Question

Find the limit of the function algebraically. limit as x approaches zero of quantity x cubed plus one divided by x to the fifth power.

Answer 1

`\displaystyle \lim_(x \to 0) \Big( x^3 + (1)/(x^5) \Big) = \text{und} \text{efined}`

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Variable Direct Substitution]:
`\displaystyle \lim_(x \to c) x = c`

Explanation:

Step 1: Define

Identify

`\displaystyle \lim_(x \to 0) \Big( x^3 + (1)/(x^5) \Big)`

Step 2: Evaluate

1. Limit Rule [Variable Direct Substitution]:
   `\displaystyle \lim_(x \to 0) \Big( x^3 + (1)/(x^5) \Big) = 0^3 + (1)/(0^5)`
2. Simplify:
   `\displaystyle \lim_(x \to 0) \Big( x^3 + (1)/(x^5) \Big) = \text{und} \text{efined}`

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits