Limits Practice (Graphically and Algebraically)

• DNE

Answer explanation

To evaluate use direct substitution to simplify.

• DNE

Answer explanation

To evaluate use direct substitution.

• DNE

Answer explanation

To evaluate the limit, multiply the numerator and denominator by the conjugate. Simplify and cancel out the common factor. Then use direct substitution to solve.

• DNE

Answer explanation

To evaluate the limit, factor the numerator and cancel out the common factor. Then use direct substitution to solve.

• DNE

Answer explanation

To evaluate the limit, factor the numerator and cancel out the common factor. Then use direct substitution to solve.

Evaluate the limit.

• DNE

Answer explanation

To evaluate the limit, we can use trigonometric identities. The limit simplifies to \( \frac{\sqrt{3}}{2} \) as it approaches the value from both sides, confirming that this is the correct answer.

Tags

CCSS.HSF.IF.A.2

• 0

• 1

• 2

• DNE

Answer explanation

Factor the numerator and denominator to eliminate the common factor. Then evaluate the limit by using direct substitution.

• 0
• ∞
• - ∞
• DNE

Tags

CCSS.HSF-IF.C.7D

• 0

• ∞

• DNE

• -∞

Answer explanation

As x approaches -2 from the left, f(x) decreases without bound, leading to the limit being -∞. Thus, the correct answer is -∞.

Tags

CCSS.HSF-IF.C.7E

• -∞

• ∞

• DNE

• -2

Answer explanation

As x approaches -2 from the right, f(x) tends to infinity, indicating that the limit is ∞. Therefore, the correct answer is ∞.

Tags

CCSS.HSF.IF.A.2