What is the limit of:
-x^5+2x^4-x^2+1?
To find the limit of a function as x approaches a certain value, we need to evaluate the function as x gets arbitrarily close to that value. In this case, let's find the limit as x approaches infinity.
To compute the limit of the given function, -x^5 + 2x^4 - x^2 + 1, as x approaches infinity, we look at the term with the highest exponent, which is x^5.
As x becomes larger and larger, the term -x^5 becomes more and more negative. This is because the negative coefficient (-1) is multiplied by an increasingly larger number. Therefore, this term dominates the expression as x approaches infinity.
Hence, the limit of -x^5 as x approaches infinity is negative infinity, (-∞).
Therefore, the limit of the given function as x approaches infinity is also negative infinity, (-∞).