1. A Preview of Calculus

Question 1

What is Calculus?

Answer 1

1. The mathematics of change
2. A field of mathematics with important applications in science, engineering, medicine, and business.

Question 2

What is the 1st major pitfall in learning Calculus?

Answer 2

1. It requires a good working knowledge of Algebra and Precalculus

Question 3

What is the 2nd major pitfall when learning Calculus?

Answer 3

1. It requires a great deal of practice

Question 4

What is the slope m of the nonvertical line passing through (x₁, y₁) and (x₂, y₂)?

Answer 4

Question 5

What is the point-slope equation of the line passing through the point (x₁, y₁)?

Answer 5

y - y₁ = m(x - x₁)

Question 6

What is the classic tangent problem?

Answer 6

• The calculation of the slope of the tangent line to a parabola at a specific point

Question 7

What is the 1st step to find the slope and an equation of the tangent line to the parabola y = x² at the point P = (2,4)

Answer 7

1. Let Q = (x,x²), x does not = 2, be another point on the parabola.

Question 8

What is the 2nd step to find the slope and an equation of the tangent line to the parabola y = x² at the point P = (2,4)

Answer 8

2. The slope of the line joining P and Q is as follows:

Question 9

What happens when the point Q approaches P in the classic tangent line problem?

Answer 9

The line joining P and Q approaches the tangent line at P

Question 10

What happens algebraically when x approaches 2 in the classic tangent line problem?

Answer 10

The slope of the line joining P and Q approaches the slope of the tangent line at P

Question 11

How do we symbolically represent the limit argument in the classic tangent line problem?

Answer 11

Question 12

What is the equation of the tangent line to the parabola at (2,4)?

Answer 12

*y - 4(x - 2)
*Or y = 4x - 4

Question 13

Find the equation of the tangent line to the parabola y = x² at the point (3,9)

Question 14

Find the equation of the tangent line to the parabola y = x² at the point (0,0)

Question 15

Find the equation of the tangent line to the cubic polynomial y = x³ at the point (-1,-1)