Math Final Proj w flowers! (BONUS questions at end)

Front

A ladder 10 ft long is leaning against a vertical wall. If the bottom of the ladder slides away from the wall at 1ft/sec, how fast is the top sliding down when the bottom is 6 ft from the wall?

Back

0.75 ft/sec

Front

A wire 10 meters long is to be cut into two square pieces. What length should be used for the circle to MINIMIZE the total area?

Back

10pi/4 + pi

Front

Find the indefinite integral of: ln(x) dx

Back

ln(x) * x - x + C

Front

If ln (x^2 + 1) = 3, then x^2 + 1 = ?

Back

e^3

Front

Find dy/dx if y = sin(x^2 + 3x)

Back

(2x + 3) * cos(x^2 + 3x)

Front

What is the Pythagorean theorem?

Back

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Front

Define the derivative of a function.

Back

The derivative represents the rate of change of a function with respect to a variable.

Front

What is the integral of a constant 'c'?

Back

The integral of a constant 'c' with respect to x is cx + C, where C is the constant of integration.

Front

What is the chain rule in calculus?

Back

The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function multiplied by the derivative of the inner function.

Front

What is the product rule for differentiation?

Back

If u and v are functions of x, then the derivative of their product is given by: (uv)' = u'v + uv'.