(1 point) Enter a Tor an F in each answer space below to indicate whether the...
1. Determine whether the statement is true or false. If false, explain why and correct the statement (T/FIf)exists, then lim ()f) o( T / F ) If f is continuous, then lim f(x) = f(r) (TFo)-L, then lim f(x)- lim F(x) "( T / F ) If lim -f(x)s lim. f(x) L, then lim f(x)s 1. "(T/F) lim. In x -oo . (T/F) lim0 ·(T / F ) The derivative f' (a) is the instantaneous rate of change of y...
Determine whether the statement is TRUE or FALSE. You are NOT required to justify your answers. (a) Suppose both f and g are continuous on (a, b) with f > 9. If Sf()dx = Sº g(x)dx, then f(x) = g(x) for all 3 € [a, b]. (b) If f is an infinitely differentiable function on R with f(n)(0) = 0 for all n = 0,1,2,..., then f(x) = 0 for all I ER. (c) f is improperly integrable on (a,...
Consider the following graph of f(x) on the closed interval (0,5): 5 4 3 2 1 0 -1 0 1 2 3 5 6 (If the picture doesn't load, click here 95graph2) Use the graph of f(x) to answer the following: (a) On what interval(s) is f(x) increasing? (b) On what interval(s) is f(x) decreasing? (c) On what interval(s) is f(x) concave up? (d) On what interval(s) is f(x) concave down? (e) Where are the inflection points (both x and...
1-4. True/False [1 point each] Write a T on the line if the statement is always true, and F oth- erwise. If you determine that the statement is false, you must give justification in the space provided to receive credit Letr be a smooth vector function. If ||r(t)|| = 1 for all t, then |r(t)|| is constant _1. Let r be a smooth vector function. If ||r(t)|| = 1 for all t, then r(t) is orthgonal to r(t) for all...
1. Answer True or False for the following questions: (a) A function can have several local minimu in points in a small neighborhood of x*. (b) A function cannot have more than one global minimum point (c) The value of the function having a global minimum at several points must be the same (d) A function defined on an open set cannot have a global minimum (e) The Hessian matrix of a continuously differentiable function can be asymmetric. (f) The...
(5 points) A continuous function f, defined for all x, has the following properties: 1. f is decreasing 2. f is concave up 3. f(26) = -5 4. f'(26) = - Sketch a possible graph for f, and use it to answer the following questions about f. A. For each of the following intervals, what is the minimum and maximum number of zeros f could have in the interval? (Note that if there must be exactly N zeros in an...
Question #1 (15 Marks) a) (8 Marks) Answer the following questions with True or False. 1) 2) 3) Every basic solution in the assignment problem is necessarily degenerate. The assignment problem cannot be solved using the transportation technique. If the gradient vector of a function at a given point is zero, the point can only be a maximum or minimum. If a single-variable function has two local minima, it must have at least one local 4) maximum 5) The Golden...
True or False Determine whet her the statement is true or false, and circle the correct answer. Each question is worth 2 points. (1) If F is a vector field and C is an oriented curve, then F dr must be less than zero. F (2) It is possible that for a certain vector field F and piecewise smooth oriented path C we have/. F. dr-2i-Sj. (3) Suppose d·is the unit square joining the points (0,0), (1,0), (1,1), (0.1) oriented...
2 6, 9、19/ 1,12 '12,13,16,16, 16,18,3‘ = 12.5 4 IQR=46 Question #1 (15 Marks) a) (8 Marks) Answer the following questions with True or False. 1) Every basic solution in the assignment problem is necessarily degenerate. 2) The assignment problem cannot be solved using the transportation technique. maximum or minimum. If a single-variable function has two local minima, it must have at least one local 4) maximum. 5) The Golden Section Search method gives better results than the Fibanocci Search...
1. If a function f(x,y) has a local maximum then it is not necessary that it has also a local minimum True False 2. If a vector field F is conservative then we can not find a potential functions. True False 3. Suppose that P and Q have continuous first-order partial derivatives on a domain D and consider the vector field F = Pi+Qj. Then F is conservative if op 80 True False 4. If D is a rectangle, then...