
[ended]Mathematics Tutoring Session #10 Differential Calculus(Limit) on Mon. 29th Feb., 2016 @ 3:00  4:00pm
Mathematics
Emmanuel Iwara(Tutor)
29022016 12:26:00 +0000Good 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 + 5x^{2} 4x^{3})
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(x^{2} + 5x + 9 )/(2x^{2} 3x + 15)
x→ 0 S0lution
Lim (x^{2} + 5x + 9)/(2x^{2}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 (x^{2} 25)/(x  5)
x→ 5
Solution
Applying difference of two squares, x^{2}  25 = (x+5)(x5)
lim (x^{2} 25)/(x  5)
x→ 5
= (x+5)(x5) / (x5)
= [x+5] Since x approaches 5, we have
5+5 = 10
Example 4. Evalute Lim (x^{2}  16x) / (2x^{2} + 4x )
x→∞ Solution
Since x tend to infinity, we have to divide by the highest power of x
(x^{2}/x^{2} 16x/x2)/(2x^{2}/x^{2} + 4x/x^{2})
= 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 (x^{2}  16)/(x4)
x→ 4
2.Evalute Lim [(x+3)(3x3)(2x+3)]
x→ 0
3.Evalute Lim (x2)(x^{2} + 3x 2) / (x^{2}  4)
x→ 2
4. Evalute lim (x^{2}1) / (x + 1)
x→ 2
Don't forget to fill our the survey after the session:
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