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Need help Continuity and differentiability!!!!?

I need help this problem. Please help me

1.) Is f(x) differentiable at x=2? Why and why not

f(x)= {x+2, x<=2

{x^2 , x>2

2.)use the definition of continuity to determine whether or not the function is continuous at x=3

tHNKS SO MUCH !!!!

f(x)= { (x^2-9)/(x-3) , x is not 3

{ 2, X=3

2 Answers

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  • 1 decade ago
    Favorite Answer

    1) Yes, because since its asking for the 2 sided limit (whether or not it is differentiable) in the first equation y = 4 and the second y = 4 also, and therefore it is differentiable.

    2) I forgot about how to do this part.

    Source(s): AP Calculus
  • ries
    Lv 4
    4 years ago

    definite. Continuity potential that any decrease of the function is nicely attained on a closed era. Differentiability demands that the tangent at any ingredient of a non-end therapy be unique. An occasion of a non-end yet no longer differentiable curve is easily the cost function y=|x| on an era jointly with x=0. it is non-end because of fact the decrease as |x|->0 of y is fairly y(0), yet there is not any unique tangent--the slope at (0,0) i undefined and could formally take any value between -one million and +one million. by potential of how--sorry for the undesirable possibility answer. it is incredibly elementary to verify how I overcounted.

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