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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

True or False? In Exercises 79 and 80, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

a b c d d ( x , y ) d y d x = c d a b f ( x , y ) d x d y

To determine
Whether the statement “abcdf(x,y)dydx=cdabf(x,y)dxdy” is true or false.

Explanation

Consider a function,

f(x,y)=x2+y2

Consider the left-side of the provided statement,

abcdf(x,y)dydx=abcd(x2+y2)dydx=ab[x2y+y33]cddx=ab[x2(dc)+(dc)33]dx=[x33(dc)+(dc)33x]ab

Further,

[x33(dc)+(dc)33x]ab=[(ba)3(dc)+(dc)3(ba)3]

Therefore,

abcd(x2+y2)dydx=[(ba)3(dc)+(dc)3(ba)3]

Now, consider the right-side of the provided statement,

cdabf<

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Chapter 14 Solutions

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