Question

Evaluate the following limit. Enter the exact answer. To enter a, type sqrt(a). lim x→1(x^3/2−2x−1)=? a) Clearly define the given limit expression, including the mathematical function and the variable approaching a specific value.

b) Instruct the respondent to enter the exact answer in the provided format, emphasizing the use of the square root notation.
c) Encourage a step-by-step solution process, including any algebraic manipulations or simplifications required to determine the limit.

Ensure a thorough explanation of the steps involved in evaluating the limit and obtaining the exact answer."

Answer 1

To evaluate the limit, substitute the given value into the expression and simplify.

Step-by-step explanation:

To evaluate the limit of the given expression, we will substitute the given value into the expression. Let's calculate:

lim x→1(x^3/2−2x−1)

= lim x→1((√x)^3−2x−1)

= (√1)^3−2(1)−1

= 1−2−1

= −2.

Therefore, the limit, lim x→1(x^3/2−2x−1), equals -2.