This is the ultimate calculus study guide for your universitylevel calculus and real analysis class. We will do 24 rigorous proofs for limits, including the epsilondelta proofs, epsilonN proofs (when x approaches infinity), Mdelta (when the limit is infinity), and MN proofs (when x goes to infinity and f(x) also goes to infinity) for limits. It's definitely the GPA saver that you need for college. Make sure you know the 4 big rigorous definitions for limits here:    • 4 BIG limit definitions  
File (public):   / 24rigorous88483708  
My handwritten notes for all these 24 proofs: (Patreons only)   / notesfor2488670205  

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0:00 24 limit proofs with definitions
Q1. 0:29 epsilondelta proof, linear case
Q2. 3:51 epsilondelta proof, rational function
Q3. 12:04 epsilonN proof, x approaching infinity, rational function
Q4. 17:18 Mdelta proof, x approaching infinity, rational function
Q5 22:19 epsilonN proof
Q6 28:34 epsilondelta proof, quadratic case
Q7 32:26 MN proof, square root function
Q8 36:06 epsilondelta proof, square root function
Q9 42:47 εδ linear case
Q10 45:00 εδ limit proof, hard
Q11 52:21 limit of 1/x^2 as x goes to infinity
Q12 55:17 limit of sqrt(x3) as x goes to infinity
Q13 58:24 limit of x^3 as x goes to 2
Q14 1:04:43 εδ linear case
Q15 1:06:40 εN proof
Q16 1:15:50
Q17 1:19:00
Q18 1:21:50
Q19: 1:26:46
Q20: 1:30:07
*start at 1:31:41, please change all the ε to M
Q21 1:32:24
Q22 1:36:42
Q23 1:41:21
*at 1:42:28, it should be 1/abs(x3) is greater than 1/δ. And then say 1/(abs(x3))^2=1/(x3)^2 is greater than 1/δ^2
Q24 1:44:15 limit of x^2/(x+1) as x goes to infinity
*at 1:48:26, we need to add the condition that N is greater than 1. So please write N=max{1, 2ε}

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