SOLUTION: For what value(s) of a and b is the function f(x) given below continuous at 0? {{{matrix(1,3, "f(x)",""="", system( matrix(3,3,sin(3x)/x, if, x<0, a, if, x=0, (5-sqrt(25-x

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Question 1200105: For what value(s) of a and b is the function f(x) given below continuous at 0?

Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!


The 3 parts of the graphs are 

, , 

The first function must approach the same value as the second function as x approaches 0 from the left. So



Therefore a = 3, so the second function is y=3

Also the third function must approach the same value as the second function as
x approaches 0 from the right.





So 





Here's the graph of the continuous function:



Edwin
Answer by ikleyn(52852)   (Show Source): You can put this solution on YOUR website!
.

Look at this web-site

https://medium.com/@nadzeya/the-wonderful-limits-in-maths-part-1-94c6b41a80e8


(free of charge), and find there the proof of one of the wonderful limits


      ---> 1  as  x ---> 0.


It is one of wonderful limits from Calculus that any Calculus student must know.



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