If f'(x)= and f(1)=5, then f(3)=
(a)1.230
(b)3.585
(c)6.230
(d)8.535
(e)11.230

E

Step-by-step explanation:

Since the given expression is an elliptic integral, it's not easy to find F(x) explicitly. However, if we use a linear approximation, we can try to estimate F(3), though it won't be too close, since 3 is not very close to 1.

At the point (1,5) the slope of the tangent line is F'(1) =

So, using that line,

F(3) = F(1) + F'(1)(3-1) = 5+2 = 7.828

Well, that didn't work out too well.

So, let's pull out our handy integral calculator, and we find that

But, we know that F(1) = 5. So we need to add C = 3.889

Now, integrating again,

Oops. I messed up the limits, but you get the idea.

first anwser choice.

step-by-step explanation:

the greater/less or equal to symbol (> or < with the line at the bottom) is a closed/filled in circle.

-5c + 2 _< _27

subtract from both sides by 2

-5c _< _ 27

divide both sides by -5

c _< _ 5.4

flip the inequality sign

c _> _5.4

the only possible answer that would match the simplified inequality is the first answer choice

1; 35 is the ratio

step-by-step explanation: