Determine where the function is continuous: : f(x)=√-2-8 (-2, 0) (-0,2) (-20.00) (-2,-2)
8. Letſ be a function that is continuous on (0, 2) and differentiable on (0,2). Suppose that (0)</(2) but that fisnor increasing on (0,2). Does' necessarily take on both positive and negative values on (0.2)?
4. f(x) is a continuous function on [0, 1] and So f (x)dx = a, where a is constant. Evaluate the following double integral f(x)f(y)dydx. (Hint: Change the order of the integration and use the property of the double integral, so that you can apply Fubini's theorem.)
Consider the function f(x) = Σ (a) Where is f defined? (b) Where is f continuous? (c) Where is f differentiable? Consider the function f(x) = Σ (a) Where is f defined? (b) Where is f continuous? (c) Where is f differentiable?
It is known that f :(0,2) + R is a differentiable function such that \f'(x) < 5 for all x € (0,2). Now let bn := f(2 – †) for all n € N. Prove that this is a Cauchy sequence.
It is known that f :(0,2) + R is a differentiable function such that \f'(x) < 5 for all x € (0,2). Now let bn := f(2 – †) for all n € N. Prove that this is a Cauchy sequence.
(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...
6 ptsSuppose that f(x) = g(x? - 4x + 2), that is a continuous function, that g'(x) > 0 where I > -1, 9(1) < 0 where I < -1, and '(-1) = 0. On which interval(s) is the function increasing On which interval(s) is f decreasing?
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...
A continuous random variable X has probability density function f(x) = a for −2 < x < 0 bx for 0 < x ≤ 1 0 otherwise where a and b are constants. It is known that E(X) = 0. (a) Determine a and b. (b) Find Var(X) (c) Find the median of X, i.e. a number m such that P(X ≤ m) = 1/2
Describe the graph of the function g by transformations of the base function f. (0,2 (-2, 0) ,0) (0, -4) 1 g(x) = f(x – 4) - 2 g(x) = f(x + 4) + 2 g(x) = f(x - 4) + 2 g(x) = f(x + 4) - 2