Limits and Continuity Questions

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Limits and Continuity Solutions

What is the limit statement for this relationship, using correct notation? (x approaches 2 from the left) ---> <---(x approaches 2 from the right) x 1.5 1.75 1.9 1.99 1.999 2 2.001 2.01 2.1 2.25 2.5 f(x) 3.5 3.75 3.9 3.99 3.999 4.001 4.01 4.1 4.25 4.5 a. f(x) = lim 4 x->2 b. lim f(x) = 2 x->4 c. lim f(x) = 4 x->2 d. lim 2 = f(x) x->4 Process/Explanation

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Limits and Continuity Solutions

For a continuous and differentiable function f given, selected values of the function and its derivatives at x = 4 are given in the table below. X X f(x) f'(x) C f"(x) f 4 2 0 6 In evaluating the limit, lim f(x) – 2 (x – 4)3 x +4 3 ...which of the following statements is true?

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Limits and Continuity Solutions

Question 6 1 pts Use the graph to evaluate the indicated limit or function value or state that it does not exist. Find lim f(x) and f(0). x-0 3 2 1 -3 -2 1 2 3 4. 10 -2- -3- Does not exist: 1 0 -1; 1 O 1:1 Does not exist: does not exist

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Limits and Continuity Solutions

Let an be the sequence 2.7, 2.71, 2.718, ... , that you obtain by terminating the number e after n decimal places. What is lim an? n-00 M Choose the correct answer below. O A. lim an exists but cannot be determined precisely. n-00 OB lim anse n-00 OC. lim an could converge to more than one number. n+00 OD. lim an does not exist because the terms of the sequence, an, do not approach 0. n-00

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Limits and Continuity Solutions

The toll T charged for driving on a certain stretch of a toll road is $4 except during rush hours (between 7 a.m. and 10 a.m. and between 4 p.m. and 7 p.m.) when the toll is $6. (a) Sketch a graph of T as a function of the time t, measured in hours past midnight. T T T T 6 owly 7 t 24 10 16 19 t t 24 7 o 7 10 7. 16 19 10 16 19 16 19 10 24 24 (b) Discuss the discontinuities of of this function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

Math

Limits and Continuity Solutions

12. (0.12/0.5 Points] DETAILS PREVIOUS ANSWERS SCALCET9 2.5.041. Show that f is continuous on (-00,00). f(x) - { ſ1 - x2 if x S 1 In(x) if x > 1 On the interval (-0, 1), f is a polynomial function; therefore f is continuous on (-00, 1). On the interval (1, 0), f is a logarithmic function; therefore f is continuous on (1, 0). At x = 1, lim f(x) = lim x-1 x-1 D- and lim f(x) = lim 1)- xtit x+1+ so lim f(x) = x1 Also, f(1) = Thus, f is continuous at x = 1. We conclude that f is continuous on (-0,co).

Math

Limits and Continuity Solutions

Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. p(v) = 5402 + 5, = a = 1 lim p(v) V +1 V1 lim 5 4v2 + 5 5 lim V 4v2 + 5 by the Constant Multiple Law V1 = 5 lim (4v2 + 5 by the Sum Law X V1 = 5 lim V1 + lim 5 V1 by the Difference Law X (4v2) + (12) + 5 4 lim V1 + lim 5 V1 by the Constant Multiple Law 5/4 (1) + 5 + by the Direct Substitution Property v Find p(1) P(1) = Thus, by the definition of continuity, p is continuous at a = 1.

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Limits and Continuity Solutions

2. [-70.5 Points] DETAILS SCALCET9 2.5.005. The graph of a function f is given. (Enter your answers as comma-separated lists.) 0 1 (a) At what numbers a does lim f(x) not exist? xa a = (b) At what numbers a is f not continuous? a = (c) At what numbers a does lim f(x) exist but f is not continuous at a? X-a a =

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Limits and Continuity Solutions

Consider the following table. 2.999 3.0001 2.9 1.789 f(x) g(x) h(x) 2.99 1.889 2.9 11.89 1.998 2.9 34.65 3 undefined 0 3. 001 1.886 2.9 22.1 1.997 2.9 51.23 2.9 3.01 1.845 2.9 10.34 9 3 Which of the following statements are reasonable conclusions? I. lim f(x) does not exist. x 3 II. lim g(x) = 0 X X->3 III. lim f(x) = 2 = x +3 IV. lim h(x) # lim h(2) + x x3 x+3+

Math

Limits and Continuity Solutions

Find the limits (that is, end behaviors) below. If an answer should be oo, then enter INFINITY (Similarly, enter - INFINITY for -00) 20(2? + 6) (a) As I > Q0 help (limits) 3 + 3.24 (b) ASX > -00, 12(x + 5)(2 – 6) -9 + 4.23 help (limits

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Limits and Continuity Solutions

3 2 -1 0 3 4 5 Created for Albert.io Copyright 2018 All Rights Reserved The function shown has a vertical tangent line at x = 4. At which values in the interval (0,5) is the function continuous but not differentiable? X =

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Limits and Continuity Solutions

* Ex. 4. Examine existence of the double integral and iterated integrals of the given function over the given set R, and prove your conclusion. (6) g(x,y) - Leshrane sin(1) sin(1) if xy +0, if xy = 0, R= = (0,1) > (0, 1). x =