'(x) < 5 for all x € (0,2). Now let bn := f(2 – †) for all n € N. Prove that this is a Cauchy sequence.
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...
2. For the function f(x)= (2x² – 3, x>2 19-2x, x<2 find the limits or explain why they do not exist. (a) lim f(x) 1-2+ (b) lim f(x) (e) lim f(x) X2
Determine lim f(x) and lim f(x) for the following function. Then give the horizontal asymptotes of f, if any. X-00 --00 2x 6x + 2 Evaluate lim f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. X-00 A. 2x lim x-00 6x + 2 (Simplify your answer.) O B. The limit does not exist and is neither o nor -0.
For the function shown in the graph, find the indicated function value and limit. Find f(2) and lim f(x). O A. 1;3 OB. 1; does not exist OC. 1:1 OD. Does not exist does not exist For the function shown in the graph, find the indicated function value and limit. Find f(2) and lim f(x). X2 10 -10-8 -4.53 12 4 6 8 10
Determine lim f(x) and lim f(x) for the following function. Then give the horizontal asymptotes of f, if any. 2x 12x + 2 Evaluate lim f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. X100 OA. lim X-00 2x 12x + 2 (Simplify your answer.) OB. The limit does not exist and is neither oo nor - 00. Evaluate lim f(x). Select the correct choice below and, if necessary, fill in...
Is the function given by f(x) = continuous at x = 5? Why or why not? 5x+2, for x 55, 5* 5x - 18, for x>5, Choose the correct answer below. O A. The given function is continuous at x = 5 because the limit is 3. OB. The given function is continuous at x = 5 because lim f(x) does not exist. X-5 OC. The given function is not continuous at x = 5 because f(5) does not exist....