(b) Determine the range of f, if f :D → R, where f (x) = x?. I. D = (-2, 2) II. D = [-7, 2] III. D = (-4,2]

Q: If f"(x)>0 on an interval I then...

A:

Q: Let f (x, y) = 1 5+√x²+y²-1 Then range of f is:

A:

Q: What three conditions must be met for a function ƒ to be continuous at the point (a, b)?

A: Continuity at points: The points of continuity are the points where a function exist and has some…

Q: For what value of the constant c is the function f continuous on the interval (-,00). Sa? – 3, x с…

A:

Q: On what domain is the function f(x) = 3 + V5x – 20 continuous?

A:

Q: The function f(x,y) =26-2x²-y² is continuous at point (2, -3). .A True .B False

A: The objective is to determine whether the statement, " The function fx,y=26-2x2-y2 is continuous at…

Q: For f(x)=3|x| does the Mean Value Theorem apply on the interval [-2, 2] and why?

A:

Q: Consider f : R → R given by f(x) = x². What are the domain, codomain and range of f?

A: Let a function f : A→B thenDomain: set ACodomain: BRange: Values that comes out after putting values…

Q: Why does the Mean Value Theorem not apply to the function f(x)=x^(1/2) on the interval [-1,1]?

A: Mean value theorem can be applied on a function f(x) in [a,b] only when the function f(x) is…

Q: Q4: Use the limit definition to compute the derivative, f(x), for 2.F(x) = Vx³ – x

A:

Q: Q1: If the function f(x) define as f: R→ R such that f(x) = (x+1, x>2 x²-1, x≤2 Show that the…

A: This is the question to check the differentiability of the function.

Q: What are the domain and range of g(x) = 3√x+4? OD: [3,) and R: [0, ∞) OD: [4,) and R: (-∞, 0) OD:…

A: The given function is: g(x)=3x+4

Q: The Range of f(x) = V1-x is 1. [-1, 0) 2. (-, 1] 3. (-0,0) 4. [0, 0) 1 2

A:

Q: To plot the function f(x) == %3D 2x over [0,5], we use fplot('exp^(-x) /2*x'[0,5)…

A: Since we are given with multiple number of questions and our guideline is solve the first question…

Q: Find the extreme values of f(r) = Vr(5 – x) in the interval [–1,3].

A: For extreme points we need to find critical points and check value of f(x) on boundary values of…

Q: Find f-(-1,1) of the function: f(x, y) = x + xy +2a°y?

A: Let's find.

Q: Describe the long run behavior of f(z) = z" As z + - 00, f(z) - As z + 0, f(z) → ( -0-

A:

Q: 6. Use an appropriate substitution to prove f(x)dr = | f(a+b- x)dx.

A: To use an appropriate substitute to prove  ∫abfxdx=∫abfa+b-xdx

Q: Is the function f(x) : 1 continuous or discontinuous on [2,+∞)? Vx - 2 Is the function f(x) : 1…

A:

Q: Use the limit definition of the derivative to find f(x) for the given functions and given valu f(x)…

A:

Q: What is the function f on (a, b) if for all x1, X2 in (a, b) when x, f(x2). is it decreasing or…

A: for all x1 , x2 in a,b when x1<x2 then fx1>fx2 claim- is it decreasing or increasing

Q: Find and sketch the domain of f(x, y) = 9-x2-y2 Vy2-1 %3D What is the range of f?

A: We have to find the points where the function is defined.

Q: The function f(x,y)=/26-2x²-y² is continuous at point (2,-3). .A False .B True

A: A function is continuous at a point if after putting the point in the function yields a positive…

Q: For what values of a, m and b does the function x = 0 0 < x < 1 1< x< 2 3, f(x) = -x² +3x + a, тх +…

A: to find the values

Q: Determine the interval(s) for which f(x) =- - 2x2 is concave down. 12

A:

Q: and the domain of the function using interval notation. To enter ∞o, type infinity. To enter U, type…

A: We can solve this as follows:

Q: Describe the long run behavior of f(x) = x* As x → ∞, f(x) → ? As x → 0, f(x) → ?

A: This question is about function behaviour near infinity

Q: Match the function with its range. f(x) = x2 + 1 - 1 [-1, 0) O [0, c0) O [1, 0) O (-0, 0) U (0, o) O…

A:

Q: Q4: Use the limit definition to compute the derivative, f(x), for 1.F(x) = x3 2.F(x) = = Vx3 - x

A:

Q: Find the number c that satisfies the conclusion of the Mean Value Theorem for the function…

A:

Q: If f : [0, 3] → R is continuous not constant, then its range be a closed, bounded interval?

A: Yes true.

Q: (1, if x 2

A: Using the given piece wise function, we can plot it in given intervals.

Q: Find a function flx) such that f(x) -llex and %3D 3. f(0)-- 주

A:

Q: If f : [0, 3] → R is continuous, must its range be a closed interval?

A: Given data: The expression for the function is f : [0,3]→R. The continuous image of the open bounded…

Q: For f(x)=(x^2+x−2)/(x+2) does the Mean Value Theorem apply on the interval [0, 2] and why?

A:

Q: - Given f(x)= -, find f(x). 2+x %3D 6.

A:

Q: Given the function of f(x) = -3 – in the interval [-8, –2], find a point x = c between -8 and -2 so…

A:

Q: Describe the long run behavior of f(x) = – x² - As x → – ∞, f(x) → ? V - As x → ∞, f(x) → (? V

A: Describe the long run behavior of f(x)=-x5As x→-∞, f(x)→?As x→∞, f(x)→?

Q: At what points c does the conclusion of the Mean Value Theorem hold for f(x) = x° on the interval [-…

A:

Q: Suppose f'(x) < 2 for all x 2 2, and f (2) = 7. Show that f(4) < 11.

A: Given that f'x &lt;2 for all x≥2 and f2=7.We need to show that f4&lt;11.

Q: Given that f(x) = 4x2 − x + 2, use the limit definition of the derivative to compute f'(x).

A:

Q: Describe the domain and range of the function. f(x, y) = In(xy-1) Dor

A:

Q: If f : [0, 3] → R is continuous, must its range be a closed interval?  use the continuous map

A:

Q: Explain why the Mean Value Theorem does not apply to the function f on the interval [0, 6]. f(x) =∣x…

A: Mean Value Theorem: Let f be a function satisfying two condition: 1. f is continuous on a,b. 2. f is…

Q: Evaluate f''(c) at the point. f(x) = (x2 - 5)(x3- 5), c = 1

A:

Q: 1 . Let f(r) 2r + 1

A:

Q: Suppose that a function f(x, y) satisfies fxx fyy – (fxy)² > 0 at a point (a, b). How is the sign of…

A:

Q: 5. Is the function given by g(x) = 4x³. 6x continuous on R?

A: