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Math 1400 - Quiz #1AFall 2009: 11.2 - 11.4 Row Name f.1-)t.--e-c_tA----t-t--"-}

This quiz is due on Friday, October 16 in class. Show your Calculus work.

Score:10

Ql: A mathematical model for the average of a group of people learning to type through instruction and practice2 hours a day, 5 days a week, is given by

N (t) = 10 + 6 ln t t > 1

where N(t) is the number of words per minute typed after t hours of instruction and practice. What is the

rate of learning after 10 hours of instruction and practice? Show your work.

1

IA/ r( MI) = .,..f_ _,. 14-167‘)-/J A. 41.:Q7/ 6 6,6,

Q2: Find the derivatives and simplify. Those emphasized with * use , at some step, the chain rule. Thisinformation will not be given to you on the test.

A. f (x) = x 5 + + 2.35

7(x) == -5)C

'00 6-x_ 4 + .•

4x + 3 GL.Ah°-

B. )1 2x + 1

C3t.thc.

C. r(z) = 3z • In z P/,0 out 14.(F.s F . s f-- F"--S

32-

D.* p (r) = (3r 2 - 5)4

PCO ==. 4(3r L-5) (31-2.-.5 )1

(3r-- 5)3 r)

E.* h(t) - 0 At r f.F, s

II it - (e--°./t)/-°./

=I-- 3 e.--°-rt

h. co 0 s e-Thrt .1_ 3 e . / .6 0-€)-1)'16(--,03-t +3)

pi( r)

= x2Find the derivative of f (x) as (1) you learned in Chapter 10 and (2) using the Quotient Rule.

T(2) f (x) = 5 -6 Use Quotient Rule

V- 1(x) - 16' T —

Y- -4 (o) _ x cs)^)

/k- 3

5(1) f (x) = = 5x-2

( x-3

c), X

e - e x-X 2-

CC1 wr

6 ,T T

Q3: Find the derivative two ways and show that the answers are the same.

Find the derivative of g (x) = 11-xx using (1) the Quotient Rule and (2) using the Product Rule.

X 2-

e. N4x C

k z.

Math 1400 - Quiz #1A Score:

Fall 2009: 11.2 - 11.4 Row Name 10

This quiz is due on Friday, October 16 in class. Show your Calculus work.

Ql: A mathematical model for the average of a group of people learning to type through instruction and practice2 hours a day, 5 days a week, is given by

N (t) = 10 + 6 In t t > 1

where N(t) is the number of words per minute typed after t hours of instruction and practice. What is the

rate of learning after 10 hours of instruction and practice? Show your work.

Q2: Find the derivatives and simplify. Those emphasized with * use , at some step, the chain rule. Thisinformation will not be given to you on the test.

f (x) = x 5 + + 2.35

4x + 3y =

2x + 1

C. r(z) = 3z • In z

D.* p(r) = (3r 2 - 5)4

E.* h(t) = 3te-"t

5

Q3: Find the derivative two ways and show that the answers are the same.

A. Find the derivative of f (x) = -1 as (1) you learned in Chapter 10 and (2) using the Quotient Rule.x2

5(2) f (x) = Use Quotient Rule(1) f (x) =

5—x2

= 5x-2

exB. Find the derivative of g (x) = —x using (1) the Quotient Rule and (2) using the Product Rule.

(1) (2)