Let f: A → B be a function and C, D, E S B. IFCED then f-'(DUE) S f-'(CUE) the above is true f-'(CUE) C f-'(DUE) the above is true None of these

Q: If a function f(z) is analytic then fy # ÷fx. Select one: True False

A: Solution is in next step

Q: Determine if the function f(x) is continuous and/or differentiable at x = 1? x +5 for - 1sxS1 f(x) =…

A: The given function is f(x)=x+5    for -1≤x≤16x       for  1>x≤4 The function is said to be…

Q: 3) Verify Rolle's Theorem for the function f(x) = [-4, 4]. Justify your answer. 5x + 6 defined over…

A:

Q: 3)Verify Rolle's Theorem for the function f(x) = 2x2 + 4 defined over the interval [-6, 6]. Justify…

A: Rolle's theorem is satisfied if : f(x) is continous at given interval. f(x) is differentiable at…

Q: 9. If a continuous, differentiable function f has values f(-2) = 3 and f(4) = 1, what can you say…

A: Give that: f(-2) = 3 and f(4) = 1

Q: Explain the Wronskian of 2 functions f and g ?

A: Let f and g are the two functions. The Wronskian of the n functions is the determinant of the matrix…

Q: Q3-A) Is the function F(Z) continuous or not at z-U? 1+|21,

A: Let z = x+iy then Re(z) = x and |z| = √(x^2 + y^2) If z = 0 => x = 0 and y = 0

Q: if f(x) is a function that is continous at (2,f(x)) then f(x) is differentiable at (2,F(2))   true…

A: Given statement is If f(x) is a function that is continous at (2,f(x)) then f(x) is differentiable…

Q: 3) Determine A and B that makes the function continuous as x approaches 0 and 1? y A x>1 x-B x<0

A: Given:           y=x2                  0≤x≤1A                   x&gt;1x-B             x&lt;0 Given…

Q: Find an example of a function on the real line, R, that is contin- uous everywhere except at x = on…

A:

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

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Q: Which of the following statements must be true for a function that is concave up everywhere?

A: Which of the  following must be there for a function than is  concave up everywhere .

Q: fスノ= 4ーズ, 〇Find!- U show thet f has Domoin f ? on inverse funyo -1 f ca) ?

A: The given function is  f(x) = 4 - x2 And x&gt;=0

Q: The graph of f', the derivative of f, is shown below. Determine all possible inferences that can be…

A: ---------------------------------------------------------------------------- Key points: If f'x…

Q: +1 Differentiate the function f (x) = In +1

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&lt;x2 then fx1&gt;fx2 claim- is it decreasing or increasing

Q: 57. Compute the derivative of f(x) = x3/2 using the limit definition. Hint: Show that f(x +h) – f(x)…

A: To show that the derivative of the given function by using limit definition is

Q: 3) If a function is continuaus at x=a, then it is differentiaoe at x-a, yes? or NO? why ?

A:

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: Describe the long run behavior of f(2) = - z As z + - 00, f(z) + ? As a + 00, f(æ) → ?

A:

Q: 3)Verify Rolle's Theorem for the function ?(?)=4?2+7 f ( x ) = 4 x 2 + 7 defined over the interval…

A: Explained below

Q: A critical point xo, Yo of a function f is obtained when O Vf(x0, Yo) = 0 or Vf(x0, Yo) does not…

A:

Q: Which of these functions have a domain of (-*, 0)? Select all that apply. A f(x)= e*+2 B g(x)=…

A: We will find such Fucntions.

Q: Let f: X --> Y be a function, and let U be a subset of X.  (1) Prove or disprove that f maps X \ U…

A:

Q: 12UJUJ Find the linearization of the function f(x) = In(x) at a = 1 and use it to approximate the…

A:

Q: Let f be the function defined as follows: [3-x, for x <1 f(x)= {ax + bx, 5x-10, for 1<x <2 where a…

A: Hello dear , I'm solving question1. for you according to our guidelines.

Q: 3)Verify Rolle's Theorem for the function f(x) = 2x² + 6 defined over the interval [-4, 4]. Justify…

A: The function is f(x)=2x2+6   Rolle's Theorem: If f(x) is continuous on the interval [a, b] and…

Q: GRuen that the divectional deivative of f(x,4,2) out the point (3,-2,1) in the divection of a=…

A: Given a→=2i^−j^−2k^ and directional derivative of fx,y,z at the point 3,-2,1 in the direction…

Q: 16 ation specify a function with independent value x? Dur onrwer above provide either the domain of…

A: The equation is given as x2+y2=16 which is the equation of the circle centered at origin and radius…

Q: Differentiate the function.

A: Given function -f(u) = lnu1+ln(2u)Differentiating with respect to u - f'(u) = ddulnu1+ln2uf'(u) =…

Q: х (1 point) If f(x) = t' dt %3D then f' (x) = f'(-5) = %3D

A:

Q: Find the values of a and b that make f continuous everywhere. x2 – 4 - 4 if x < 2 X - 2 f(x) = ax2 -…

A: Here, we need to find the values of a and b. We are given that f is continuous everywhere.  So,…

Q: If f is increasing on the interval [a, b), then f' does exist. Select one: a. True b. False

A: Let f is increasing on the interval [a, b]. Since, there is not given that the function is…

Q: Show that Rolle’s theorem is false for the function f(x) = |x| on the interval [−2, 2]. How can a…

A: Given function f(x)=|x|interval [-2,2] We apply Rolle's theorem only when the function is continuous…

Q: Suppose f is a bounded real function on [a, b), and f' eR on [a, b). Does it follow that fe R? Does…

A:

Q: The domain of the function g(t) = vt – 5 is O R-{5} O R O (5, O [5, 0) о (-оо, —5) (5, 00)

A: From the given function: gt=t-5

Q: Check the validity of Cauchy’s mean value theorem for the functions f(x)=x4 and g(x)=x2 on the…

A: We need to check the validity of Cauchy's Mean Value

Q: Let f(z) = 12 -エ %3D f(z) = f(2)

A: Given,          fx=12-x

Q: Let f(x) dr = -8, f(z) dr = 3, g(x) dr = 7, g(1) dr = - = -15,

A: Given∫02f(x)dx=-8, ∫03f(x)dx=3, ∫02g(x)dx=7, ∫23g(x)dx=-15

Q: In calculus was claimed  that increasing (or decreasing ) functions  defined on a single interval is…

A: Consider a one - to - one function in an fixed interval.  For the function f(x), in the interval 0…

Q: Suppose that ƒ is a continuous and differentiable function s 2000 and that f'(x) > 7 for all x. What…

A: Lagrange's means value theorem: -Let f: [a, b] R be a continuous function on [a, b] and…

Q: akes the following function continuous on (-∞, ∞).

A:

Q: (i) Let ƒ be the function defined on (-o, 0) by f(x) = r$(3 – x)}. (2 – x) -2 Given that f'(x) = and…

A:

Q: Verify the Mean value Theorem for the function f(r) = 2z² – 8z + 6 on [1.3] %3D

A:

Q: a) Evaluate f at x = -1,0, and 5. If not defined, explain. {ogentsY

A: We are given the function,                         .

Q: 6. For each of the cases, give an example of function f: Z → Z. Verify your examples. (a).…

A:

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

A:

Q: 3. Let # 0, 0, r = 0. f(x, y) = Find f.(x, y), fy(x, y) at all points. Leave your answer as a…

A: We need to find differentiation of f(x,y) with respect to x and y.