Evaluate the following limit, writing your answer as either a number or using inf for ∞ if needed. lim𝑥→∞𝑥4+35𝑥2+8=

To evaluate the limit of the function as x approaches infinity, we can use the rule of thumb that says: for large x, the highest power of x dominates the function.

Here, the highest power of x in the numerator and denominator is 4.

So, we can divide every term in the function by x^4 to simplify it:

lim (x→∞) (x^4/x^4 + 35x^2/x^4 + 8/x^4)

This simplifies to:

lim (x→∞) (1 + 35/x^2 + 8/x^4)

As x approaches infinity, the terms 35/x^2 and 8/x^4 will approach 0 (since any number divided by infinity is essentially zero).

So, the limit of the function as x approaches infinity is 1.