Limits Urgent :)

[uniqueownz]

lim x->0[sup:nwb5xszf]-[/sup:nwb5xszf] of (2x + 3 + (sin3x/|x|))

 

[galactus]

Pay attention to the \(\displaystyle \frac{sin(3x)}{|x|}\)

Since it is an absolute value it will have a negative value when approaching 0 from the left and a positive when approaching 0 from the right.

What is \(\displaystyle \lim_{x\to 0}\frac{sin(3x)}{x}\)?.

This is a famous limit based on \(\displaystyle \lim_{x\to 0}\frac{sin(x)}{x}=1\)

The rest is straightforward. That 3 in there should be clue.

 

[Deleted member 4993]

lim x->0[sup:1q3nt7rc]-[/sup:1q3nt7rc] of (2x + 3 + (sin3x/|x|))

Please share with us your work/thoughts - so that we know whwere to begin to help you.

Plot the function in your graphing calculator - what does the limit look like? How can you justify that graph?

 

[uniqueownz]

i knew about changing the |x| to -x where the limit approaches 0 from the left
but i still dont kno where to go from there

 

[galactus]

I assume then you can't evaluate \(\displaystyle \lim_{x\to 0}\frac{sin(3x)}{x}\)?.

Multiply the top and bottom by 3 and let t=3x, then use the 'famous' limit I mentioned.

 

[galactus]

You got it here:

http://www.mathhelpforum.com/math-help/ ... rgent.html