Calculus in Surveying

Question 1

Constants

Answer 1

Derivative of a constant is zero

Question 2

Exponents

Answer 2

The derivative of x to the power of n is n times x to the power of n-1

Question 3

Products of constants and variables

Answer 3

The derivative of the product of a constant and a variable is the product of that constant and a derivative of the variable

Question 4

Sums of functions

Answer 4

The derivative of the sum of a number of differentiable functions is the sum of their derivatives

Question 5

Products of functions

Answer 5

The derivative of the product of differential functions

Question 6

Formula for high point of vertical curve

Answer 6

x = (g1 * L) / (g2 - g1) where x is distance from beginning to HP, g1 is PVC, g2 PVT, L is length of curve

Question 7

Formula for low point of a curve

Answer 7

x = (g1 * L) / (g1 - g2) where x is distance from beginning to HP, g1 is PVC, g2 PVT, L is length of curve