The derivative of the function B is given by B′(t)=8e0.2cost , and B(2.2)=4.5 . If the linear approximation to B(t) at t=2.2 is used to estimate B(t) , at what value of t does the linear approximation estimate that B(t)=9 ?

The linear approximation of B(t) at t = 2.2 estimates B(t) = 9 for t = 2.8328

Step-by-step explanation:

b'(2.2) = 8 * e^(0.2cos(2.2)) = 7.1117 and b(2.2) = 4.5. The linear approximation of B(t) at t = 2.2 is

L(t) = 7.1117*(t-2.2) + 4.5

We want t so that L(t) = 9

9 = 7.1117*(t-2.2) + 4.5

4.5 = 7.1117 *(t-2.2)

t-2.2 = 4.5/7.1117 = 0.6327601

t = 2.2+0.6327601 = 2.8328

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for