Recent content by tg43fly

im too confused as with limit laws in general, ill find some more basic examples to start with. ty for helping.

i'm looking at an similar example lim x->5 f(x) / (g(x) + 4) however they've given the values of lim x-> 5 f(x) = 2 and g(x) = -4 albeit this function does not limit in my case how would i determine g(x)? can i rewrite g(x) into a polynomial function that gives a constant c given lim x-> 1?

would lim x->1 g(x) = 8?

lim x->1 (f(x)-8)(g(x)) / (x-1) = 10*g(x) so i have to find g(x) which is a constant?

i'm so lost. does that mean f(x) can just be (x-1) to factor out the denominator?

does (f(x) - 8) / (x - 1) = 10 need to hold true for lim x->1? i thought id have to factor out the x-1 since it'd give a 0 denominator

would this also address the 0 denominator given lim x->1 for (x-1)? f(x) * g(x) = 10x-2 would this be on the right path?

so i.e. lim x->1 -8/(x-1) * f(x) where i can make up a new limit for f(x) which will also need (x-1)? do i need to get rid of lim x->1 (x-1) on the denominator with the f(x)?

i don't comprehend... do you mean bringing (x-1) to above by inversing it? i tried that. the whole f(x) within another function boggles me.

its find lim x-> 1 f(x)

no, that was all that given; find f(x) at lim x-> 1 any idea where i should start, i did trial and error on lim x->1, f(x) = (x-1)^n, but i don't think that worked

yeah sorry, it is indeed the latter lim x->1 (f(x)-8)/(x-1) = 10

Homework Statement lin x-> 1 f(x)-8 / x-1 = 10 find f(x) Homework Equations The Attempt at a Solution i don't know where to start on finding f(x), i assume it includes (x-1) to eliminate the 0 denominator, i need some hints

ok i may have expressed myself wrongly there. i wanted to know is how (1 / sqrt(x) - 1) can be converted into (-sqrt(x) - 1) / (1 - x) noticed it was just multiplying denominator and numerator by its conjugate. so yeah, should've noticed the elephant in the room. thanks for the help anyway.

Homework Statement lim x->1 (x^3-1)/(x^1/2-1) ans:6 Homework Equations The Attempt at a Solution (x^1/2-1)^-1 can be converted into (plugged into wolfram): (-x^1/2-1)/(1-x) i want to how this done if I'm factorize out the 0 in the denominator