Definiteness of Matrices - HELP

[dark_chocolate]

Continuity of Function - HELP

Hi, I am stuck with this one. Anyone can solve it please? Great appreciation

1. Let f(x) = x² +1 if x < 1 and = 3 if x ≥ 1

By constructing a suitable sequence {x_n} to the transition point (given k >1) , discuss whether the Function is
(i) Continuous
(ii) C¹
(iii) C^k

 

[HallsofIvy]

Hi, I am stuck with this one. Anyone can solve it please? Great appreciation

1. Let f(x) = x² +1 if x < 1 and = 3 if x ≥ 1

By constructing a suitable sequence {x_n} to the transition point (given k >1) , discuss whether the Function is
(i) Continuous
(ii) C¹
(iii) C^k

What have you done on it? Do you know what the "transition point" is? Do you know what \(\displaystyle C^1\) and \(\displaystyle C^k\) mean? Frankly, I would consider this problem pretty close to trivial- because it asks you to "construct a suitable sequence", exactly what definition of "continuous" are you using.