Evaluate the Limit

Problem

(lim_x→−2)(√(,7*x4+x2))

Solution

1. Identify the limit type and check if the function is continuous at the target value x=−2

2. Apply the direct substitution property for limits, as the function √(,7*x4+x2) is defined and continuous at x=−2

3. Substitute the value −2 for every instance of x in the expression.

√(,7*(−2)4+(−2)2)

4. Evaluate the powers inside the square root.

√(,7*(16)+4)

5. Multiply the terms inside the radicand.

√(,112+4)

6. Simplify the expression by adding the numbers and taking the square root.

√(,116)

7. Factor the radicand to simplify the radical further.

√(,4⋅29)

8. Extract the square root of the perfect square.

2√(,29)

Final Answer

(lim_x→−2)(√(,7*x4+x2))=2√(,29)

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