If continuous or f differentiable is [ Select] on [a , b] then the [Select ] integral of definite or f indefinite on [a , b] is equal to G(b)–G(a) where G is [ Select] of f the derivative or an antiderivative or the definite integral

Q: The function f (x) called invariant under differentiation operator function (IUDO. function) if:…

A: The given functions are ux=-2coshxvx=-sinhx+coshx Now firstly we will find the derivatives of u(x)…

Q: Examine if f(x) = x3sin(1/x) is uniform continuous on the interval (0,2]

A:

Q: What does it mean for f to be concave down on an interval (a,b)? Select all answers that apply.

A: Solution: Given data, f is concave down on an interval (a,b)

Q: Q.10. Q.10./ Let [a, b] be an interval of R. Let f[a,b] R be a function such that f is M-times…

A: I will use Taylor theorem of remainder form to prove this.

Q: Use the definition to show that the function f (x) = 1/x^2 is continuous on the interval [c,…

A:

Q: If f is an entire functions then h(z) = e² f(1/2²) is analytic on C\ {0}, and its derivative h'(2) =…

A:

Q: Suppose f" () > 0 on some interval (a, b). Check all of the following statements that must be true.…

A: Step 1: Let write the given .We are given that f"(x)>0 on some interval (a,b). Step 2: Let write…

Q: Is a function Continuous ?why? integrable anod

A:

Q: what is the domain of f(x,y,z)=ln(z-y)+xysinz

A: what is the domain of f(x,y,z)=ln(z-y)+xysinz

Q: Left- and right-continuity a. Is hlx2 = Vx - 9 left-continuous at x = 3? Explain. b. Is h1x2 = Vx -…

A: To Determine: find left hand and right hand continuity at x=3 and explain this Given: we have a…

Q: (c) Give one example of a function g(1, y) that is continuous with respect to r and y, but not…

A: We take an example g(x, y)=(x+y)2x2+y2 . It is continuous w.r.to x  and y but jointly not

Q: Let f(x) — sin(nx) n³ n=1 Show that f is differentiable on R and that f' is continuous on R.

A: Within its interval of convergence, the derivative of a power series is the sum of derivatives of…

Q: Use the intermediate value theorem to prove that any continuous function with domain [0, 1] and…

A:

Q: Use right hand rule to find area under the curve   f(x)= x2-x on interval [1,3]

A:

Q: Let esinx SoN f(t) dt and f is a continuous function, determine the value of f ()

A: If we have F(x)=∫0xf(t)dx then we have F'(x)=f(x). This is called the fundamental theorem of…

Q: A function f is defined on [0, 1] as follows : 1 f(x)=, when 1 <x< a <*< =1, 2, 3, ..) (r=. f(0)=0,…

A:

Q: each

A:

Q: 64. Continuous extension Define f(0, 0) in a way that extends x² - y? f(x, y) = xy x² + y? to be…

A:

Q: If f is a continuous function on [a, b], ƒ is differentiable on (a, b), and if both f(a) and f(b)…

A: This question is based on Rolle's theorem which is explained in step 2.

Q: Determine if the function f(x)= e*¯ er uniform continuous on the interval I= [1,00 [

A:

Q: Let f be a twice differentiable function such that f(1) = 2 and f (3) 7. Which of the following must…

A: We have to choose correct option  Here using Lagrange mean value theorem

Q: Find the antiderivative of the improper interval xe-x^2 from negative infinity to positive infinity

A:

Q: me that h: [a, b] R is a continuous function and let G: [a, b] → R denote ollowing function, G(x)=…

A: Differentiation under integral sign