Continuity and Differentiability

Welcome to the "Continuity and Differentiability" category of Questions LLC! This category is dedicated to answering all your queries and doubts regarding the concepts of Continuity and Differentiability. Whether you are a newbie exploring the fundamentals or a seasoned learner seeking advanced insights, we have got you covered. Our expert contributors have curated a diverse range of questions and answers to help you deepen your understanding of these crucial topics in mathematics. So, whether you need assistance in grasping the basic definitions, understanding the theorems and properties, or solving complex problems, you're in the right place. Explore the questions, find the answers, and enhance your knowledge of Continuity and Differentiability with us.

Questions (18)

Which of the following functions is continuous but not differentiable at x = 1?Functions: I.y=3√x-1 II.y={x^2,x≤1 2x,x>1
1. 5 answers
2. asked by Racquel
3. 4,216 views
let f be the function defined by|x-1|+2 for X<1 f(x)= ax^2-Bx, for X>or equal to 1. where a and b are constants a)if a=2 and b=3
1. 4 answers
2. asked by Yoona
3. 1,660 views
True or false?If f is continuous at x = c, then f is differentiable at x = c.
1. 4 answers
2. asked by Gary
3. 2,564 views
goo.gl/photos/2RPU1dAWoKzUn4Pf81. Which of the above functions are not continuous where they are defined? Why? 2. Which of the
1. 3 answers
2. asked by Ray
3. 548 views
f(x)=x/e^xShow that f is continuous and differentiable for all real numbers.
1. 4 answers
2. asked by anonymous
3. 823 views
1. Provide an example of a function f that is continuous at a = 2 but not differentiable at a = 2.2. Provide an example of a
1. 4 answers
2. asked by Andy
3. 1,437 views
Consider the function below. (If an answer does not exist, enter DNE.)f(x) = e^arctan(7x) I did the problem but I have mistakes
1. 3 answers
2. asked by D
3. 1,840 views
1. Which of the above functions are not continuous where they are defined? Why?2. Which of the above functions are not
1. 2 answers
2. asked by Ray
3. 538 views
If a function f is continuous, is the function f also differentiable? If not, give a counterexample. Explain your answer.
1. 3 answers
2. asked anonymously
3. 33 views
Which of the following functions is continuous but not differentiable at x = 1?Functions: I.y=3√x-1 II.y={x^2,x≤1 2x,x>1
1. 1 answer
2. asked by Rachel
3. 412 views
g(x)={1+cos(pi/2-x/1)0 for-2 <or= x <or=2 for x<2 or x>2 is g(x) continuous at x=2 is it differentiable at x=2? ex[lain in
1. 1 answer
2. asked by angie
3. 327 views
let f be the function defined by|x-1|+2 for X<1 f(x)= ax^2-Bx, for X>or equal to 1. where a and b are constants a)if a=2 and b=3
1. 1 answer
2. asked by Yoona
3. 480 views
i got answers for this one, but i feel like i did something wrong.f(x)= 2x+1 when x is less than or equal to 2 (1/2)x^2 + k when
1. 3 answers
2. asked by jane
3. 558 views
Let f be the function defined by f(x)= sqrt(x), 0 <or= x <or= 4. and f(x)= 6-x, 4 < x <or= 6a. Is f continuous at x=4? justify.
1. 3 answers
2. asked by lisa
3. 1,446 views
True or FalseIf f is continuous at x = c, then f is differentiable at x = c.
1. 2 answers
2. asked by Gary
3. 1,033 views
For the following function, find the values of the constants 𝑎 and 𝑏 for which the function is continuous, but not
1. 2 answers
2. asked by Brett
3. 890 views
given h(x) =kx+1, X<1(k is constant) X^2, x > and equal to 1 A) find value of k such that h(x) is continous at x=1 B) determine
1. 2 answers
2. asked by hy
3. 835 views
Letf(x) = x^2 if x ≤ 1 ax + b if x > 1. Find the values of a and b so that f is continuous and has a derivative at x = 1.
1. 2 answers
2. asked by Amy
3. 644 views