Question

Please help! Will FAN AND MEDAL!

f is a differentiable function for all x. Which of the following statements must be true?

I. the derivative with respect to x of the integral from 0 to 4 of f of x, dx is equal to f of x
II. d/dx of integral from x to 4 of f of t d t equals negative f of x
III. the integral from 4 to x of f prime of x, dx is equal to negative f of x

a. II only
b. III only
c. I and II only
d. II and III only

Answer 1

Can you please help? @agent0smith @ganeshie8 @Kainui @mathmale @MrNood @Nnesha @zepdrix

Answer 2

I is correct a believe, due to the fundamental theory of calculus.

Answer 3

III is wrong.

Answer 4

Okay so then my answer is C? Since it is the only one with "I" in it?

Answer 5

It's either A or C I believe.

Answer 6

Not sure why f(t) is in there...

Answer 7

I don't think I is true. The integral from 0 to 4 is a constant, so its derivative is 0

Answer 8

Can you please help me with the one more question? @xGuardians

Answer 9

@peachpi That's incorrect. Why would it be a constant?

Answer 10

@aryana_maria2323 Yes.

Answer 11

FTC, part I:
\[\frac{ d }{ dt }\int\limits_{a}^{x}f(t)dt=f(x)\]

I isn't true because the limits on the integral are both constants
II is true because if you reverse the order of the integral's limits, the result has the opposite sign
III, I'm not entirely sure about

Answer 12

What are the limits of integration if the summation the limit as n goes to infinity of the summation from k equals 1 to n of the product of the quantity of the square of 2 plus 7 times k over n and the quotient of 7 and n is written as a definite integral with integrand x2?

a. 0,2
b. 1,7
c. 2,9
d. 2,7

Answer 13

@xGuardians it's constant because that's a definite integral, which will return a specific number, not a function

Answer 14

On the previous question, I'd lean toward III being false because there's nothing in that integral that would make it negative.

Answer 15

Can you please help me with my new question?

Answer 16

can you write that out with the equation tool?

Answer 17

I did?

Answer 18

if the summation the limit as n goes to infinity of the summation from k equals 1 to n of the product of the quantity of the square of 2 plus 7 times k over n and the quotient of 7 and n is written as a definite integral with integrand x2?

^that's what I'm seeing. Only text

Answer 19

Okay one second

Answer 20

\[\lim_{n \rightarrow \infty}\sum_{k=1}^{n} [2+\frac{ 7k }{ n }]^2 (\frac{ 7 }{ n })\]

Answer 21

sorry, I don't know how to do that