Q.Let f: [1,4] R be continuous function. Define F(x) = S* f(t)dt. Then a. F(x) is differentiable on [1,4] and E = f(3x). b. F(x) is differentiable on (1,4) and c. F(x) is differentiable on (1,4) and d. F(x) is differentiable on [1,4] and %3D %3D f(3x). %3D = 3f(3x). dF = 3f(3x). %3D

Q: (d) (e) Determine the range f(A) where A = (a, 0] for some fixed a < 0,a # Determine the supremum…

A:

Q: Theorem 11. Let f be a continuous function on R such that f(x+y)-f(x)+fv) vx, yER. Show that f(x)3cx…

A:

Q: D. On what point/domain will the f(x, y) = Vx ey will be continuous? Explain your answer!

A: Solved below

Q: Let f(x)= V x³ at the interval of [0,2] ; then , use the mean valune theorem to find c.

A:

Q: x² - y² z = g(x, y) = x² + y² 0 for for (x, y) = (0,0) (x, y) = (0,0)

A: Given function is z=gx,y=x5−y5x4+y4 for x,y≠0,00            for x,y=0,0. We have to check whether…

Q: 2. f(x) = Vx – 1 at x = 5

A: Function is continuous and differentiable both at x= 5.....for detail...go through the solution

Q: If the function 2²+y? if (x, y) # (0,0) f(x, y) = 1-e(z2+y2) ? т, if (x, y) = (0,0) is continuous…

A:

Q: Consider the following function of two variables: xy g(x, y) = x² + y? Prove that the above function…

A:

Q: Answer the following questions given the function f below. ху if (x,y) # (0,0) f(x,y) = X +y if…

A:

Q: Answer "True" or "False" for the following: Let f(x) be a continuous function on [a, b]. Suppose…

A: Definition of the antiderivatives helps to validate the given statement. A function F(x) is said to…

Q: Find the numbers at which the function if a 2 I+1, f(1) = {2-1, %3D is continuous.

A: To find the points where f is continuous.

Q: 3. Let A be the set of all functions ƒ : 0, 1] → R that are continuous in the interval [0, 1].…

A:

Q: At what points of R is the following function continuous? xy if (x-y) (0.0) f(x y) = 7x +y 0. if…

A: We have to find set of continuity of given functions.

Q: Assume g: [0, 8] → R is a continuous function for which: on the intervals [0, 3) U (5, 8], the…

A: Given: g:0, 8→ℝ is a continous function for which on the intervals [0, 3)∪(5, 8], the values of gt…

Q: continuous function h(x),

A: Differential equation

Q: 9z 21. Answer the following questions given the function f below. xy if (x.y) # (0,0) f(x,y) = x+y?…

A: As there are multiple parts of this question and you didn't mentioned which part the question's…

Q: f(x) = {*- Įx² +px + 2,x # 3 3, x = 3

A:

Q: Use a software program or a graphing utility with matrix capabilities to write v as a linear…

A:

Q: Determine whether or not the following functions are continuous at (0,0). -1 for (x, y) = (0,0) a)…

A:

Q: Determine the set of points domains at which the function is continuous.  G(x,y)= 2x tan y

A: To Find: Set of points in domain at which the function 2x tany is continuous.

Q: of the apples is equal to 3 of the oranges. If there are 12 mor 5 In a fruit stall, - - annles than…

A: Fraction:  A small part of something.  In other words, numerical value that is not a whole number A…

Q: be de by 8 <x3 + y3 f(x, y) = x2 + y2 if (x, y) = (0, 0) if (x, y) = (0, 0). %3D (a) Is f continuous…

A: Note- Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

Q: (4.2) Consider the following function and determine the set of points at which it is continuous: 2²…

A:

Q: Which of the following functions are continuous at (0,0)? a. f(x, y) = 2x²y³ 2r?ys b. f(x, y) = X -…

A: A function is Said to be continuous when 1. The sum, multiplication and subtraction of continuous…