Mohammed Yaaseen Gomdah MATH 203 Winter 2016 F WeBWorK assignment number Assignment 5 W14 is due : 02/17/2016 at 03:00am EST. The (* replace with url for the course home page *) for the course contains the syllabus, grading policy and other information. This le is /conf/snippets/setHeader.pg you can use it as a model for creating les which introduce each problem set. The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are making some kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you are having trouble guring out your error, you should consult the book, or ask a fellow student, one of the TA's or your professor for help. Don't spend a lot of time guessing - it's not very efcient or effective. Give 4 or 5 signicant digits for (oating point) numerical answers. For most problems when entering numerical answers, you can if you wish enter elementary expressions such as 2 3 instead of 8, sin(3 pi/2)instead of -1, e (ln(2)) instead of 2, (2 + tan(3)) (4 sin(5)) 6 7/8 instead of 27620.3413, etc. Here's the list of the functions which WeBWorK understands. You can use the Feedback button on each problem page to send e-mail to the professors. 6. (1 pt) Differentiate the following function: 1 f (t) = 6 t 6 t f (t) = 1. (1 pt) Given that f (x) = x10 h(x) h(1) = 3 h (1) = 6 7. (1 pt) Find the equations to both lines through the point (2,0) that are tangent to the parabola y = x2 + x + 3. y= (enter here the line with the SMALLER slope) y= (enter here the line with the LARGER slope) Calculate f (1). [HINT: Use the product rule and the power rule.] 8. (1 pt) Find the exact value of each expression: 2. (1 pt) Let f (x) = (3x2 9)8 (6x2 + 7)11 (a) sin1 ( 3/2) (b) cos1 (1) f (x) = 3. (1 pt) Find the derivative of the function (a) g(x) = (4x2 + 5x + 5)ex (b) 9 9. (1 pt) If cos(t) = 11 where < t < the following trigonometric functions. 3 2 , nd the values of g (x) = Note: Give exact answers, do not use decimal numbers. The answer should be a fraction or an arithmetic expression. If the answer involves a square root it should be enter as sqrt; e.g. the square root of 2 should be written as sqrt(2). 4. (1 pt) Find the derivative of the function g(x) = ex 2 3x g (x) = cos(2t) = sin(2t)= t cos( 2 )= t sin( 2 )= 5. (1 pt) Differentiate the following function: f (x) = ex + xe f (x) = 1 10. (1 pt) If tan x = 1/3, cos x > 0,, then sin 2x = ; cos 2x = ; tan 2x = . Generated by the WeBWorK system c WeBWorK Team, Department of Mathematics, University of Rochester 2 Mohammed Yaaseen Gomdah MATH 203 Winter 2016 F WeBWorK assignment number Assignment 6 W14 is due : 02/22/2016 at 03:00am EST. The (* replace with url for the course home page *) for the course contains the syllabus, grading policy and other information. This le is /conf/snippets/setHeader.pg you can use it as a model for creating les which introduce each problem set. The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are making some kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you are having trouble guring out your error, you should consult the book, or ask a fellow student, one of the TA's or your professor for help. Don't spend a lot of time guessing - it's not very efcient or effective. Give 4 or 5 signicant digits for (oating point) numerical answers. For most problems when entering numerical answers, you can if you wish enter elementary expressions such as 2 3 instead of 8, sin(3 pi/2)instead of -1, e (ln(2)) instead of 2, (2 + tan(3)) (4 sin(5)) 6 7/8 instead of 27620.3413, etc. Here's the list of the functions which WeBWorK understands. You can use the Feedback button on each problem page to send e-mail to the professors. 1. (1 pt) Differentiate y = sec x tan x. y = 6. (1 pt) If f (x) = cos(sin(x2 )), then f (x) = 2. (1 pt) cos x For what values of x in [0, 2] does the graph of y = 2+sin x have a horizontal tangent? List the smaller value of x rst. x= x= 3. (1 pt) An object with weight W is dragged along a horizontal plane by a force acting along a rope attached to the object. If the rope makes an angle t with the plane, then the magnitude of the force W is F = sint+cost , where is a constant called the coefcient of friction. Let W = 50 lb and = .6. 7. (1 pt) Let 1 f (x) = sin . x f (x) = Let . g(x) = g (x) = 1 . sin x . 8. (1 pt) Match the functions and their derivatives: (a) Find the rate of change of F with respect to t. (b) When is this rate of change equal to zero? Round your answer to the nearest hundredth. F (t) = t= 1. 2. 3. 4. A. B. C. D. rad. 4. (1 pt) Let f (x) = sin(ex 3 cos(x) y = tan(x) y = sin(x) tan(x) y = cos3 (x) y = cos(tan(x)) y y y y = sin(x) + tan(x) sec(x) = 1 + tan2 (x) = 3 cos3 (x) tan(x) = sin(tan(x))/ cos2 (x) ) f (x) = 9. (1 pt) 5. (1 pt) Let Differentiate y = y = f (x) = 6ex cos x f (x) = x+ x + x. 10. (1 pt) Let f (x) = tan1 (cos(6x)). Find f (x). f (x) = Generated by the WeBWorK system c WeBWorK Team, Department of Mathematics, University of Rochester 1 Mohammed Yaaseen Gomdah E WeBWorK assignment due : 02/22/2016 at 03:00am EST. 5. (1 pt) Evaluate the integral 1. (1 pt) Which of the following is the correct form of the partial fracx1 tion decomposition of 3 ? x + x2 A B C A. + 2 + x x x+1 Ax + B Cx + D E B. + + x x2 x+1 Ax + B Cx + D Ex + F + + C. x x2 x+1 Ax + B Cx + D Ex + F + + D. x x2 x+1 Z 1 3 2x 8x 20 0 dx 6. (1 pt) Make a substitution to express the integrand as a rational function and then evaluate the integral 1e2x dx e2x + 3ex + 2 Note: Use an upper-case \"C\" for the constant of integration. Z 7. (1 pt) 2 Find the average value of the function f (t) = 8tet on the interval [0, 5]. fave = 2. (1 pt) Which of the following is the correct form of the partial frac1 tion decomposition of 6 ? x x3 A B Cx + D A. 3 + + x x 1 x2 + x + 1 A B C D Ex + F B. + 2 + 3 + + x x x x 1 x2 + x + 1 D E A B C + 2 C. + 2 + 3 + x x x x1 x +x+1 A B C Dx + E D. + 2 + 3 + 3 x x x x 1 8. (1 pt) Find the average value of the function h(r) = 15/(1 + r)2 on the interval [1, 6]. have = 9. (1 pt) A car drives down a road in such a way that its velocity ( in m/s) at time t (seconds) is v(t) = 2t 1/2 + 5 . Find the car's average velocity (in m/s) between t = 4 and t = 7. 3. (1 pt) Evaluate the integral Z x2 x 6 8(x 9) dx (x + 5)(x 2) 10. (1 pt) In a certain city the temperature (in degrees Fahrenheit) t hours after 9am was approximated by the function t T (t) = 60 + 19 sin 12 Determine the temperature at 9 am. Determine the temperature at 3 pm. Note: Use an upper-case \"C\" for the constant of integration. 4. (1 pt) Evaluate the integral Z 3 1 2 x2 1 Find the average temperature during the period from 9 am to 9 pm. dx Generated by the WeBWorK system c WeBWorK Team, Department of Mathematics, University of Rochester 1