3. Consider the following piecewise function (a) Draw an accurate graph of f(). (b) As always, f(...
Please solve this problem completely. (1) Length of graphs a) Let a path C be given by the graph of y - g(x), a b, with a piecewise C function g : [a,b] → R. Show that the path integral of a continuous function f : R2 → R over the path C is b) Let g: a bR be a piecewise Cl function. The length of the graph of g on (t, g(t)). Show that [a,b] is defined as...
showing multivariable calculus functions are differentiable Please help! 2. Recall that by Theorem 3 of Section 14.3, a function f(x,y) is differentiable if its partial derivatives fa and fy both exist and are continuous. (a) Use this idea to show that the function f(x,y)-esin ry is differentiable. (b) Let o be a differentiable function and f(,)Jy Find the partial derivatives of f and determine whether they are continuous. Hint: The Fundamental Theorem of Calculus gives us that Ø has an...
Suppose that the piecewise function J is defined by f(2)= {**** -1<<3 - 3x2 + 2x + 23, 2> 3 Determine which of the following statements are true. Select the correct answer below: O f() is not continuous at I = 3 because it is not defined at I = 3. Of() is not continuous at 2 = 3 because lim f(x) does not exist. f() is not continuous at I = 3 because lim f() f(3). ->3 f(x) is...
e2 3 does not have a complex antiderivative on CV 3. (a) The continuous function f(z) = 0 (b) The continuous function g(z) does not have a complex antiderivative on C 1 + 1리- e2 3 does not have a complex antiderivative on CV 3. (a) The continuous function f(z) = 0 (b) The continuous function g(z) does not have a complex antiderivative on C 1 + 1리-
f(x)= The domain of the piecewise function is (-00,00) a. Graph the function b. Use your graph to determine the function's range, a. Choose the correct graph below. ОА. OB x+1 if x<-4 x-1 if x2 - 4 ос. OD 10 Q Q
PROBLEM 2: THE INDICATOR FUNCTION OF THE RATIONAL NUMBERS For a while, it was believed that any given function should be mostly continuous. This is reasonable, given the types of functions one typically sees in Calculus courses, where the worst case scenario involves a function that is defined piecewise and is continuous everywhere, except for some finite set of discontinuities, where the value of the function drops or jumps. It was also believed that every function should be integrable, which...
The domain of the piecewise function is (-00,00). a. Graph the function. b. Use your graph to determine the function's range. if x2 f(x) = 2x - 2 if x22 a. Choose the correct graph below. OA. B. у 10- 10- 10 х 10 10 -10 -10 b. The range of f(x) is (Type your answer in interval notation.)
The domain of the piecewise function is (-00,00). a. Graph the function. b. Use your graph to determine the function's range. f(x) = X+ 3 if x < 1 X-3 if x21 a. Choose the correct graph below. OA. B. C. OD. AY 10 10- 10 10 10 -10 -10 10 10 -10 -10 -10 -10 b. The range of f(x) is (Type your answer in interval notation.)
Sketch a graph of the piecewise defined function. sz if x <3 f(x) = x 1 if x 2 3
a. Find f( 5), f(-3), and f(8) b. Sketch the graph of the piecewise-defined function. xif xs0 f(x) 1 if x>0 c. Determine the domain of f d. Determine the range of f. X f(- 5) %3D а. (Simplify your answer. Type an integer or a fraction.) f( -3) = (Simplify your answer. Type an integer or a fraction.) f(8) = (Simplify your answer. Type an integer or a fraction.) b. Choose the graph of f(x). O A. В. C....