Show how to prove a function is continuous on an interval. Show how to prove a function is negative. Provide an example, if necessary. Suppose that a function f(x,y) is defined for all points (x,y) \neq (0,0) an
Show how to prove a function is continuous on an interval. Suppose that f is an even function, g is odd, both are integrable on the closed interval from -5 to 5, and we know that int_0^5 f(x)dx = 24, while int_0^5 g(x)dx = 4.5. I...
We make a change of variables y=x/a, so∫^a_0 f(x)dx=∫^1_0 ayady=a^2∫^1_0 ydyThe function f(y)=y is continuous on ℝ, so the definition integral ∫^1_0f(x) dx can be calculated as a limit of Riemann sums. Using an equally spaced partition of [0,1] of size n...
Thread starter gilabert1985 Start date Mar 11, 2012 Tags Form Function Mar 11, 2012 #1 gilabert1985 7 0 Hi, I have the following problem that is part of a project, and I have been stuck on it for the last couple of hours ... Thanks a lot for any help you can...
Suppose that f(x) = (7 - 3x) e^x. Use interval notation to indicate where f(x) is increasing and decreasing. Consider the derivative of a function f(x) : f'(x) = (x - 2)e^{-2x}. On what intervals is f increasing or decreasing?
If, for , where is a nonnegative continuous function on , and , and are constants, then Here is the version of Gronwall's inequality that I am using: **Gronwall:** Suppose that and let and be nonnegative continuous functions defined on the interval . Moreover, suppose that is d...
Show that the equation4x3−3x−p=0 has a unique root in the interval [1/2, 1] and identiify it. (ii) Let f(x), x ge 0, be a nonnegative continuous function , and letF'(x)=f(x)=(4a−3)(x+log5)+2(a−7)cotx2sin2x2,x≥0. If for some c>0,f(x)<cF(x)...
If f(x)=f(a+x), then prove that, int(a)^(a+t)f(x)dx is independent of ... 02:26 Statement-I: int(0)^((pi)/(2))sin^(n)xdx=int(0)^((pi)/(2))cos^(n)xdx,n... Text Solution Statement-I: int(-4)^(-5)sin(x^(2)-3)dx+int(-2)^(-1)sin(x^(2)+12x+33)...
How backwards America still is in to many things and one of the reasons why is, for too many years, this country was being controlled by the religious right wing in this country and thank God that is no longer. Wake up America...a huge dung pile of crap was laid on our country ...
Prove the following theorem. Theorem: Let u be a differentiable function of x, and let f be a continuous function of u. Then \int f (u(x)) \cdot \frac{du}{dx} = \int f(u) du + C where C is an arbit Let f and g be function...