Solve it step by step so I can't do the rest.
lim x->-infinity (ax^2+b)/(cx+d)
Thank you!
To find the limit of the function as x approaches negative infinity, we can simplify the expression and then analyze it.
Start by factoring out the highest power of x in both the numerator and the denominator:
lim x->-infinity (ax^2+b)/(cx+d) = lim x->-infinity (x^2(ax^2+b))/(x^2(cx+d))
Now, divide both the numerator and the denominator by x^2, which will approach zero as x approaches negative infinity:
lim x->-infinity (x^2(ax^2+b))/(x^2(cx+d)) = lim x->-infinity (ax^2+b)/(cx^2+d/x^2)
As x approaches negative infinity, the term d/x^2 approaches zero since the denominator grows much faster than the numerator. Therefore, we can ignore this term in the limit calculation:
lim x->-infinity (ax^2+b)/(cx^2+d/x^2) = lim x->-infinity (ax^2+b)/(cx^2)
Now we can see that the limit depends on the ratios of the coefficients. If c is positive, then the function will approach positive infinity, and if c is negative, it will approach negative infinity.
In summary, the limit as x approaches negative infinity of (ax^2+b)/(cx+d) depends on the ratio of the leading coefficients a/c. If a/c is positive, the limit is positive infinity, and if a/c is negative, the limit is negative infinity.