Limit Theorems (Part 1) PDF
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CMNS, Colegio de Matemáticas y Ciencias Naturales
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This document provides theoretical concepts and practical application of limit theorems in mathematics. It details examples and calculations for understanding limit properties for polynomial functions.
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LIMIT THEOREMS (Part 1) What are the Limit properties? Limit Theorems 𝑓 𝑥 =4. lim 4 = 4 lim 4 = 4 lim 4 = 4. 𝑥→2 𝑥→0 𝑥→3.. How about 𝑥 → −5??? lim 4 = 4....
LIMIT THEOREMS (Part 1) What are the Limit properties? Limit Theorems 𝑓 𝑥 =4. lim 4 = 4 lim 4 = 4 lim 4 = 4. 𝑥→2 𝑥→0 𝑥→3.. How about 𝑥 → −5??? lim 4 = 4. 𝑥→−5. Limit Theorems 𝑓 𝑥 =𝑥. lim 𝑥 = 2 lim 𝑥 = 0 lim 𝑥 = 3. 𝑥→2 𝑥→0 𝑥→3.. How about 𝑥 → −5??? lim 𝑥 = −5. 𝑥→−5. Limit Theorems lim 𝑥 + 7 = lim 𝑥 + lim 7 = 4 + 7 = 11 𝑥→4 𝑥→4 𝑥→4... lim 2𝑥 − 3 + 3𝑥 − 5 = lim 2𝑥 − 3 +lim 3𝑥 − 5 𝑥→4 𝑥→4 𝑥→4... Limit Theorems lim 2𝑥= lim 2 lim 𝑥 = 2 3 = 6 𝑥→3 𝑥→3 𝑥→3.. lim 2𝑥 3𝑥 − 1 = lim 2𝑥 lim (3𝑥 − 1). 𝑥→4 𝑥→4 𝑥→4... Polynomial Function 𝑓 𝑥 = 𝑐0 + 𝑐1 𝑥 + 𝑐2 𝑥 2 + ⋯ + 𝑐𝑛 𝑥 𝑛 lim 𝑓 𝑥 = lim 𝑐0 + 𝑐1 𝑥 + 𝑐2 𝑥 2 + ⋯ + 𝑐𝑛 𝑥 𝑛 = 𝑓(𝑎) 𝑥→𝑎 𝑥→𝑎... Remark. Substitute 𝑎 in 𝑓(𝑥) to obtain the limit of a polynomial. function as 𝑥 approaches 𝑎... Evaluate the following: 1. lim 2𝑥 3 + 3𝑥 2 − 1 = 2(23 ) + 3(22 ) − 1 = 27 𝑥→2 2. lim 3𝑥 7 − 5𝑥 4 + 2𝑥 3 + 9 = −1 𝑥→−1...... Summary Limit Theorems Polynomial Function... Substitute 𝑎 in 𝑓(𝑥) to obtain the limit of the polynomial. function as x approaches 𝑎...
