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Unformatted text preview: ( x ) + v ( x )) d) f ( x ) = g ( u ( x ) /v ( x )) Comments: Should I have written f ( x ) = g ( u ( v ( x ))) in a) above as f ( x ) = g u v ( x ) ! to make the question clearer and more fun typographically? By the way, real computations similar to these denitely arise in elds as widely separated as thermodynamics and economics. 7. Let f be the function such that f ( x ) is the value of the sine of an angle which measures x degrees . (NOTE: For most values of x , f ( x ) 6 = sin x . Why not?) Let g be dened similarly for cosine. a) Express f and g in terms of sin and cos. b) What is df dx ? What is dg dx ? (Hint: Use part a) and the chain rule.) c) Express df dx and dg dx in terms of f ( x ) and g ( x ). (No mention of sin or cos allowed.) d) Is it still true that ( f ( x )) 2 + ( g ( x )) 2 = 1? e) Why dont we use degrees in calculus?...
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This note was uploaded on 04/11/2011 for the course MATH 1400 taught by Professor Grether during the Spring '08 term at North Texas.
- Spring '08