"Let f(x) = x \ln x, and let the function g(x) be defined as:
g(x) = \int_1^x f(t) \, dt = \int_1^x t \ln t \, dt
(a) Find an explicit expression for g(x).
(b) Determine the value of g{\prime}(x) and verify that it matches f(x).
(c) Evaluate the limit:
\lim_{x \to 0^+} \left( x \ln x \right)."
That was the calculus equation Zoey had written out on the board.
For a moment, seeing her stagger to the board full of confidence made Kate's heart skip a beat.
She was able to nail the role of Brielle Sloane on her first try—could she also be good at calculus?
But over the next few minutes, Kate almost laughed at the gibberish Zoey had scribbled all over the board.
Not only did she deviate completely, but it was also so meaningless she doubted even the dumbest student in class could make sense of it.
To top it off, Zoey was scribbling so seriously, like she actually knew what she was writing.
It was too hilarious.
"And done," Zoey mummed, turning to return the marker to the table.
Gary Garfield took one look at the board and thinned his lips.
Utter gibberish.
Good thing he hadn't expected much. She was from the countryside, anyway.
"Listen up, class. This school hadn't expected me back so soon, so another class was already scheduled for today with class B. Starting next week, everything will be back to normal, and we'll return to general classes."
Hearing him, Zoey was perplexed.
Why was he just ignoring her? She had given it her all to think up the worst possible solution to that question, and he wasn't even calling her out?
What a bummer.
Sighing inwardly, she glanced around the class.
She figured if she showed her lack of intellect today, Kate would lay off her for a while. But if this teacher wasn't going to play along, her genius plan would be ruined.
Just a few seats away from her, Kate was also fuming.
This was the second time he was casually letting her off.
Why? He couldn't have developed a soft spot for her so easily already… right?
No. That probably wasn't it. Until a moment ago, he didn't even know she existed.
Turning to the board, Gary picked up the wipe and erased everything Zoey had written, chiding her without turning, "Return to your seat and pay closer attention. At this rate, you might fail calculus in your CSAT."
Simultaneously, Zoey and Kate's eyes lit up in relief.
"CSAT? That's thinking too far, teacher. Sister didn't even want to continue high school until our parents forced her to," Kate laughed.
"It's good she doesn't intend to. If Mr. Garfield said something like that, I can only imagine how awful she must be," Natalie added, elated, leaning forward and propping up her hand with her arm.
Even she was bad at calculus, yet he had never said anything like that to her.
If Zoey got such a remark, then she must be so terrible.
Hmph! How dare she put that much cake in her hair yesterday?
Because of that stupid cake, she spent hours last night trying to get everything off. Then early this morning, she had to race down to the salon to deal with the remnants.
Feeling the scornful looks being thrown her way, Zoey beamed inwardly and walked back to her seat, her face expressionless.
Calculus was a vital part of their studies.
Being in that house was depressing, so she'd be sure to suggest to her parents later that they send her to cram school once Kate reported her.
Being away from Kate and her biological parents was a bliss she couldn't wait to have.
Thinking she partially subdued Zoey this time, Kate returned to class triumphantly.
The rest of the classes breezed by, and soon, it was time for lunch.
The second the bell rang, a figure darted into the classroom.
"The craziest thing just happened! Dylan Berschwith asked his minions not to touch me!"
"He said something about how he was only letting me go because he's in a good mood. But that actually scares me. I've never seen that punk in a good mood."
It was Austin and he was babbling as usual.
But Zoey had something else in mind and beckoned onto him, "I've been thinking, does your Cross family have a ton of expensive cars?"
"Mhm." Though confused by the sudden deviation, he nodded.
"Have you ever considered selling the car that brings you to school every day?"
"I have. Unfortunately, no one will buy a car registered to my family without a signature from them on the sale document."
Zoey leaned toward his ear, whispering, "What about selling it part by part?"
His eyes lit up almost immediately but they dimmed the next second.
"Wait, doesn't that mean I'll have to walk to school every day?"
She shook her head, smiling sheepishly. "Not at all. I may not know much about cars, but I know you'd be able to buy a flashy motorcycle with the money and eat good food every day for a few months. As long as we don't feast, we'll be fine."
He went silent, eyes twinkling as he seriously considered it.
The motorbike did seem cool. It was definitely better than being stuck in that stuffy car every morning.
Just as he was deep in thought, Zoey suddenly shifted, her hands darting toward his neck.
She tugged him by the tie, roughly yanking him out of the way using it.
As he choked on the tightness around his neck and turned to her in surprise, he was taken aback to see a shocking sight.
"What? If your hair didn't get enough cake last night, you could've just asked politely instead of trying to sneak up on me."
It had been almost five minutes since the bell rang, hence, they were only a few students left in the classroom at this moment.
Even though they had been hurrying to leave just moments ago, they froze in place when they saw Natalie Langley being held by the throat, a huge pile of cake smeared into her hair by Zoey.