   Chapter 2.8, Problem 67E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Let f be the tangent line to the parabola y = x2 at the point (1, 1). The angle of inclination of ℓ is the angle φ that ℓ makes with the positive direction of the x-axis. Calculate φ correct to the nearest degree.

To determine

To find: The value ϕ to the nearest degree.

Explanation

Given:

The tangent line to the parabola y=x2 at (1,1) is l.

The angle of inclination of l is angle ϕ that l makes with positive direction of the x-axis.

Result Used:

Let l1 and l2 be two lines whose slope are m1 and m2 respectively.

The angle ϕ  between l1 and l2 is given by the relation tanϕ=|m1m21m1m2|

Calculation:

Calculate the slope of y=x2.

Derivative of y=x2 is calculated as follows,

dydx=limh0y(x+h)y(x)h=limh0(x+h)2x2h=limh0x2+h2+2xhx2h

Simplify the terms in numerator

dydx=limh0h2+2xh

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 