The Ultimate Calculus Jeopardy

horizontal asymptotes

100

f(x) = 14x/7x²+4 

When y = 0

*Bottom heavy 

200

f(x) = 19x³/3x²+1

No horizontal asymptote

*Top heavy 

300

y= 12x-6/3x+4 + 2

y= 6

400

y= 5/x+2

y= 3

500

f(x) = 2x+1/3x-5

When y = 2/3

*equal degree

holes

100

f(x)= x²+4x+4/x²+5x+6

find the point

(-2, 0) 

200

f(x)= x²+2x-15/x²+7x+10

find point

(-5, 8/3)

300

y= x²-4/x+2

find point

(-2, -4)

400

f(x)= x²-9/x+3   

find point

(3, 0)

500

y= (x²-16)/3x+4

find point

no hole

simple derivates

100

y= -7x³-3

dy/dx= -21x²

200

y= 4x⁴-3x-6

dy/dx= 16x³-3

300

f(x)= 9x⁵+9x⁴+8x³-7x²-6x

f'(x)= 45x⁴+36x³+24x²-14x-6

400

y= ln (5x²+8x)

y'= 1/5x²+8x (10x+8)

500

y= ln (2x⁶-5x⁵)

y'= 1/2x⁶-5x⁵ (12x⁵-25x⁴)

complex derivates

100

y= (-x-3)⁴

dy/dx= 4(-x-3)³(-1)

200

y= 2 ⁴√8x²+6x

dy/dx= 1/2(8x²+6x)^-3/4(16x+6)

300

y= -3√ cos x

dy/dx= 3sin x/2√cos x

400

-3y²-5= -y³+2x²+y

dy/dx= 4x/3y²-6y-1

500

y= -4+xy= -4y-4x²

dy/dx= -y-8x/x+4

Trig

100

find exact value of cot 5π/4

1

200

convert 210 degrees to radians

7π/6

300

convert 195 degrees to radians

13π/12

400

simplify cotθ/tanθ 

cot²θ 

500

simplify csc²θ /cot²θ 

sec²θ