test 1 soln

# test 1 soln - Calcul diff´ erentiel et int´ egral pour...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

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

Unformatted text preview: Calcul diff´ erentiel et int´ egral pour les sciences de la vie I MAT1730 Test 1 Professeur: Benoit Dionne Question 1 Find the derivative of the following function : f ( x ) = x 4 ln( x ) 2 x + 8 e x . 4 points Solution: We have f ( x ) = g ( x ) /h ( x ), where g ( x ) = x 4 ln( x ) and h ( x ) = 2 x + 8 e x . Since g ′ ( x ) = 4 x 3 ln( x ) + x 4 parenleftbigg 1 x parenrightbigg = 4 x 3 ln( x ) + x 3 = x 3 (4 ln( x ) + 1) , we have f ′ ( x ) = g ′ ( x ) h ( x ) − g ( x ) h ′ ( x ) h 2 ( x ) = x 3 (4 ln( x ) + 1)(2 x + 8 e x ) − x 4 ln( x )(2 + 8 e x ) (2 x + 8 e x ) 2 Question 2 Over the course of a year, the city of Ottawa has its highest average monthly temperature 4 points of 26 ◦ C in August and its lowest monthly average of − 8 ◦ C in February. Assume that temperature varies sinusoidally over a period of one year. Find the parameters in the standard cosine description , i.e., f ( x ) = M + A cos parenleftbigg 2 π P ( t − T ) parenrightbigg , where t is in months, and t = 0 correspond to the month of January. Draw the graph of the function and identify the four parameters A, B, Φ , T in the graph. Give the names of the four parameters. Solution: The mean is M = 26 − 8 2 = 9, the amplitude is A = 26 + 8 2 = 17, the period is 12 months and the phase is T = 7 months. We get the following graph. 2 2 4...
View Full Document

## This note was uploaded on 04/08/2010 for the course MATH MAT1330 taught by Professor Rad during the Spring '10 term at University of Ottawa.

### Page1 / 5

test 1 soln - Calcul diff´ erentiel et int´ egral pour...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online