LIMITS & DIFFERENTIATION
Evaluate: lim(x→2) (x² − 4)/(x − 2)
Answer: 4
The position of a particle is: s(t) = t³ − 6t² + 9t
Find the particle’s velocity at t = 2.
Answer: −3 units/time
Convert to the opposite form: 2^5 = 32
Answer: log_2(32)= 5
Solve for x: log_2(x)=8
Answer: x=256
This US state is made entirely of islands
What is Hawaii?
Evaluate: lim(x→0) sin(5x)/(3x)
Answer: 5/3
Find f′(x) if: f(x) = √(x² + 4)
Answer: f′(x) = x/√(x² + 4)
Convert to the opposite form: log_7(49)=2
Answer: 7^2=49
Evaluate: log_3(243)
Answer: 5
This is the place where honey is made, but it’s also the name given to the devoted fanbase of which singer?
What is Beyonce (bey hive)?
Find a so that f(x) is continuous at x = 3: f(x) = x² + a, if x < 3 f(x) = 2x + 4, if x ≥ 3
Answer: a = -1
Find dy/dx: x² + y² = 25
Answer: dy/dx = −x/y
Convert to the opposite form: log_3(81)=4
Answer: 3^4=81
log(x^3/y)
Answer: 3log(x)-log(y)
This officer offered to buy the whole club food and hasn't done so
What is : Ansh Shah?
Using the limit definition of the derivative, find f′(x) for: f(x) = x² + 3x
Answer: f′(x) = 2x + 3
Find f′(x) if: f(x) = sin(x² + 3x)
Answer: f′(x) = cos(x² + 3x)(2x + 3)
Solve for (x): log_2(x)=6
Answer: x=64
Simplify:log_2(32)-log_2(4)
Answer: 3
This movie went viral in the summer of 2026, all starting with a broken stick.
Find the equation of the tangent line to: f(x) = x³ −2x
at x = 1.
Answer: y = x − 1
Given f(2) = 5 and f′(2) = 4, find: (f⁻¹)′(5)
Answer: 1/4
Solve for x: 3^x=81
Answer: x=4
Solve for x: log_3(x)+log_3(9)=5
Answer: x=27
He is credited with writing “The Star-Spangled Banner,” but he didn't compose its melody; the tune was actually adapted from an older British song.
Who is Francis Scott Key?