LIMIT EXPLORER
WHAT IS LIMITS?
It basically focuses on the actions performed by the function, as they tend to arrive at a fixed point. This concept letsusknowthevaluethefunctionstrivestoattain,evenifit does not actually attain the value. This concept focuses on approaching, not on touching. Enabling math to analyze continuouschange.
WHY IS IT IMPORTANT?
"Limit of x squared minus 25 over x minus 5 , as x approaches5."
TABLE VALUES
1. LIM (X³ + 2X + 1)
X → −3
= (−3)³ + 2(−3) + 1 (BY THE POWER RULE)
= −27 − 6 + 1 = −32
∴ LIM (X³ + 2X + 1) = −32 X → −3
2. LIM (X² + X − 20) / (X + 5)
X → −5 = LIM ((X + 5)(X − 4)) / (X + 5)
X → −5 = LIM (X − 4)
X → −5
USING LIMIT OF THE IDENTITY FUNCTION AND LIMIT OF A CONSTANT:
= LIM X − LIM 4
X → −5 X → −5
= −5 − 4 = −9
∴ LIM (X² + X − 20) / (X + 5) = −9
X → −5
SINCE X → ∞ , 1/X → 0 AND 1/X² → 0: = (4 − 0) / √(64 + 0 + 0) = 4 / 8 = 1/2 = 0.50 ∴ LIM (4X − 3) / √(64X² + 6X + 3) = 1/2 = 0.5 X → ∞