lim as x approaches negative infintiy (x^2+x^3)
I just don't know where to start
x^2(1+x)
lim x^2(1+x)=limx^2 * lim (1+x)
= +inf * - inf= - inf
oh! I was trying to make it harder than it was! thank you!
To find the limit as x approaches negative infinity of the function f(x) = x^2 + x^3, you can use some properties of limits and factoring. Here's how you can approach it step by step:
Step 1: Identify the highest power of x in the expression, which is x^3. This power will have the most significant impact as x approaches negative infinity.
Step 2: Divide the entire expression by the highest power of x. This step helps you simplify the function and focus on the term that has the most significant effect on the limit.
So, divide both the terms (x^2 and x^3) by x^3:
f(x) = (x^2 / x^3) + (x^3 / x^3) = x^(-1) + 1.
Step 3: Now, when x approaches negative infinity, x^(-1) approaches 0 since the negative exponent changes the sign and inversely scales the value.
Step 4: Simplify the expression to:
f(x) = 0 + 1 = 1.
Therefore, the limit as x approaches negative infinity of f(x) = x^2 + x^3 is 1.
In summary, to find the limit as x approaches negative infinity, you divide the function by the highest power of x, simplify the expression, and evaluate the limit of the simplified function.