Exercises 6-14 deal with the logistic family of functions given by FA(x) Az(1 -z). 6. For which v...
The following exercises deal with the family of functions F(x) = x3 6. for λ > 0. a. Find all periodic points and classify them when 0< A<1. b. Prove that, if Ixl is sufficiently large, then lf"(x)| → oo. C. Prove that if λ is sufficiently large, then the set of points which do not tend to infinity is a Cantor set.
12:22 x 4.2 Exercises.pdf @ E 4.2 Exercises In Exercises 1-4, determine the exact values of the six trigonometric functions of the angle amo Boty 6- in Exercises 5-12, find the point (x, y) on the unit circle that corresponds to the real number t. 5.1 7.17 11. r = 3 12. 1 = 7 In Exercises 13-22, evaluate (if possible) the sine, cosine, and tangent of the real number. 13. 1 = 14. 1 = 1 AREA (442 in...
1 SECTION 3.2: EXERCISES 1.) Let f(x) = =+*+ ** - 6x? + 9x + 14. Find all points of inflection of f(x). Justify and verify using valid calculus techniques. 6 2.) Use both the FDT and the SDT to find and classify the critical values of 24 V(x) = 2x2 + Which was more straightforward to use?
11. Circle true or false. No justification is needed. (14 points) (a) If f(x) - o(g(x), and both functions are continuous and positive, then fix dz converges. TRUE FALSE (b) If f(x)- o(g(x)), then f(x)gx)~g(x). TRUE FALSE (c) If the power series Σ an(x + 2)" converges atェ= 5, then it must km0 converge at =-6. TRUE FALSE (d) There exists a power series Σ akz" which converges to f(z)-I on some interval of positive length around FALSE TRUE (e)...
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x Discuss the continuity of the functions given in problem #2 above. Also, determine (using the limit concept) if the discontinuities of these functions are removable or nonremovable 3. Find the value of the constant k (using...
= x-2 2x+1 Given the functions f(x) = x²+x-1, and g(x) x2 +5x+6 a. Which function has an oblique asymptote? [10] b. Determine the equation and end behavior of the oblique asymptote. [3A]
3. Suppose f(x,y,z) - sin2(x) - 2 sin(x)+y'-4yz+52-6z. Find the minimum value of this function- you must find the point at which the minimum occurs and "prove" that the function really has a mini- mum there. Does the function have a maximum? If we restrict the variables to the ball of radius 1, centered at the origin, does the function have a maximum on that set? (You don't have to try to find the maximum but you should try to...
3. Suppose f(x,y,2)-sin2(x)-2sin(x) + y. 4 y z + 52.62. Find the minimum value of this function. you must find the point at which the minimum occurs and "prove" that the function really has a mini mum there. Does the function have a maximum? If we restrict the variables to the ball of radius 1, centered at the origin, does the function have a maximum on that set? (You don't have to try to find the maximum but you should...
#1,2,4,5,7 Chapter 4 Functions of Two Variables Applied Calculus 272 4.3 Exercises For problems 1 through 6, find f/, f, and f, for the function given. Confirm that ух 3. f(t,y)-Sxy 4. f(x, y)-e" 5.(x,y)-In(axy+2x-6y) y4-5 7. Find the critical points of f(x,y)-ys_x3 + 15x2-12y+12 and use the Second Derivative Test to classify them. If the test fails, say "the test fails. 3 Chapter 4 Functions of Two Variables Applied Calculus 272 4.3 Exercises For problems 1 through 6, find...
help please! thank you! (a) Show that an members of the family y-ve-1ฐ are-lutkn-ed Medaterntial mpalii (b) Use part (a) to find a fornvula for the solution to the ini- tial value problem v (0)-2. Then, sketch your solution on the slope field shown to the right. 2. Figure 1. Slope field for 3. (a) Show that all members of the family yarlutions of the disferential equation (b) Find the solution to the initial value problem ry'-tra-Zy·y(1)-S. 4. For what...