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Mathematics

Emmanuel Iwara(Tutor)
29-02-2016 12:26:00 +0000

Good day all

This session has ended for today

The concept of Limit is the most fundamental in mathematics often tested on JAMB and other exams. so lets take a quick look into this topics.

Differentiation. - The derivative is the instantaneous rate of change of a function with respect to one of its variables. This is equivalent to finding the slope of the tangent line to the function at a point.

Limit in calculus - In mathematics, a limit is the value that a function or sequence "approaches" as the input or index approaches some value. Limits are essential to calculus (and mathematical analysis in general) and are used to define continuity, derivatives, and integrals.

Example lim f(x) = 4
x→ 2

Is the notation for the limiting value of f(x) as x approaches 2 from the left.

Example 2.Evalute lim (7- 2x + 5x2 -4x3)
x→ 2

Solution

lim [7 -2(2) + 5(2)2 -4(2)3 ] x→ 2 ----------------------------(1)

that is putting (2) where we find x in equation (1)

= 7- 4 + 20 -32

= -9

Example 3. Evalute lim(x2 + 5x + 9 )/(2x2 -3x + 15)
x→ 0 S0lution

Lim (x2 + 5x + 9)/(2x2-3x + 15)
x→ 2

Putting the value of (0) in the place of x above,we have

= (0 + 0 + 9)/(0 + 0 + 15)

9/15

= 3/5.

Example 3.Evalute lim (x2- 25)/(x - 5)
x→ 5
Solution

Applying difference of two squares, x2 - 25 = (x+5)(x-5)

lim (x2- 25)/(x - 5)
x→ 5
= (x+5)(x-5) / (x-5)

= [x+5] Since x approaches 5, we have

5+5 = 10

Example 4. Evalute Lim (x2 - 16x) / (2x2 + 4x )
x→∞ Solution

Since x tend to infinity, we have to divide by the highest power of x

(x2/x2 -16x/x2)/(2x2/x2 + 4x/x2)

= 1 - 16/x ÷2 +4/x

But 16/x as x tend to ∞ is zero.then we havess

= 1/2

Now see if you can try solving the following past jamb questions;

1.Evalute Lim (x2 - 16)/(x-4)
x→ 4

2.Evalute Lim [(x+3)(3x-3)(2x+3)]
x→ 0

3.Evalute Lim (x-2)(x2 + 3x -2) / (x2 - 4)
x→ 2

4. Evalute lim (x2-1) / (x + 1)
x→ 2

Don't forget to fill our the survey after the session:
Survey Feedback Link - http://goo.gl/forms/Tasr40Ck1Z

• Omotayo Olalekan

1. = 8

0 29-02-2016 12:42:00 +0000

• Omotayo Olalekan

2. = -3

0 29-02-2016 12:46:00 +0000

• Omotayo Olalekan

3. = 8/4 = 2

0 29-02-2016 12:50:00 +0000

• Omotayo Olalekan

4. = 1

0 29-02-2016 12:53:00 +0000

• olusegun tosino

ur number Girlly

0 29-02-2016 13:03:00 +0000

• Emmanuel Iwara(Tutor)

@Omotayo thanks for solving, but i think your no.3 need to be solve again.

0 29-02-2016 14:06:00 +0000

• Omotayo Olalekan

Oohh! Wait. I don't know there is / in between the question no 3

0 29-02-2016 14:08:00 +0000

• Emmanuel Iwara(Tutor)

@Olusegun am yet to see your solutions, am waiting

0 29-02-2016 14:14:00 +0000

• Emmanuel Iwara(Tutor)

Hello class are we there! please someone should help me with solution of ( x^3 -27) / (x-3) as x tend to 3.

0 29-02-2016 14:20:00 +0000

• Emmanuel Desire

tayo can u help out number 2's formula

0 29-02-2016 14:22:00 +0000