Project ForgeEngineering Mathematics
Calculus
GATE 2019
Medium
Compute lim (x→3) (x⁴−81) / (2x²−5x−3).
- A1
- B53/12
- 108/7
- DLimit does not exist
Explanation
Both numerator and denominator vanish at x=3 (0/0 form), so factor: x⁴−81=(x−3)(x+3)(x²+9), and 2x²−5x−3=(2x+1)(x−3). Cancel the common (x−3) factor, leaving (x+3)(x²+9)/(2x+1). At x=3: (6)(18)/7 = 108/7.
Source: GATE CS 2019 (Set-2) (2019)
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