{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chap2_Sec7

# Chap2_Sec7 - TANGENTS Let Q approach P along the curve C by...

This preview shows pages 1–6. Sign up to view the full content.

Let Q approach P along the curve C by letting x approach a . square4 If m PQ approaches a number m , then we define the tangent t to be the line through P with slope m . square4 This m amounts to saying that the tangent line is the limiting position of the secant line PQ as Q approaches P . TANGENTS

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Notice that, as x approaches a , h approaches 0 (because h = x - a ). square4 So, the expression for the slope of the tangent line becomes: 0 ( ) ( ) lim h f a h f a m h + - = TANGENTS 2. Definition
Find an equation of the tangent line to the hyperbola y = 3/ x at the point (3, 1). TANGENTS Example 2 (2.7)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Suppose that a ball is dropped from the upper observation deck of the CN Tower, 450 m above the ground. a. What is the velocity of the ball after 5 seconds? b. How fast is the ball traveling when it hits the ground? VELOCITIES Example 3 (2.7)
In fact, limits of the form arise whenever we calculate a rate of change in any of the sciences or engineering— such as a rate of reaction in chemistry or a marginal cost in economics.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}