Calc-pardy

Limits

100

lim x → ∞ 2x¹¹/x⁵⁶

What is 0?

200

lim x → ∞ x¹¹+9x⁸⁴/x⁸⁴

What is 9?

300

lim x → ∞ -x³-x⁶+20/4x³+7x²-40x-70

What is DNE?

400

lim x → ∞ (5x-4)(3+2x²)/(7-3x)(2x²-1)

What is -5/3?

500

lim x → ∞ √36x⁸+19x²+40x³/10x⁴+3x+5x³

What is 3/5?

Derivatives

100

The derivative of y = -5x⁴

What is -20x³?

200

The derivative of y = 1/2x⁴.

What is -2/x⁵?

300

The derivative of f(x) = x/3-5x³.

What is 10x³+3/(3-5x³)²?

400

The derivative of f(x) = (-7x³ - 1 + 2x^-2)(2x² - 3).

What is f'(x) = (−21x²−4x^-3)(2x²−3)+(4x)(−7x³−1+2x^-2)?

500

The derivative of f(x) = 2 cos [(x²-2)⁴].

What is f'(x) = −16x(x²−2)³ sin [(x²−2)⁴] ?

Logarithms

100

The value of log₄64.

What is 3?

200

The value of ln e⁴.

What is 4?

300

The value of x in log₃x = -5.

What is 1/243?

400

The values of x when log_-2x-2(x²-10x-20) = 2

What is -2 or -4?

500

The expanded logarithm of log x⁴/zy³.

What is 4 log x - log z - 3 log y?

Linear Asymptotes

100

The horizontal asymptote of f(x) = 10/3x + 5.

What is y = 5?

200

The horizontal asymptote of f(x) = x + x² - 8x³.

What is ∞ ?

300

The horizontal asymptote of f(x) = x⁵-2x³/6x+4x².

What is -∞ ?

400

The vertical asymptote of f(x) = 2x²-50/3x²+11x-20.

What is x = 4/3?

500

The horizontal asymptote of f(x) = 2x³-e^-x/3x²+3x³.

What is y = 2/3?

Trigonometry

100

sin²x+cos²x

What is 1?

200

1 - sin²x

What is cos²x?

300

The ratio between the lengths of each side in a 30:60:90 triangle.

What is 1:√3:2?

400

DAILY DOUBLE: The derivative of (-5cos(-x)).

What is -5sin(-x)?

500

The value of sin θ if an angle's terminal side passes through (-5, -12).

What is -12/13?