B Calculus

• A function is an equation that shows how two values are related.
• A limit is the value we get around a point.
• The value of the graph at 2 is 3.
• If there's no gap, every number will be the same.
• The general equation for a limit is the limit of f of x, as x approaches c, equals L, where L will be the value of the y-axis.
• To find the limit of a function, locate c and trace the graph, stopping just before c.
• The left and right limits of a function are similar numbers, which is your limit.
• To find the limit of a function at a specific point, locate c and trace the graph, stopping just before c.
• The limit 𝑥 → 5 𝑓 (𝑥) exists and is equal to 1.
• The limits 𝑥 → 5 − 𝑓 (𝑥) and 𝑥 → 5 + 𝑓 (𝑥) do not match, hence the limit does not exist.
• The limit 𝑥 → 1 𝑓 (𝑥) exists and is equal to −2.
• The limits 𝑥 → 5 − 𝑓 (𝑥) and �� → 5 + 𝑓 (𝑥) are similar.
• The limits 𝑥 → 1 − 𝑓 (𝑥) and �� → 1 + 𝑓 (𝑥) are similar.
• For example, x → 2.
• The limit of 𝑥 → 10 − 𝑓 (𝑥) = 5 can be found by evaluating the function at the left and right limits.
• To evaluate f of c, you look right into the middle of the c value instead of its sides.
• The limit of 𝑥 → 10 + 𝑓 (𝑥) = 𝑢𝑛𝑑 can be found by evaluating the function at the left and right limits.
• The limit of 𝑥 → 8 + 𝑓 (𝑥) = 5 can be found by evaluating the function at the left and right limits.
• The limit of 𝑥 → 8 𝑓 (𝑥) 𝐷𝑁𝐸 can be found by evaluating the function at the left and right limits.
• The limit of 𝑥 → 10 𝑓 (𝑥) 𝐷𝑁𝐸 can be found by evaluating the function at the left and right limits.
• 0 0 0c 0 1 3 4 5 lim 𝑥 → 𝑐 𝑓 ( 𝑥 ) 𝑓 ( 𝑐 ) 0
• c 0 1 3 4 5 lim 𝑥 → 𝑐 𝑓 ( 𝑥 ) 𝑓 ( 𝑐 ) 0
• 0 0 0 2 5 𝐷𝑁𝐸 5 5 5 5 5 4 4 4 𝑢𝑛𝑑c 0 1 3 4 5 lim 𝑥 → 𝑐 𝑓 ( 𝑥 ) 𝑓 ( 𝑐 ) 0
• 0 0 0 2 5 𝐷𝑁𝐸 5c 0 1 3 4 5 lim �� → 𝑐 𝑓 ( 𝑥 ) 𝑓 ( 𝑐 ) 0
• 0 0 0 2 5 𝐷𝑁𝐸 5 5 5 5 5c 0 1 3 4 5 lim 𝑥 → 𝑐 𝑓 ( 𝑥 ) 𝑓 ( 𝑐 ) 0
• 0 0 0 2 5 𝐷𝑁𝐸 5 5 5 5 5 4 4 4 𝑢𝑛𝑑 3 2 𝐷𝑁𝐸 6
• 0 lim 𝑥 → 𝑐 + 𝑓 ( 𝑥 ) lim 𝑥 → 𝑐 − 𝑓 ( 𝑥 )
• The limit of a constant is itself, regardless of the value of c.
• The limit of x, as x approaches c, is c.
• The Constant Multiple Theorem states that lim 𝑥 → 𝑐 𝑘 ∙ 𝑓 ( 𝑥 ) = 𝑘 ∙ 𝐿.
• C lim 𝒙 → 𝒄 𝟐𝟎𝟏𝟖 lim 𝒙 → 𝒄 𝒙 - 2 - 1/2 0 3.14 10 1/3 2018 2018 2018 2018 2018 - 2 - 1/2 0 3.14 10 1/3
• An example of the Division Theorem is lim 𝑥 → 𝑐 𝑓 ( 𝑥 ) = 4 and lim 𝑥 → 𝑐 𝑔 ( 𝑥 ) = − 5, resulting in lim 𝑥 → 𝑐 𝑓 𝑥 𝑔 𝑥 = − 4 57.
• An example of the Multiplication Theorem is lim 𝑥 → 𝑐 𝑓 ( 𝑥 ) = 4 and lim 𝑥 → 𝑐 𝑔 ( 𝑥 ) = − 5, resulting in lim 𝑥 → 𝑐 𝑓 𝑥 𝑔 ( 𝑥 ) = 4 ( − 5 ) = − 206.
• The Division Theorem states that lim 𝑥 → 𝑐 𝑓 𝑥 𝑔 𝑥 = 𝐿 𝑀.
• An example of the Power Theorem is lim 𝑥 → 𝑐 𝑓 ( 𝑥 ) = 5 and lim 𝑥 → 𝑐 𝑓 ( 𝑥 ) = 5 3 = 125, resulting in lim 𝑥 → �� 𝑓 𝑥 𝑝 = 5 3.
• The Power Theorem states that lim 𝑥 → 𝑐 𝑓 𝑥 𝑝 = 𝐿 𝑝.
• The Multiplication Theorem states that lim 𝑥 → 𝑐 𝑓 𝑥 𝑔 ( 𝑥 ) = 𝐿 ∙ 𝑀.
• An example of the Radical Theorem is lim 𝑥 → 𝑐 𝑓 ( 𝑥 ) = 9 and lim 𝑥 → 𝑐 𝑓 ( 𝑥 ) = 9, resulting in lim 𝑥 → 𝑐 𝑓 𝑥 𝑔 𝑥 = 9 𝑛 𝐿.
• The Radical Theorem states that lim 𝑥 → 𝑐 𝑛 𝑓 ( 𝑥 ) = 𝑛 𝐿.