True and False (No need to solve). 1. Every bounded continuous function is integrable. 2. f(x)=|x|...

True and False (No need to solve).

1. Every bounded continuous function is integrable.

2. f(x)=|x| is not integrable in [-1, 1] because the function f is not differentiable at x=0.

3. You can always use a bisection algorithm to find a root of a continuous function.

4. Bisection algorithm is based on the fact that If f is a continuous function and f(x₁) and f(x₂) have opposite signs, then the function f has a root in the interval (x₁, x₂). As a consequence, one can infer that if a continuous function f(x) has a root at x=a, then there exists a number h such that f(a- h) and f(a+ h) have opposite sign.

5. The total areas of step function, f(k)=k feet, for k ranging from 1 to 1000 is 500.50 ft², assuming each step has a width of 1 foot.

6. if f is continuous then d/dx (integral(from a to x) f(t)dt= f(x).

7. The total areas of step function, f(k)=k feet, for k ranging from 1 to 1000 is 550 ft², assuming each step has a width of 1 foot.

Expert Solution

milcah answered 2 years ago

Prove that if f, g are integrable, then the function (f(x) + cos(x)g(x))2is integrable.

1) Show the absolute value function f(x) = |x| is continuous at every point. 2) Suppose...

1) Show the absolute value function f(x) = |x| is continuous at every point. 2) Suppose A and B are sets then define the cartesian product A * B Please answer both the questions.

Consider a continuous, integrable, twice-differentiable function f with input variable x. In terms of the units...

Consider a continuous, integrable, twice-differentiable function f with input variable x. In terms of the units of f and the units of x, choose the units of each function or expression below: (a) The units of f ' are the units of f the units of x (the units of f)(the units of x ) the units of f the units of x the units of f (the units of x)2 the units of f (the units...

2. Let f(x) ≥ 0 on [1, 2] and suppose that f is integrable on [1,...

2. Let f(x) ≥ 0 on [1, 2] and suppose that f is integrable on [1, 2] with R 2 1 f(x)dx = 2 3 . Prove that f(x 2 ) is integrable on [1, √ 2] and √ 2 6 ≤ Z √ 2 1 f(x 2 )dx ≤ 1 3 .

Prove that a continuous function for sections(subrectangles) is integrable in R^N

Prove that if f is a bounded function on a bounded interval [a,b] and f is...

Prove that if f is a bounded function on a bounded interval [a,b] and f is continuous except at finitely many points in [a,b], then f is integrable on [a,b]. Hint: Use interval additivity, and an induction argument on the number of discontinuities.

Part A. If a function f has a derivative at x not. then f is continuous...

Part A. If a function f has a derivative at x not. then f is continuous at x not. (How do you get the converse?) Part B. 1) There exist an arbitrary x for all y (x+y=0). Is false but why? 2) For all x there exists a unique y (y=x^2) Is true but why? 3) For all x there exist a unique y (y^2=x) Is true but why?

True or False. The production function f(x,y)=x^(2/3)+y^(2/3) has increasing returns to scale

For the following exercises, determine whether or not the given function f is continuous everywhere...f(x) = tan(x) + 2

For the following exercises, determine whether or not the given function f is continuous everywhere. If it is continuous everywhere it is defined, state for what range it is continuous. If it is discontinuous, state where it is discontinuous.f(x) = tan(x) + 2

f(x) = (x^2 )0 < x < 1, (2−x), 1 < x < 2 A) Solve...

f(x) = (x^2 )0 < x < 1, (2−x), 1 < x < 2 A) Solve this integral, writing An as an expression in terms of n. Write down the values of A1,A2,A3,A4,A5 correct to 8 significant figures. b) Use MATLAB to find the coefficients of the first five harmonics and compare the results with those from part (e). Your solution should include a copy of the m-file fnc.m which you use to obtain the coefficients c) Using MATLAB, plot...

Question