Algebraically Evaluate the Limit (If It Exists)by the Appropriate Technique(s) $\lim _ { x \rightarrow 0 ^ { - } } \frac { \sqrt { x + 2 } - \sqrt { 2 } } { x }$

question 152

Multiple Choice

Algebraically evaluate the limit (if it exists) by the appropriate technique(s) .Round your answer to four decimal places. $\lim _ { x \rightarrow 0 ^ { - } } \frac { \sqrt { x + 2 } - \sqrt { 2 } } { x }$

• A) \(\lim _ { x \rightarrow 0 ^ { - } } \frac { \sqrt { x + 2 } - \sqrt { 2 } } { x } = \frac { \sqrt { 2 } } { 4 } \approx 0.3536\)
• B) \(\lim _ { x \rightarrow 0 ^ { - } } \frac { \sqrt { x + 2 } - \sqrt { 2 } } { x } = \frac { 2 \sqrt { 4 } } { 4 } \approx 1\)
• C) \(\lim _ { x \rightarrow 0 ^ { - } } \frac { \sqrt { x + 2 } - \sqrt { 2 } } { x } = - \frac { 2 } { 4 } \approx - 0.5\)
• D) \(\lim _ { x \rightarrow 0 ^ { - } } \frac { \sqrt { x + 2 } - \sqrt { 2 } } { x } = \frac { 2 } { 4 } \approx 0.5\)
• E) \(\lim _ { x \rightarrow 0 ^ { - } } \frac { \sqrt { x + 2 } - \sqrt { 2 } } { x } = \frac { 4 \sqrt { 2 } } { 2 } \approx 2.8284\)

---

Definitions:

Babinski Reflex

A reflex action in infants which involves the toes fanning out when the sole of the foot is stroked.

Newborn's Introduction

The initial period following birth when a newborn adjusts to the external environment and begins early interactions with caregivers.

Immersed In Water

The state of being completely covered or submerged in water.

Dynamic Systems View

A perspective that emphasizes the complex and changing interactions among various systems within development over time.