Examples. Justify your answers briefly. (a) Let A be the family of functions defined everywhere on R so that lim f(x) converges. Show that A is an algebra of functions. x→∞
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- a. What is the domain of f? Express your answer in interval notation. f(x)= 1 - x^4 / x^2 - 1 b. Use a sequence of values of x near a=1 to estimate the value of limx→1 f(x). The sequence should include values such as 1.01, 1.001, etc. c. Use algebra to simplify the expression 1 - x^4 / x^2 - 1 d. True or false: f(1)=-2 e. Based on all of your work above, construct an accurate, labeled graph of y=f(x) on the interval [0,2].Given lim (4x-3) as x approaches 1. Use the definition of a limt to find a number delta such that the absolute value of x-a is less than delta when the absolute value of f(x)-L is less than 0.08Movie expenditures, in billions of dollars, on advertising in a certain format from 1995 to 2004 can be approximated by f(t) = 0.04t + 0.33 if t ≤ 4 −0.01t + 1.5 if t > 4, where t is time in years since 1995. (a) Compute lim t→4− f(t). (If an answer does not exist, enter DNE.) Interpret the answer. Shortly 1999 (t = 4), annual advertising expenditures were close to $ billion. Compute lim t→4+ f(t). (If an answer does not exist, enter DNE.) Interpret the answer. Shortly 1999 (t = 4), annual advertising expenditures were close to $ billion. (b) Is the function f continuous at t = 4? YesNo What does the answer tell you about movie advertising expenditures? Movie advertising expenditures in 1999.
- Find the limit Lim(x,y) - (3,4) x+y/ x^2+y^2-25 Note: This is a Calculus 3 question5)Suppose ….. Fill in the blanks below. (Note that it is common to say a limit "has a value of" o if the function output increases without bound or - ∞ if the output decreases without bound. Use that notation in this question.) Solve this question by hand without using any tools (no graphing tools).True or False. If a statement below must always be true, write True and give the brief justification . Otherwise, write False, and give an example in which the statement is not true. Your example may be a graph. a. If lim x->a+ f(x)= lim x->a- f(x), then f(x) is continuous at x=a b. If f(2) = 6 and f"(2)= 8, then f(x) is increasing at x=2
- a)Find the domain of the function f and graph the domain of f. b) Show that lim (x,y) —>(0,1) f (x, y) cannot be found.. f (x) = x^2 +2 x<3 10 x=3 -3+4x x>3 1. At what value is this function discontinuous, if any? What is the lim f (x) 3 ? What is the lim f (x) 1? d. What is the value of f (4) ?The graph of the function f is shown above. Which of the following statements is true? A) f is discontinuous at x = 0 because limx→0 f(x) does not exist. B) f is discontinuous at x = 3 because limx→3 f(x) ≠ f(3) C) f is discontinuous at x = 5 because limx→(5−) f(x) does not exist. D) f is discontinuous at x = 6 because limx→(6−) f′(x) ≠ limx→(6+) f′(x) Thank you
- Referring to the graph of a function f given below, nd each limit. Evaluate the limit. lim x!1+ x2f(f(x)) (b) Evaluate the limit. lim xx2 + f(f(x))Fast pls solve this question correctly in 5 min pls i need urgently pls solve Nid Create a table of values for the function and use the result to estimate the limit, lim x-4 [1/(x+1)]-(1/5)/x-4[3 - x x 2 let fx)=+1 a) Find lim fx) and lim f) X-2 X-2+ exist? why? Sx) b) Dose lim X2