11-09-2014 (Calculus Lecture 5th semester BBA)

11/09/2014

Example:

Property 01:

F(X) = C Limit (Xàa) (C) = C

Limit (Xà3) =  (100)  = 100

Property 02:

F(X) = Xn Limit (Xàa) (X)n = an

Limit (Xà10) = (-2)3  = 8

Property 03:

F(X) = C.F(X) Limit (Xàa) (C) = C . F(X) è C. Limit (Xàa) (X)

Limit (Xà10) = (5 X2) è 5  Limit (Xà10) = (X2)  = 5(10)2= 500

Property 04:

{F(X) ± G(X)} Limit (Xàa) {F(X) ± G(X)} Limit (Xàa) F(X) ± Limit (Xàa) G(X)

Limit (Xà-1) =  (X5 - 10) Limit (Xà-1) =  X5 - Limit (Xà-1) =  10 (-1)5 – 10 è - 11

Property 05:

{F(X) . G(X)} Limit (Xàa) {F(X) . G(X)} Limit (Xàa) F(X) . Limit (Xàa) G(X)

Limit (Xà4) =  [(X2 - 5).(X + 1)] Limit (Xà4) = (X2 - 5). Limit (Xà4) =  (X + 1) [Limit (Xà4) =X2 - Limit (Xà4) =5].[ Limit (Xà4) =X + Limit (Xà4) = 1] [42 - 5].[4 + 1] è [16 - 5].[5] è 11(5) è 55

Exercise:

Q: 01	Q: 02
Limit (X à 0) = (3X2 – 5X + 3) Limit (X à 0) 3X2 – Limit (X à 0) 5X + Limit (X à 0) 3 3(0)2 –5(0) + 3 0 – 0 + 3	Limit (X à 2) = (2X3 – 10X) Limit (X à 2) 2X3  – Limit (X à 2) 10X 2(2)3  –10(2) 16 – 20
Answer: 3	Answer: – 4
Q: 06	Q: 07
Limit (X à -4) = 250	Limit (X à 0) = 175
Answer: 250	Answer: 175
Q: 09	Q: 10
Limit (X à 1) = (3X3 + 2X2 + X) Limit (X à 1) 3X3 + Limit (X à 1) 2X2 + Limit (X à 1) X 3(1)3 + 2(1)2 + 1	Limit (X à -2) = (-X4 + 8X2) Limit (X à -2) -X4 + Limit (X à -2) 8X2 -(-2)4 + 8(-2)2
Answer: 5	Answer: 16
Q: 11	Q: 15
Limit (X à -2) = (-X3 + 5X2 + 10) Limit (X à -2) -X3 + Limit (X à -2) 5X2 + Limit (X à -2) 10 -(-2)3 + 5(-2)2 + 10	Limit (X à -3) = (6X3 + 2X) (5X – 10) [Limit (X à -3) = (6X3 + 2X)].[ Limit (X à -3) = (5X – 10)] [Limit (X à -3) 6X3 + Limit (X à -3) 2X] [ Limit (X à -3) 5X  – Limit (X à -3) 10] [6(-3)3 + 2(-3)].[5(-3) – 10] è [-168].[-25]
Answer: 38	Answer: -193