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industrial mathematics - i

industrial mathematics - i. TIP – FTP – UB. limits. Industrial mathematics - i. What is limits ?. Let’s see the equation Solution : (1) approach the equation from x < 1 (2) approach the equation from x > 1 We can conclude that = 4.

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industrial mathematics - i

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  1. industrial mathematics - i TIP – FTP – UB

  2. limits Industrial mathematics - i

  3. What is limits ? • Let’s see the equation • Solution : (1) approach the equation from x < 1 (2) approach the equation from x > 1 We can conclude that = 4. Limit is a value that explains the characteristic of a function as the input is approaches some value.

  4. The limit theorem • If and (1) = k (2) = = A B (3) = = A x B (4) (5) = An (6)

  5. The limit theorem • Try these examples ! (1) Limx2 x2(2x – 3x) (2) Limx2(5x2 + 3x – 2)2 (3) Limx2 (4x + 4)2 (4) Limx2

  6. Solution of limits • Steps to find the solution of limits function : (1) Direct substitution (2) Factorization (3) Divide with the highest powers variable (1) Direct substitution Find the limit value of ! a. = b. = -

  7. Solution of limits (2) Factorization Try ! = 0 / 0 = – (needs to be factorized !) = = = = -2

  8. Solution of limits (3) Divide with the highest power variable Try !

  9. Forms of limits • Limit Forms (1) Limit of ~/~ form then : a. R = a/p if n = m  b. R = 0 if n < m  c. R = ~ if n > m  

  10. Forms of limits • Limit Forms (2) Limit of ~ – ~ form 1. R = ~ if a > p 1. R = ~ if a > p 2. R = 0 if a = p 2. R = if a = p 3. R = – ~ if a < p 3. R = – ~ if a < p

  11. Thank you Industrial mathematics - i

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