1 if oと ×く1, f Cx) = x € [1, 2] if Let Fl)- Sofledt for each Jof(t)dt for each X E [0,2] which of the following statemens ARE True ? a) Fw = X for all X EC 0,1] b) FaN こ 2 for all X E [1, 2] c) F is dis continuous at x = 1 d) F is con tinuous at x=1 but not differentiable e) F is differentiable at x=1 and F'(1) = 1

Q: Suppose  f ( 200 , 300 ) = 1000and ∂ f ∂ x ( 200 , 300 ) = 12 and ∂ f ∂ y ( 200 , 300 ) = 10.…

A: Given, f(200,300)=1000 ∂f∂x(200,300)=12∂f∂y(200,300)=10

Q: 34) If f is an even function that is continuous on [-1,3] and if f f(t)dt f₁f(t)dt = 8, then f…

A:

Q: Suppose f:R→IR is a diffexetiuble function which satısfies flo) = 0 . We wort to shouw f': IR → IR…

A: We have to do implicit differentiation.

Q: Suppose 2 < f'(x) < 6, for –1 < x< 1. Then f(1) – f(-1) is between A) 2 and 10. B) 4 and 12. C) 0…

A: GIVEN : 2 ≤f'(x) ≤6,  for -1 ≤x≤1 TO FIND : f(1) - f(-1) HINT : Mean value theorem

Q: cide whether the following function is one-to-one and whether it is onto. Then prove your answers…

A: In this question, concept of one-one function is applied. One-to-one function The term "one to one…

Q: Suppose f is a function defined and continuous on the open interval (a, b). Suppose g is a function…

A: Given that: f is a function defined and continuous on the open interval (a, b).g is a function…

Q: suppose

A:

Q: is The functionFIO-Vx4iscontinusus onR. It cosă

A:

Q: Prove that: cscz- cot z = 1 2. 2. %3D

A: We need to prove the identity  csc2z-cot2z=1

Q: Prove that if f:X + Y is a one-to-one and onto function with inverse function f- : Y → X, then fof-l…

A: Given that, f:X→Y is a one-to-one and onto function with inverse function f-1:Y→X

Q: ,10 If f is a continuous function and F'(x)=f(x) for all x € R, then A 2[F(5) – F(1)] B 2[F(10) –…

A:

Q: 1. Evaluate: 1 1+x 2. Find Fa) given f'a)=3Sinx-4e*, FET)=4e"

A:

Q: Prove that the derivativeo P(zx tJ's 4(2Xbjusiy Pirst Princiele 4(2X+)by jusing first Princiele…

A:

Q: f 'C) =7x*+7-3 ond fl0) 3D8

A:

Q: If f is a function from X to Y and C, D are subsets of Y then A O f(C-D) =f(C)-f (D) B f'(Cn…

A:

Q: Determine all analytic functions f on nEN. D(0, 1) satisfying f() = 1 for all

A: The identity theorem for analytic functions :The identity theorem states that if two analytic…

Q: Show that if f (x, y, z) = 0 then = -1.

A:

Q: 2.) Determine the set of points at which the function is continuous. а. F(x,у) — 1+x²+y² 1-x2-у? ху…

A: Here, to find the set of points at which the function is continous.

Q: 4. If /(r.y)=- , find f, and f,. V+y

A:

Q: 11. Let f be a f maximum at I. f'(c II. If f' III. If f" (А) П only

A: Given : f has relative maximum at x=c Suppose f is an absolute function then f has relative maximum…

Q: 12. Let f(z,y) = < then f(1,2) = (b) 글 (d) 금

A: Given :fx, y=x-yx+y-1

Q: Question 3. the interval(s): a) (-00, 00) b) (-0, -) and (, +0) c) Nowhere (it's always con- cave…

A: Given function is f(x) = e-x2

Q: 1. Given a set X and a subset A CX, define a function ƒÃ : X → {0, 1} by setting f₁(x) 1 if ¤ ¤ A…

A: (a) fA : X → {0, 1} is defined as             fA(x) = 1 when x ∈ A                       = 0 when x…

Q: Use Exercise 69 together with the identitiessin (h + c) = sin h cos c + cos h sin c,cos (h + c) =…

A:

Q: Suppose fx) is a continuous function. Then a function F(x) Such that F'(x) =f{x) is called:

A: Given:- Suppose f(x) is a continuous function Then a function F(x) F'(x) = f(x) is called

Q: a) Evaluate [-ri-yj+2: k) - n ds, (-a i- where a is the portion of the paraboloid z = 3r + 3y…

A:

Q: Let f(r) = |r|. The derivative of f at r = 0: Question 1. a) Equals to ±1 b) There are infinite…

A: the given function is f(x)=|x| we know that x=x if x≥0-x if x&lt;0 to find the derivative proceed as…

Q: a) What is the binary representation of the integer 756? Explain your work. b) What is the octal…

A:

Q: Let f(x) = |r|. The derivative of f at a = 0: Question 1. a) Equals to +1 b) There are infinite…

A:

Q: 5. Assume f: [0, 1] → [0, 1] is continuous with f(0) = f(1). Prove there are x, y = [0, 1] with |x -…

A: We have to assume f: [0, 1] → [0, 1] is continuous with f(0) = f(1). and prove that there are x, y ∈…

Q: continuous at (C

A:

Q: 3. Define f(x) so that S(2) = {ap(). f(x) = 0, |피 1 (a) Explain why the function f(x) must be…

A: As per our guidelines we can answer only 3 subparts. please ask others seperately.