Application of Differentiation
1. Find the equation of the normal to the curve y =

where x = 4.
at the point on the curve
[6]

y = 1/2 x + 10.

Step-by-step explanation:

To find the slope of  a tangent to the curve we find the derivative:

f(x) = (x^2 + 8) / (x - 2)

Using the quotient rule:

f'(x) =   (x - 2)(2x) - (x^2 + 8) / (x - 2)^2

= (2x^2 - 4x - x^2 - 8) / (x - 2)^2

= (x^2 - 4x - 8) / (x - 2)^2

At x = 4 , the slope of the tangent

= (16 - 16 - 8) / 4

= -2.

So the slope of the normal = -1/-2 = 1/2.

The equation of the normal is

y = 1/2 x + c

When x = 4, y =  (4^2 + 8)  / 4 -2 =  24/2 = 12, so

12 = 1/2(4) + c

c = 12 - 2 = 10.

The required equation is y = 1/2 x + 10.

when we toss two coin , total possible outcome=[h h, h t, t h, t t]==4

when two coins are tossed for 100 times ,then total possible outcome=

probability of an event =

theoretical probability[two heads ,when two coins are tossed for one time]=

two coins being flipped for 100 times,

theoretical probability that tossing of coin results in two heads=

experimental probability that a coin toss results in two heads ==

probability [ two tails when two coins are tossed ]=1/4

theoretical probability[coin toss results in two tails ] =

experimental probability that a coin toss results in two tails = =

probability [ one head one tail in single throw of two die]=2/4=1/2

theoretical probability that a coin toss results in one head and one tail after 100 flips when two coins are tossed=

experimental probability that a coin toss results in one head and one tail after 100 flips when two coins are tossed=

in theoretical probability we can calculate probability by dividing total possible outcome to total favorable outcome. so it is always lie between 0≤p≤1.

but in experimental probability we count number of times that event has happened, like in above case 1.there will be two heads in each case if we flip two coins 100 times.2.there will be two tails if we flip two coins 100 times.3.there will be 200 head and tail (ht or th) if we flip two coins 100 times.

experimental probability=

so,yes we can calculate experimental probability and we get closer to theoretical probability if we increase the number of trials in an experiment.