okay i have three limits, i did one and the two others i m stuck...(adsbygoogle = window.adsbygoogle || []).push({});

well here

1.

limit when x tends to zero of

(x-sin(px)) / (x-sin(qx))

p and q are positive integers.

for this one i have no idea what to do, i never worked with p or q...

2.

limit when x tends to zero of the function:

(x(1-cosx)) / (sin3x - 3sinx)

for this one, i expanded the denominator to get [ sinx(3cos²x-sin²x) ], then i finally have

(x(1-cosx)) / (sinx(3cos²x-sin²x))

and the limit is +infinty i think; am i right?

3.

f(x)=(x-1)/(x+1-|x|)

i first need to find the domain of definition, then find the limits in those points.

first, i need to separate that function into :

f(x)= (x-1)/(2x+1) [x<0] (x shouldn't equal 1/2)

f(x)= x+1 [x<o]

so, the limit in -infinity is -infinity

the limit in +infinity is 1/2

the limit in 1/2+ is -infinity

the limit in 1/2- is +infinity

is that right ^^

thanks!

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# Find the domain of definition and then the limit

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