Pre-Calc Homework Solutions 104

Pre-Calc Homework Solutions 104 - 104 dy dx Section 3.7 d...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 104 dy dx Section 3.7 d [sin (x dx 5 [sin (x 4 5 [sin (x 4 16. 5)]5/4 5)]1/4 d sin (x dx (c) Differentiating both sides of the given equation 5) 5) f (x) x 1/3 gives f (x) 1 4/3 x . 3 1 4/3 x , so it must be true 3 5)]1/4 cos (x that f (x) (d) If f (x) 17. x d (x) dx tan y d (tan y) dx dy sec2 y dx 1 cos2 y sec2 y 3 2/3 x 2 6, then f (x) x 1/3 , which matches the given equation. Conclusion: (b), (c), and (d) could be true. 22. (a) If g (t) g (t) 4 4 1 dy dx t 4, then 4) t 3/4 18. x d (x) dx sin y d (sin y) dx dy cos y dx 1 sec y cos y d (4t 1/4 dx 1 , which matches the t 3/4 given equation. (b) Differentiating both sides of the given equation g (t) 1 t 3/4 1 dy dx t 3/4 gives g (t) 4 4 3 7/4 t , which is not 4 consistent with g (t) 19. d (x) dx . t x tan xy 0 0 0 0 (c) If g(t) g (t) t t 3/4 1 d (tan xy) dx d 1 sec2 (xy) (xy) dx dy (sec2 xy)[x (y)(1)] dx dy dx dy dx dy dx 7 16 5/4 t , then g (t) 5 1 t 3/4 1 4t 1/4 and , which matches the given equation. (d) If g (t) 1 1/4 t , then g (t) 4 1 3/4 t , which 16 (sec2 xy)(x) 1 1 (sec2 xy)(y) y sec2 xy y x x sec2 xy 1 cos2 xy x contradicts the given equation. Conclusion: (a) and (c) could be true. 23. x2 d 2 (x ) dx y2 1 d (1) dx 20. d (x) dx x sin y xy d (xy) dx dy x (y)(1) dx 1 (cos y) x) d (sin y) dx dy dx dy dx dy dx d 2 (y ) dx 2x 2yy 2yy y 0 2x x y d dx x y (x)(y ) y2 x y (cos y 1 1 cos y y y x x 1 y cos y y 21. (a) If f (x) f (x) x 3 2/3 x 2 1/3 (y)(1) 3, then 1 4/3 x 3 y x and f (x) which contradicts the given equation f (x) (b) If f (x) f (x) 9 5/3 x 10 x 1/3 . x2 y2 y2 y3 7, then x 1/3 3 2/3 x and f (x) 2 , Since our original equation was x 2 substitute 1 for x 2 y 2, giving y y2 1 . y3 1, we may which matches the given equation. ...
View Full Document

This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Fall '08 term at University of Florida.

Ask a homework question - tutors are online