Evaluate the following limits
1) lim
x→∞		 ____7x -1____
√(4x2 + 3x + 8)		 2) lim
x→-∞		 __2x2 - x + 5__
4x3 - 1

Solution:
STEP 1: Separate the original expression to two fractional terms
= ______7x______
√(4x2 + 3x + 8)		 - _____1_____
√(4x2 + 3x + 8)
STEP 2: Bring down the numerator of the first fractional term to become the denominator of the denominator
= ______7______
_√(4x2 + 3x + 8)_
x		 - _____1_____
√(4x2 + 3x + 8)
STEP 3: Insert the x term inside the radical sign and manipulate.
= ______7______
√(4x2/x2 + 3x/x2 + 8/x2)		 - _____1_____
√(4x2 + 3x + 8)
= ______7______
√(4 + 3/x + 8/x2)		 - _____1_____
√(4x2 + 3x + 8)
STEP 4: Evaluate the limit
= ______7______
√(4 + 3/∞ + 8/∞2)		 - _____1_____
√(4(∞)2 + 3(∞) + 8)
= ______7______
√(4 + 0 + 0)		 - _____1_____
√(∞ + ∞ + 8)
= _7_
√(4)		 - _1_
∞
= _7_
2		 - 0
= _7_
  2

To follow yung number 2! Ang hirap kasi magcode ng fractional terms sa HTML. Basta ang sagot sa 2 ay lim =0.

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