Limits and Continuity

Welcome to the "Limits and Continuity" category of Questions LLC! Whether you are a math enthusiast, a student preparing for a calculus exam, or someone who simply wants to delve deeper into the fascinating world of mathematical concepts, you have come to the right place. In this category, you will find a wide range of questions and discussions related to limits and continuity, one of the fundamental concepts in calculus. Explore the queries from both beginners and experts, and join the community in unraveling the intricacies of these mathematical principles. We encourage you to ask your own questions, provide insights, and engage in lively discussions to expand your knowledge and enhance your understanding of limits and continuity. Happy exploring!

Questions (111)

What is the maximum value of the function y= 18/x^2-9 over the interval -3<x<3?A. 0 B. 2 C. -2 D. Infinity
1. 4 answers
2. asked by Katherine
3. 1,037 views
A particle moves along the x axis so that its position at any time t>= 0 is given by x = arctan tWhat is the limiting position
1. 3 answers
2. asked by Jen
3. 2,866 views
Let f be defined as follows, where a does not = 0,f(x) = {(x^2 - 2a + a^2) / (x-a), if x does not = a 5, if x = a Which of the
1. 6 answers
2. asked by Mishaka
3. 4,091 views
What is the limit of g(x)=x as x approaches pi?Would it just be pi??
1. 6 answers
2. asked by Ray
3. 6,850 views
lim as x --> infinity of (x^2-16)/(x-4) is 8By graphing, find an interval for near zero such that the difference between your
1. 4 answers
2. asked by Brittany
3. 539 views
Determine the vertical asymptotes of the graph of the following functionsf(x)=cotx f(x)=x-2/x^2-4
1. 2 answers
2. asked by Sinachi
3. 68 views
What are the points of discontinuity?y =(x-2)/(x^2 + 5x - 6) A. x = 6, x = –1 B. x = 1, x = 6 C. x = –6, x = 1 D. x = 8
1. 2 answers
2. asked by Blake
3. 44 views
Continuity ans discontinuity
1. 1 answer
2. asked by Fuad Faji Jemal
3. 99 views
how to find constraints of domain
1. 4 answers
2. asked anonymously
3. 49 views
What are the points of discontinuity?y = x-2/x^2+5x-6
1. 1 answer
2. asked by skittlez
3. 66 views
4. For what value of the constant k the functionf(x)= x^ 2 -4/x-2 if x=2, 2k - x if x=2 is continuous at x = 2 A) -3 B) -1 C) 3
1. 1 answer
2. asked by Arshal
3. 80 views
r(t)= < lnsqrt(t+2) , 4t , t/(9-t^2) >find the domain of r and answer in interval notation Will the domain have any brackets or
1. 1 answer
2. asked by Ken
3. 97 views
Note that f is continuous on (−∞, 6) and (6, ∞). For the function to be continuous on (−∞, ∞), we need to ensure
1. 4 answers
2. asked by Anonymous
3. 5,719 views
f(x) = tan x / sin xFind the vertical asymptote. Describe its behavior to the left and right of the vertical asymptote.
1. 4 answers
2. asked by David
3. 3,151 views
Suppose f and g are continuous functions such thatg(3) = 2 and the limit as x approaches 3 of [3f(x) + f(x)g(x)] = 15. Find
1. 4 answers
2. asked by Anonymous
3. 1,273 views
Let f be the function defined as:f(x) = (x^2 - 4)/ (x-2) if x≠2 1 if x=2 Which of the following statement(s) about f is true?
1. 4 answers
2. asked by Amy
3. 1,903 views
If limx→af(x)=L , where L is a real number, which of the following must be true?A) f'(a) exists B) f(x) is continuous at x=a.,
1. 5 answers
2. asked by jer
3. 9,526 views
Show that f is continuous on (-infinity, infinity).f(x) = x^2 if x<1 and the square root of x if x is greater than or equal to
1. 4 answers
2. asked by Amy
3. 2,347 views
Let f be the function defined by f(x)=2x+3e−5x, and let g be a differentiable function with derivative given by
1. 4 answers
2. asked by samantha
3. 8,797 views
When one-sided limits are not equal to each other at a point, what can be said about the continuity of the function at that
1. 4 answers
2. asked by Sarah
3. 737 views
For what values of k is lim x -> INF coshkx/sin2x finite?
1. 4 answers
2. asked by Abi
3. 729 views
Let f be defined as follows, where a does not = 0,f(x) = {(x^2 - 2ax + a^2) / (x-a), if x does not = a 5, if x = a Which of the
1. 3 answers
2. asked by Cleewef
