8. (5 points) Is the following function continuous at (1, 1)? Explain 2.0? - TY -...
Exercise 4: (5 points) consider the following differential equation 3y - y Let = f(ty) be the right-hand side of the above equation. a. Compute a/ay. b. Determine and sketch the region in the ty-plane where functions. and array are both continuous C. For the initial condition y(0) = 1 (i.e.to = 0, y = 1), would a unique solution of the equation exist? Explain.
is: 6. (8 points) / is a function that is continuous on (-0,00). The first derivative of /"(x) = (3x - 1)x+3X5 - x) Use this information to answer the following questions about : a. On what intervals is increasing or decreasing? Internal in which fis increasing or -- 8x-1) (x+3)(5-x) > 0 x=112, -3, -5 b. At what values of x does f have any local maximum or minimum values? - V2 ; Location(s) of Minima: Location(s) of Maxima:...
Problem 3. (10 points) For the function f(x,y) = r? - Ty + y2 – 21+ y, find all the critical point(s) and investigate whether it is (or they are) a saddle, local max or local min.
At what points of R2 is the following function continuous? 6 f(x, y) = x® (+64) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. {(x,y): y2 + (Use a comma to separate answers as needed.) OB. {(x,y): x* }(Use a comma to separate answers as needed.) O C. All points except for (Type an ordered pair. Use a comma to separate answers as needed.) OD. R?
(8) 2 points Let f be a function defined and continuous, with continuous first partial derivative at the origin (0,0). A unit vector u for which D.f (0,0) is the maximum is: maximum a 1 (0,0)), A. /(0,0)x,0),y (0 af B. (0,0) 8x0,0),(0,0)), af 1 ((0,0),-y C. (0,0), /(0,0) D. None of the above. (8) 2 points Let f be a function defined and continuous, with continuous first partial derivative at the origin (0,0). A unit vector u for which...
ty f) -1 0 2 The above diagram is a plot of a function f(x) Is f(x) continuous at 0 and why? Choose the best response below: Yes, the function is continous at x=0, as it has a two-sided limit as x approaches 0, which is equal to f(0) itself No, because the function does not have a two-sided limit as x approaches 0 No, because the function is not defined at x0. No, because the limit of the function...
5. Y is a continuous random variable with pdf f(y) = (4 – y)/8, 0<y< 4. (a) Find E(Y). (b) Find E(Y2). (c) Find Var(Y).
Find the stationary points of the following function f(t, y) = 2.3 + 3xy? – 322 – 3y2 + 10 Select one or more: a. (-2,2) O b. (1, -1) O c.(-1,1) d. (0,0) e. (1,1) O f. (2,0) g: (2,2) h. (0,2)
5. (28 points) A continuous random variable X has probability density function given by f(x) = 3x^2,0<x< 1 O otherwise (c) What is the c.d.f. of Y = X^2 - 1? What is the p.d.f. of Y = X^2 - 1?
My Notes 5. -'2 points SCalcET8 1.2.505.XP. (a) Graph the function fix) = x + 5/x and the secant line that passes through the points (1·6) and (10. 1 0.5) In the viewing rectangle [D, 1 2jby [D, 1 2]. 12 12 10 10 12 12 12 12 10 10 1 12 (bFind the numher c that satisfies the concluslon of the Man ale Theorem for this function fand the Interva [, 1D Need Help Read ItWatch It Talk to...