Reputation's Bloom

Chapter 26. Red Flag

Chapter 26

Lily

"Dean?" Lily tapped on the boy's arm who was seated beside her at the library.

Dean was in her calculus class and since she was avoiding Gabriel like the pledge, Lily decided it was the best course of action to join Dean's study group. He was sweet enough to invite her when he saw her face fall after their last test. Lily, disheartened over her score, agreed and since then, she had been joining Dean in the library every Thursday night.

"What's up?" Dean looked up from his text book. His curly brown hair fell over his eyes, stopping over the rim of his classes. His crooked nose was slightly red from the cold he was recovering from and his old band t-shirt looked as if he had been cherishing it for generations.

"Question six," Lily slid her notebook toward him. "What am I doing wrong?"

Dean sighed and pushed his glasses back on to his nose, "Let's see."

He scanned the problem, his fingers tapping lightly on the edge of her notebook. After a moment, he straightened up and began to explain, the gears in his brain turning faster than his voice could keep up.

"Okay, so for question six, you're dealing with a limit approaching infinity, right? So first, you want to look at the highest power of x in both the numerator and denominator, because that's going to tell you how the function behaves as x gets really large. Now, since this is a rational function, we need to apply L'Hopital's Rule if it's indeterminate, but only after confirming—"

Dean's words flew out at lightning speed, his hands gesturing wildly as he explained. His eyes lit up with enthusiasm, but Lily could feel herself getting lost in the rapid-fire math jargon. She blinked, trying to focus, but it was like being swept up in a tidal wave of numbers and theorems she couldn't grasp. Her mind wandered, catching on random details—the way Dean's crooked nose twitched slightly when he was concentrating, or the fact that his glasses kept sliding down no matter how many times he adjusted them.

"...And once you differentiate both the top and bottom, you'll get this expression here," Dean continued, scribbling equations in the margin of her notebook. The numbers seemed to blur together, and Lily's head started to swim. He was talking so fast, she could barely process a single word, let alone the entire explanation.

"Wait, hold on," Lily interrupted, her brow furrowing as she tried to follow the cascade of terms flying at her. "What does differentiating both sides do again?"

Dean blinked at her, pausing for a split second before launching right back into his explanation. "Oh, right! So differentiation helps you determine the rate of change of the function as x approaches infinity. It's key for solving these kinds of limit problems because—"

There he went again. Lily nodded politely, pretending to absorb the information while internally panicking. The math made no sense, and Dean's excitement, while endearing, was only making it harder to keep up.

Eventually, Dean stopped and looked at her expectantly, his grin widening as if he had just revealed the key to solving all of calculus. "So, does that make sense?"

Lily stared at the mess of numbers and symbols on her notebook, completely at a loss. She opened her mouth to answer, but no coherent words came out. Instead, she just nodded slowly, offering him a weak smile. "Uh... yeah. Totally."

"Cool," Dean smiled. "Hey, I'm going to go get some tea from the cafe. You want anything?"

"No," Lily shook her head. "But thank you.....I'll just try number six again."