Hello, dokrbb!
That's what I tried. . .
. .
. .
I don't follow your steps after this.
Divide numerator and denominator by
. .
Can you please show me how all the algebra works for evaluating the limits of this function as x-> +/_ infinity for this function
lim f(x),x-> +/_ inf sqrt(x^2 + 10x +1) –x
That's what I tried, and I figured out the first asymptote:
lim f(x),x-> +/_ inf sqrt(x^2 + 10x +1) –x=
lim f(x),x-> +/_ inf sqrt(x^2 + 10x +1) –x*([sqrt(x^2 + 10x +1) +x]/[sqrt(x^2 + 10x +1) +x])=
lim f(x),x-> +/_ inf [(x^2 + 10x +1) – x^2]/sqrt(x^2 + 10x +1) + x =
a)
divide by x both the numerator and the denominator:
lim f(x),x-> + inf [(x + 10 + 0) – x]/sqrt(1 + 0 +0) + 1 = 10/2 = 5
this would be the horizontal asymtote to which f(x) approaches when x becomes large positive,
b) but what happens when x becomes large negative? I see from the graph that f(x) tends to positive infinitive, but I can't fugure it out algebraically.
lim f(x),x-> - inf [(x^2 + 10x +1) – x^2]/sqrt(x^2 + 10x +1) + x = ...
Thanks
I really do not know what more to say.
Look at this graph
For any then and . So the sum increases to .