Clicker Question 1 What is the exact average value of f(x) = 1/x 2 between x = 1 and x = 3? – A....

Clicker Question 1 What is the exact average value of f(x) = 1/x 2 between x = 1 and x = 3? – A. 1/3 – B. 2/3 – C. 2/9 – D. ln(3) – E. ln(3)/2

Upload
toby-richardson
Category

Documents
view
219
download
0

Embed Size (px):

Transcript of Clicker Question 1 What is the exact average value of f(x) = 1/x 2 between x = 1 and x = 3? – A....

Clicker Question 1

What is the exact average value of f(x) = 1/x2

between x = 1 and x = 3?– A. 1/3– B. 2/3– C. 2/9– D. ln(3)– E. ln(3)/2

Clicker Question 2

What is the exact average height of the graph of g(x) = x sin(x2) on the interval [0, ]?– A. 2– B. 2 /– C. 1 /– D. 1– E.

Page 3: Clicker Question 1 What is the exact average value of f(x) = 1/x 2 between x = 1 and x = 3? – A. 1/3 – B. 2/3 – C. 2/9 – D. ln(3) – E. ln(3)/2.

Areas between Curves (1/29/14)

If two curves are described algebraically, we can use the definite integral to compute the area they enclose.

It will be the integral of the upper curve minus the lower curve (by the Difference Rule). Watch out if they cross!

We must, of course, find out where they intersect if no other boundaries are given.

Page 4: Clicker Question 1 What is the exact average value of f(x) = 1/x 2 between x = 1 and x = 3? – A. 1/3 – B. 2/3 – C. 2/9 – D. ln(3) – E. ln(3)/2.

Three Examples

Find the exact area enclosed by f(x) = 2x – x2 and g(x) = -3x .

Find the exact area enclosed by the y-axis, the line y = e2 and the curve y = ex .

Find the area in the first quadrant enclosed by the line y = (1/e)x and the curve y = ln(x)?

Page 5: Clicker Question 1 What is the exact average value of f(x) = 1/x 2 between x = 1 and x = 3? – A. 1/3 – B. 2/3 – C. 2/9 – D. ln(3) – E. ln(3)/2.

Clicker Question 3

What is the exact area in the first quadrant enclosed by the axes and f (x) = 3 - x ?– A. 9 sq. units– B. 9 – 23 sq. units– C. 12 sq. units– D. 10 1/3 sq. units– E. 18 sq. units

Page 6: Clicker Question 1 What is the exact average value of f(x) = 1/x 2 between x = 1 and x = 3? – A. 1/3 – B. 2/3 – C. 2/9 – D. ln(3) – E. ln(3)/2.

Assignment for Friday

Read Section 6.1 On page 427, do Exercises 1, 5, 7, 9, 13, 15,

23 and 25.

$ln x t - Mr. Shewan's Math Classroom · (ln 3)34 3. e7 4. –2e 5. y= ln 5 25 x+ 1+2ln 5 25 6. y=3e 4x!9e4 7. a) 250 b) i) approximately 17.3 h ii) approximately 27.5 h iii) approximately$

ln x t - Mr. Shewan's Math Classroom · (ln 3)34 3. e7 4. –2e 5. y= ln 5 25 x+ 1+2ln 5 25 6. y=3e 4x!9e4 7. a) 250 b) i) approximately 17.3 h ii) approximately 27.5 h iii) approximately

Answers for NSSH exam paper 2 type of questions, based on ... for NSSH exam pa… · 7 (b) Find ln(3 1) 3 2 2 3 1 1 3 1 2 x dx x dx x 8. dx x dx x x c x dx x x 2 1 2 4 2 ln 4 1 2

AP Calculus BC 705 More e^x and ln(x)!

Today: 5.4 General log and exp functions (continued) · You try: Recall loga(x)=ln(x)/ ln(a),sothatd dx loga(x)= 1 ln(a)x. Complete a similar analysis of the graphs of y = loga(x).Namely,

Chapter 4 Exponential and Logarithmic Functions2013/07/31 · xx x xx x xx xx xx 4 or 5 Both values produce true statements. ... 9 ex 107 ln 9 x 2.48 31. 5 5 5 3 1977 659 ln ln659

CHAPTER 5: MAXIMUM LIKELIHOOD ESTIMATIONdzeng/BIOS760/Chapter5_Slide.pdf · 2019-09-29 · MLE deﬁnition Ln( ) = Yn i=1 p (X i); ln( ) = Xn i=1 logp (X i): Ln( ) and ln( ) are called

6. 2 3 5= 7. = 3 - 5homepage.smc.edu/wong_betty/math28/s/C11 SSM Ch 4 pt 6.pdf · CHAPTER 4 REVIEW 207 12. d dx x6 ln x = x6 d dx ln x + (ln x) d dx x6 = x6 1 x" # $ % & ' + (ln x)6x5

$Math 1432 DAY 20 Dr. Melahat Almus almus@math.uhalmus/1432_day20_after.pdfJust know: xedxxeeCxxx and ln lnxdx x x x C 3 2. Integrate: a) cos sin32x xdx b) sec tan42x xdx 4 3. Integrate:$