Continuity Definition and 909 Threads

let f be a function defined by f(x)=4-x^2 when x=<1 and k+x when x>1 What value of k will f be continuous at x=1? I know the answer is k=2, however, I don't know how to show to correct work. I got 2 when I sketched a graph of 4-x^2 and plugged in some numbers but I don't know how to show it...

Help on continuity! 1) Ok, i know how to find x, but how do you know if something is nonremovable or removable discontinuity? like for this: f(x)=|x+2|/(x+2) i knoe its x=-2, but is it nonremovable or removable? 2) How do u do the continuity stuff with there: f(x)=csc2x...

Hi, I have just one more problem :) here it is: (because I don't know how to do theta, "@" will equal theta) Find a value of K so that f(2) is continuous at @=0 ( != means "not equal") f(@) = ( (2sin@)/@ , @ !=0 ) ( 5k , @=0 ) f(@) is a piecewise function I don't know...

Hi guys. I am solving the axisymmetric free jet of an incompressible fluid. But I have troubles at r=0. Continuty equation can be written in cylindrical coordinates as: 1/r*d(rv)/dr + du/dz=0 v=radial velocity (v=0 at r=0) u=axial velocity. hz=delta(z) hr=delta(r) What happens at...

How do I show that f(x)=x^2 is continuous at any given point, say x=3. Thank you.

Consider f(x)=x^3-x^2+x+1 g(x)=\left\{\begin{array}{cc}{max\{f(t),0\leq t \leq x\}}\;\ 0\leq x \leq 1 \\ 3-x\;\ 1< x \leq 2\end{array}\right Discuss the continuity and differentiability of g(x) in the interval (0,2) I know how to do it As f(x) is increasing function therefore max...

i'm trying to define what it would mean for a set to be continuous. what i'd like to say is that S is continuous if it is homeomorphic to [0,1], (0,1], or (0,1). (perhaps that's redundant already?) but I'm not sure if that captures all the sets i'd like to think of as continuous. my...

'Time and Indeterminacy vs. Continuity' Sorry; I couldn't resist that. (Peter Lynds theory) What is time? Dictionary.com/time: 'Time is a nonspatial continuum in which events occur in apparently irreversible succession from the past through the present to the future. An interval separating...

Is it just me or is it the text didn't explain well enough about continuity? I totally don't understand it. Not only that, when it covers about derivatives it first introduced another defination of slope. Then it says that the derivative of x^2 is 2x. How does slop relate to derivative? Can...