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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Find the slope of the tangent line to the given curve at the point corresponding to the specified value of the parameter.

21. x = ln t, y = 1 + t2; t = 1

To determine

To find: The slope of the tangent line to the given curve at the point corresponding to x=lnt , y=1+t2 and t=1 .

Explanation

Given:

The parametric equation for the variable x is as follows.

x=lnt (1)

The parametric equation for the variable y is as follows.

y=1+t2 (2)

The parametric equation for the variable t is as follows.

t=1 (3)

Differentiate equation (1) with respect to t .

dxdt=1t (4)

Differentiate equation (2) with respect to t .

dydt=2t (5)

Divide the equation (5) by (4).

dydx=2t1t

dydx=2t2 (6)

Substitute t=1 in the equations (1), (2) and (6)

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