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Real Analysis

Finding Limits from a Table of Values

Estimate the value of the limit by filling out a table and then making an educated guess about the tendency of the numbers. Then graph the lim of tanx///x as x approaches 0 to verify own conclusion lim of tanx///x as x approaches o table should be 2 colums with the headings |x|tanx/x|

Function of Limits

The function has a limit as f(x) = (1/x) + 3 has a limit of L=3 as x approaches x. This means that if x is sufficiently large (that is if x > N for some number N), the values of f(x) are closer to L=3 than a number epsilon > 0. a) Sketch the graph y=(1/x) +3 and a horizontal strip of points (x,y) such that (if y

Finding Algebraic Limits

Use algebra and limits to find the limits: a) lim of x+1/x-2 as x approaches +infinity b) lim of x^2+1/x^2 - 5 as x approaches -infinity c) lim of x^2+1/x^3 - 2 as x approaches + infinity d) lim of x^3+1/x^2 + 2 as x approaches - infinity check answers by graphing the functions

Evaluating Limits by Graphing

Graph the appropriate functions (first try by hand and then verify your sketches with a grapher and then determine the limits. a) lim of lx as x approaches 0+ b) lim of 1/x as x approaches 0+ c)lim of ln 1/x as x approaches 0- d)lim of 1/x as x approaches 0 e)lim of 1/ x^2 as x approaches 0+ f)lim of -1/ x^2 as x approac

Limits and Continuous Functions

Sketch by hand the graph of F that satisfies: (a) f(0) is not defined, (b) lim as x approaches 0 from left of f(x) does not exist and (c) lim as x approaches 0 from right f(x)=2. is the function f(x)continuous from the left at x = 0? Is the function f(x) continuous at x=0 from the right? is the function f(x) continuous at x = 0

Evaluating Limits

Use limit laws to find the limits lim as x approaches 7 lim of square root (x) - square root (7)/x-7

Evaluating Limits as they Approach Values

Find the limits: a)lim as x approaches zero from left of 2x b)lim as x approaches 3 from righ of 2x of x c)lim as x approaches 3 from right of 5 d)lim as x approaches -1 from left of|x-2|

Limits

Find lim as x approaches-1 from the left of f(X). find lim as x approaches-1 from the right of f(X). Are these limits the same? What can you say about find lim as x approaches 1 of f(X)?

Investigating Limits

Estimate the value of the lim as x approaches zero of cosx/x, if it exists, by filling out a table and than making an educated guess about thr tendency of the numbers. The first row in the table should start like this: X|cosx|x, with approximately 6 more values added for both x and cox/x Then graph y=cos/x to verify your

Find the Limits

What is the limit as x approaches infinity of 4x^2 / (2x^3 - 3x + 6)? Is it 0? What is the limit as x approaches -4 of (x^2 -16)/(x+4)? I got -8.

Real analysis question with collection of subsets

I have a problem deal with the subject of real analysis and it is about the collection of subsets. I hope someone can help me with detail explanation. See attached file for full problem description.

Real Analysis : Countability

1. Show that the set of infinite sequences from is not countable. Hint: Let be a function from to . Then is a sequence . Let . Then is again a sequence from , and for each we have . This method of proof is known as the Cantor diagonal process. 2. Show that is uncountable. (Use Problem 1) Please see the

Limits and Continuity

Find Lim g(x) x>1+ , Lim g(x) x>1- , Lim g(x) x>1 Find g(1) Is g continuous at x=1? Why, why not? Find Lim x>-2 Find g(-2) Is g continuous at x= -2? Why, Why not?

Analysis: Finding a Limit

Find limit x>> -1^+ f(x) f(x)= x - 2, for x <= 3; x - 1, for x > 3 Also: When you first begin to draw the graph of f(x), why do you start where you do? How high do I go when drawing a graph? How do I know when to stop?

Limit

Lim (2x^3 - 7x^2 + 3x - 4)/(3x^3 + 5x - 6) = x=> oo 2/3 3/2 0 1 -1 oo none of these

Anti-Derivatives

Please choose the correct answer 19. [g(x)]^-1g'(x) dx = (-1/2)[g(x)]^(-2) + C -[g(x)]^(-2) + C ln |g(x)| + C -1/[g(x)] + C none of these 20. True or False: x^14/14 + sqrt(13) + e^x is an antiderivative of x^13 + e^x True False.

Find Functions and Evaluate Limits

1. Find functions f and g such that f(x) = (f.g)(x) where f(x) = (x^2+1)^0.205 2. Evaluate lim lim f(x) = -x^2+1 x< = -1 x-> -1 f(x) = 2x^2+3x x > -1.

Finding and Evaluating Limits

Please find the limits and justify the answer: a) lim 2^x - x² + pi x‾0 ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾ x^10 b) lim sin 2x x‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾ c) lim (1 - 1/x)^x

Real Analysis: Find the Limit

Find the limit lim 3e^2x - 3 x→0 ¯¯¯¯x¯¯¯¯ by recognizing it as a derivative f'(a) of the appropriate function at a suitable value of a. Please specify the function f in the answer - numerical computation of the limit is not enough. (^ means exponent and 3e^2x - 3 is over x).

Problem: Finding Limits

Find the limit lim cos x x&#8594;&#8734; ¯¯x¯¯¯ (cos x is over x - I am not able to make a continuous line)

Limit: L'Hopital's Rule

Please explain the steps and solutions, thanks: Evaluate the limit: lim (1+ x)^1/x x&#8594;&#8734; (^ means exponent and 1/x is the exponent)