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1. Consider the function -F5 sin(r) for r f(x) =2 for 1< 3 2-25 for 3...
clear explanation . tks (thumb) In this question you must state if you sandwich theorem. You do not need to justify usi...
clear explanation . tks (thumb)
In this question you must state if you sandwich theorem. You do not need to justify using limit laws. use any standard limits, continuity, l'Hôpital's rule or the C (a) Find the following limits if they exist 2 5 3x13 (i) lim x-o0 213 +9-1' (cosech r (ii) lim т-0L 2 COS (b) Let a, bE R be two arbitrary constants and consider the function for 1 2 — sech (аx —1) f(ar) 1 for...
(0, 1) given by f (x) - sin (). Is f Let f b e the...
(0, 1) given by f (x) - sin (). Is f Let f b e the function t on the domain uniformly continuous? Explain. (You may take it as given that sin is a continuous function) Suppose that f [0, oo) -R is a continuous function, and suppose also that lim, ->oo f (x)- 0. Prove that f is uniformly continuous Just to be clear: to say that lim,->o f (x) - 0 means that
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x D...
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x Discuss the continuity of the functions given in problem #2 above. Also, determine (using the limit concept) if the discontinuities of these functions are removable or nonremovable 3. Find the value of the constant k (using...
2. [1 mark] Calculate the limit of the vector valued function f: ACRY-R lim G logy)...
2. [1 mark] Calculate the limit of the vector valued function f: ACRY-R lim G logy) 3. Consider the function :R? - R. given by Flv = 0 if if (,y) (0,0): (x,y) -(0,0) (a) (1 mark] State the definition of continuity of a function at the point. (1 mark] Then calculating the limit (by any technique of your choice) show that f is continuous at (0,0). (b) [2 marks] Find the partial derivatives and at (x,y) + (0,0). and...
2 *3 X3 6. Consider a function y = f(x) such that lim f(x) = 2,...
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...
f(x, y) = y/(sqrt(z? + y2) + x) Evaluate the limits below, if they exist. If the limit does not exist, explain why it d...
f(x, y) = y/(sqrt(z? + y2) + x) Evaluate the limits below, if they exist. If the limit does not exist, explain why it does not exist Yon musi elearly staie if you ity, lopital's rle or the sandwch theorem in your working. You do not need to justify using limit laws. (i) lim f(x, y) (ii) im f(r, y (iv) zlin2-1.0 arctan ^Ca.v)l
f(x, y) = y/(sqrt(z? + y2) + x)
Evaluate the limits below, if they exist. If...
Real analysis 10 11 12 13 please (r 2 4.1 Limit of Function 129 se f: E → R, p is a limit point of E, and li...
Real analysis
10 11 12 13 please
(r 2 4.1 Limit of Function 129 se f: E → R, p is a limit point of E, and limf(x)-L. Prove that lim)ILI. h If, in addition, )o for all x E E, prove that lim b. Prove that lim (f(x))"-L" for each n E N. ethe limit theorems, examples, and previous exercises to find each of the following limits. State which theo- rems, examples, or exercises are used in each case....
1. Find lim f(x) and lim f(x) for each of the following. Assign oo or -...
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,...
Obtain graphical and numerical evidence concerning the existence of the questions below
math 171 calculus projects 1, can you please help with the math questions 1,2, and 3 they have been attached below.MATH 171 - CALCULUS IPROJECT lNote: Make sure to show all supporting work to receive full credit. Your answers should be stated in the context of the problem and include appropriate units where applicable.1. Obtain graphical and numerical evidence concerning the existence of \(\lim _{x \rightarrow 0} \frac{50 x^{2}}{\sin x+50 x^{2}} .\) You must provide:- A graph using a window...
Evaluate the following limits. If you use L'Hopital's Rule, indicate on your paper that you have...
Evaluate the following limits. If you use L'Hopital's Rule, indicate on your paper that you have done so. If a limit is oo or - 0, then write oo or -oo. You may write DNE for does not exist. x² – 1 a.) lim Preview 7+1 In 4.q7 = - b.) lim 1+ I-4 2 – 3. - 4 Preview et -1 c.) lim 1+0 - sin(4x) Preview d.) limsin 4x = Preview Preview
clear explanation . tks (thumb)
In this question you must state if you sandwich theorem. You do not need to justify using limit laws. use any standard limits, continuity, l'Hôpital's rule or the C (a) Find the following limits if they exist 2 5 3x13 (i) lim x-o0 213 +9-1' (cosech r (ii) lim т-0L 2 COS (b) Let a, bE R be two arbitrary constants and consider the function for 1 2 — sech (аx —1) f(ar) 1 for...
(0, 1) given by f (x) - sin (). Is f Let f b e the function t on the domain uniformly continuous? Explain. (You may take it as given that sin is a continuous function) Suppose that f [0, oo) -R is a continuous function, and suppose also that lim, ->oo f (x)- 0. Prove that f is uniformly continuous Just to be clear: to say that lim,->o f (x) - 0 means that
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x Discuss the continuity of the functions given in problem #2 above. Also, determine (using the limit concept) if the discontinuities of these functions are removable or nonremovable 3. Find the value of the constant k (using...
2. [1 mark] Calculate the limit of the vector valued function f: ACRY-R lim G logy) 3. Consider the function :R? - R. given by Flv = 0 if if (,y) (0,0): (x,y) -(0,0) (a) (1 mark] State the definition of continuity of a function at the point. (1 mark] Then calculating the limit (by any technique of your choice) show that f is continuous at (0,0). (b) [2 marks] Find the partial derivatives and at (x,y) + (0,0). and...
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...
f(x, y) = y/(sqrt(z? + y2) + x) Evaluate the limits below, if they exist. If the limit does not exist, explain why it does not exist Yon musi elearly staie if you ity, lopital's rle or the sandwch theorem in your working. You do not need to justify using limit laws. (i) lim f(x, y) (ii) im f(r, y (iv) zlin2-1.0 arctan ^Ca.v)l
f(x, y) = y/(sqrt(z? + y2) + x)
Evaluate the limits below, if they exist. If...
Real analysis
10 11 12 13 please
(r 2 4.1 Limit of Function 129 se f: E → R, p is a limit point of E, and limf(x)-L. Prove that lim)ILI. h If, in addition, )o for all x E E, prove that lim b. Prove that lim (f(x))"-L" for each n E N. ethe limit theorems, examples, and previous exercises to find each of the following limits. State which theo- rems, examples, or exercises are used in each case....
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,...
Evaluate the following limits. If you use L'Hopital's Rule, indicate on your paper that you have done so. If a limit is oo or - 0, then write oo or -oo. You may write DNE for does not exist. x² – 1 a.) lim Preview 7+1 In 4.q7 = - b.) lim 1+ I-4 2 – 3. - 4 Preview et -1 c.) lim 1+0 - sin(4x) Preview d.) limsin 4x = Preview Preview
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