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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Evaluating Functions of Several Variables In Exercises 1–14, find and simplify the function values. See Example 1.

g ( x , y ) = x y 1 t d t

(a) g(4, 1) (b) g(6, 3)

(a)

To determine

To calculate: The value of two variable function g(x,y)=xy1tdt at x=4 and y=1.

Explanation

Given Information:

The provided two variable function is g(x,y)=xy1tdt.

Formula used:

The integration formula:

tndt=tn+1n+1,n1

Logarithmic properties:

ln|m|ln|n|=ln|mn|,ln|(m)n|=nln|m|

Calculation:

Consider two variable function,

g(x,y)=xy1tdt

Now substitute the value of x=4 and y=1 in g(x,y)=xy1tdt

Therefore,

g(4,1)=411tdt

Apply, tndt=tn+1n+1,n1 in above integral

"

(b)

To determine

To calculate: The value of two variable function g(x,y)=xy1tdt at x=6 and y=3.

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