3. 2,093 views
lim t-->0 h(t), where h(t)= cos(t)-1/t^2.for the table values t is +/- .002 , .0001 , .00005 , .00001 what do you guys get for
1. 4 answers
2. asked by Jake
3. 510 views
Let f be defined as follows, where a ≠ 0, f(x) = { (x^2-2ax+a^2)/x-a if x ≠ a, 5 if x = aWhich of the following are true
1. 4 answers
2. asked by Olivia
3. 911 views
What is the vertical asymptote of the graph of y=log4(x-3) ?
1. 4 answers
2. asked by Diamond
3. 1,787 views
evaluatelim of x as it approaches infinity for sqrt of x^2 -1/2x+1
1. 3 answers
2. asked by musuma
3. 1,169 views
Horizontal asymptote for f(x)=10x/5x^2+1
1. 4 answers
2. asked by Pam
3. 532 views
Sketch a possible graph for a function where f(-2) exists, lim as x->-2 exists, f is not continuous at x=-2, and lim x->1
1. 4 answers
2. asked by Kenny
3. 2,072 views
Find the domain of the function enter your answer using interval notationf(x)=1/3x-15
1. 2 answers
2. asked anonymously
3. 46 views
for each k in R find the limit(x,y)-->(0,0) [((x^4)(y^3))/(x^10 + y^5)] along the path y=kx^2
1. 1 answer
2. asked by xiny
3. 57 views
Hello everyone!I'm having a hard time figuring out how to do this problem. Any help would be highly appreciated! Show that U =
1. 1 answer
2. asked by Ashley
3. 82 views
ill in the following:lim f(x)= x→ 1 + lim f(x)= x→ 1 − lim f(x)= x→ 1 f (1) = lim x→− lim f(x)= x→ 2 + lim
1. 1 answer
2. asked by hasaanen
3. 114 views
If (z_n) goes to p, then there is a real number M such that for every z_n,|z_n| less than or equal to M.
1. 4 answers
2. asked by Sasha
3. 111 views
Given lim_(x->2) (2x-2) = -6, what is the best choice of d such that |(2x-2)-(-6)| < 0.03 whenever |x+2| < d?
1. 4 answers
2. asked by Anonymous
3. 321 views
f(x) = { x^2sin(1/x), if x =/= 00, if x=0} a. find lim(x->0)f(x) and show that f(x) is continuous at x=0. b, find f'(0) using
1. 2 answers
2. asked by Anonymous
3. 517 views
9.0/1 points | Previous Answers SSTCalc6 2.3.046.My NotesQuestion Part Points Submissions Used Let f(x) = 4x2 if x > 2 4x + 3 if
1. 1 answer
2. asked by John
3. 458 views
what is the lim((n+4)/(n+1))^n when it tend to infinityhelp
1. 1 answer
2. asked by buj
3. 323 views
Evaluate the limit using l'hospitals rule. lim->0 (3^x-6^x)/x. Do not know where to even begin on this one... please help.
1. 1 answer
2. asked by Lisa
3. 398 views
Determine the domain of the following functions, write answer using interval notation.T(x)=log12(x^2+14x)
1. 1 answer
2. asked by Juniper
3. 451 views
limx---> 2 4x+1/3x-4 illustrate definition 2 by finding values of delta that correspond to epsilon=0.5 and epsilon= 0.1 I having
1. 2 answers
2. asked by feather
3. 631 views
Find the constant c so that lim x->8 x^2+2x+c/x^2-15x+56 exists. For that value of c, determine the limit. (Hint: Find the value
1. 2 answers
2. asked by Charlotte
3. 660 views
lim ((1-2x)/(√1+x^2)-1)x→∞ Find the value.
1. 1 answer
2. asked by Marc
3. 393 views
Note that f is continuous on (−∞, 6) and (6, ∞). For the function to be continuous on (−∞, ∞), we need to ensure
1. 1 answer
2. asked by Anonymous
3. 1,247 views
((1/-2-h)-1)/h
1. 1 answer
2. asked by alex
3. 231 views
Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it.lim x→∞ (x
1. 2 answers
2. asked by TayB
3. 660 views
I'm trying to factor this equation in order to find its limit, but I'm not sure how to go about it. I can get the answer by
1. 2 answers
2. asked by Pax
3. 483 views
True or false:a) if f(x) is continuous at a, then the limit of f(x) as x approaches a exists b) if the limit of f(x) as x
1. 1 answer
2. asked by Anonymous
3. 358 views
In general, if lim x->a m(x) does not exist andlim x->a n(x) does not exist, is it true that lim x->a [m(x)+n(x)] does not
1. 1 answer
2. asked by Sam
3. 385 views
Find lim as x approaches 0 of (e^x-1-x/2-x^3/6)/(x4)
1. 1 answer
2. asked by Sarah
3. 347 views
Consider the sequence: (a,sub(n))={1/n E(k=1 to n) 1/1+(k/n)}Show that the limit(as n-> infinity) A(sub(n))= ln 2 by
1. 1 answer
2. asked by chelsea
3. 334 views

Limits and Continuity

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