Last day for week 3

tangent lines

100

find the equation of the line tangent to y = x² at x = 0

what is y = 0

200

find the equation of the line tangent to x + 1 at x = 3

what is x + 1

300

what is the equation of the line tangent to x² + 3x at x = 2

y - 10 = 7(x - 2)

400

what is the equation of the line tangent to x² + y² = 25 at (3, 4)

what is y - 4 = -3/4(x - 3)

500

what is the equation of the line tangent to x³ + y³ = 6xy at the point (3, 3)

what is y - 3 = -(x - 3)

higher order derivatives

100

second derivative of x³

what is 6x

200

third derivative of sin(x)

what is -cos(x)

300

4th derivative of e^2x

what is 16e^2x

400

second derivative of x² ln(x)

what is 3 + 2ln(x)

500

third derivative of x³e^x

what is x³e^x + 9x²e^x + 18xe^x + 6e^x

related rates

100

A balloon is being inflated so that its radius increases at a rate of 2 cm/s. At what rate is the volume increasing when the radius is 5 cm?

what is 200 pi

200

Water is being poured into a cylindrical tank with radius 3 m at a rate of 4 m³/min. How fast is the water level rising?

what is 4/9pi

300

A 10-foot ladder is leaning against a vertical wall. The bottom is sliding away at 1 ft/s. How fast is the top sliding down when the bottom is 6 feet from the wall?

what is -3/4

400

A conical tank with radius 2 m and height 4 m is being drained at 3 m³/min. At what rate is the water level falling when the water is 3 m deep?

what is -4/3pi

500

A camera is located 20 m away from a straight road. A car drives along the road at 30 m/s. At what rate is the camera’s angle changing (the rate it must rotate) when the car is 40 m from the point on the road closest to the camera and driving away from the camera?

what is 3/10 

chain rule

100

derivative of sin(x² + 5)

What is 2x cos(x² + 5)

200

derivative of e^{ln(x^3 + 2x^2 + 3x + 4)}

what is 3x^2 + 4x + 3

300

find the derivative of e^sin(cos(x))

what is -cos(cos(x)) * sin(x) * e^sin(cos(x))

400

find the derivative of sin(x²) * tan(cos(x³ + x²))

what is -sin(x²) * sec²(cos(x³ + x²)) * sin(x³ + x²) * (3x² + 2x) + tan(cos(x³ + x²)) * cos(x²) * 2x

500

find the derivative of e^{(x + 2)^2} / sin(cos(x))

what is (sin(cos(x)) * e^{(x + 2) ^ 2} * 2(x + 2) - e^{(x + 2)^2} * cos(cos(x)) * -sin(x)) / (sin(cos(x)))2

miscellaneous

100

compare 50⁵¹ and 51⁵⁰

What is >

200

how many digits are in 2¹⁰⁰

what is 31

300

you have a plastic knife. What is the most amount of pieces you can cut the following objects into with 3 cuts? Pizza, pie, cheese, weight plates(metal), all of these are a circle from a bird's eye view.

What is 7, 7, 8, 1

400

John goes north 100m then goes east 100m and finally goes south 100m, what is the closest he can get to his initial position (explanation required to get the points)

what is 0m

500

play a game with me, if you win you get the points

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