11th grade calculus pleas help 😭🙏

[coarse stratus]

im so cooked (im dookie at calculus)

[tame crater]

Good luck bro, you’ll need it

[dusty plover]

@coarse stratus Work on each floor function seperatley. For different domains for x in [0,8], find the value for each floor function.

Example for the first floor function:
for 0 <= x < 2, it's equal to 3. However for 2 <= x < 4, it's equal to 4.

Once you've done this for both functions, subtract the values over [0,8] and I'd even quickly sketch it out! The non continuous points will therfore be easy to see.

[obsidian shell]

I agree with @dusty plover on the advice on sketching.

I would start by sketching $y = \frac{x}{2} + 3$

and then (in another colour) $y = \left[\frac{x}{2} + 3\right]$

Focus primarily on the interval $x\in[0.,8]$.

Then, repeat for $y = \sqrt{x}$ and $y = \big[\sqrt{x}\big]$

Then, you can sketch $y = f(x)$ and find all elements of $S$.

FYO, I find five $x$-values on $0 \le x \le 8$ where $f(x)$ is not continuous.

[tight knot]

Jay

[coarse stratus]

i tried

i got 8

that correct?

[dusty plover]

@coarse stratus @obsidian shell
Just by using a graphing calculator I find three x-values on [0,8] where f is not continuous: 1, 2, and 6 **
Therfore the sum we're looking for should be 9**, right?

[obsidian shell]

The domain of x includes its end points

[coarse stratus]

@dusty plover @obsidian shell is this the correct solution?

cant graph it because i suck at graphing

and in my country they dont let us use graphing calculator during exams

[obsidian shell]

You've missed that it is discontinuous at $x=0$ as well, though the sum remains 17.

[tight knot]

Jay