Suppose that while waiting for a big wave, a surfer is being propelled toward the beach in such a way that the distance (in meters) traveled is given by f (t) = 10t2 for 0 ≤ t ≤ 1, where t is in seconds. find the velocity v 1 10 of the surfer at t = 1 10 sec.

The velocity at t=1/10s will be:

Explanation:

The distance in meter as a function of time is:

, for 0 ≤ t ≤ 1 where t is in seconds.

We need to find the velocity of the surfer at .

For this we can use the definition of instantaneus velocity (in it's limit form):

At , we have:

.

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.