## anonymous one year ago Find the constant such that f(x)= {-4*((sin x)/(x)), x<0 -------{a + 10x, x>=0 is continuous on the entire real line. a)4 b)-4 c)-10 d)10 e)1 **I know that the answer is -4(B), but I need to know how to get it**

1. anonymous

Help please, I have test corrections

2. anonymous

Use this to take a left sided limit. $\lim_{x \rightarrow 0}\frac{ \sin x }{ x }=1$ Then take a limit of the right side approaching 0 of $$a+10x$$. The limits have to be equal to each other and f(0) for f(x) to be continuous.

3. anonymous

@peachpi how is sin x/x = 1? that was what stumped me

4. anonymous

(sin x)/x isn't 1. The limit approaching 0 is. $\lim_{x \rightarrow 0}\frac{ \sin x }{ x }=1$ and $\lim_{x \rightarrow 0}\frac{ 1-\cos x }{ x }=0$ are two limits you need to be able to recognize on sight. I'll see if I can find links to proofs.

5. anonymous

For the sine limit: http://math.ucsb.edu/~jcs/SqueezeTheorem.pdf For the cosine limit: http://math.hws.edu/~mitchell/Math130F12/tufte-latex/TrigLimits.pdf