Sx², lo, (0, x is irrational. x is rational Let f(x) Show that f is differentiable at x = 0.

Q: The fuction f(x)=[x] is contionous at a=0 O True O False

A: a function is contionous if right hand limit and left hand limit is equal to functional value at x=0

Q: f(z) = (x²+y)+i(y²-x) is analytic

A: Let  fz=fx,yu+iv=x+iy the function must be continuous and differentiable at all points in it's…

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

A: Solved below

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A: conditions of function to be continuous: At each joining point the value of limit from both sides…

Q: a. Find the value of (k) that make fhe fimction contimuous at x = 0 3k -3 =0

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Q: Q3) For what values of a and b are ax + 2b , y = x? + 3a -b, 3x-5, x 2 Continuous at every x ?

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Q: Locate and classify the local extremum of the function f (x, y) x² + y? – 8x – 2y + 6. | -

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Q: *z + yz? + 2ry? - = 0 ve z = f (x, y) ise =? what is the f(0,1) at

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Q: 1) Find the absolute extremum values of f(x) = x? [1, 2]. 2x +24 over the interval %3D -

A: Topic - maxima minima

Q: Easy Calculus question, I will rate and like! Thank you for your work!

A: We have to find

Q: sketch f(x)=sec x over the half-open interval -r,27). 2 1 3/% 27t 52

A: Given query is to find sketch the graph of sec(x) .

Q: x* - 2y* (d) Is the function f(x)=- Vx +. homogeneous? If, yes, then find the degree of f(x).

A: We have to examine that the given functions  is homogeneous or not

Q: find the nUmbers b such that the auerage due of f(x)2+6x-3x on the interval E LO,b) is equel to 3

A: Average value of function is given by taking the integral of the function over the interval and…

Q: 3. Consider the function f(2, y) = x° + 7a? + 2æy + y? – 19r – 4y + 1. Find all critical points of f…

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Q: 4: Find the approximate value of f(-2.001, 1.002) where f(x, y) 3x?y + y? – xy +1

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Q: c) Find the second degree polynomial approximation to f at (a, b) = (1, – 2) T2(x, y)

A: Given :- The second degree polynomial approximation to f at a,b = 1,-2 f x,y = -x2y2x2 +y2

Q: 1. Suppose that f f(x) dx = In x + Vx+1+C. Can f be a rational function? Explain.

A: To explain f is a rational function or not.

Q: ind the critical points of the function f(x, y) = x² + y² + 10x – 9y + 3. List your answers as point…

A: In this question, concept of critical points is applied. Critical Points The critical points of a…

Q: -2? + 15z - 27 f(z) = 3z2 + 7z + 6 C, I= 3 What value of C would make f(x) continuous at z = 3?

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Q: 2) Consider the function g(x) = x³ + 3x? – 9x + 2 on the interval [-4, 2]. Find all local extrema,…

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Q: Consider the function f(a) = 7x° + 5x° - 5x 3. Enter the antiderivative of f(x)

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Q: Let f (x) = 2x3 – 0.0064x? – 1.5x + la (a) Indicate that f(x) = 0 has a root in the interval [-3, 0]…

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Q: Calculate the derivative of the following functions

A: Given: y=fx gx5 To determine: Derivative of the given function

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

A: Given: xyx2+y20,x=0,x≠0 According to the given problem: At x=0. fx(x,y)=fy(x,y)=0

Q: 3 Let f(x) = 8x° 1 df 15x - 5, x2 1.5. Find the value of dx at the point x= 2004 = f(7). %3D

A: Known fact: derivative of f-1x=1f' f-1x.

Q: 2. For which values of a is f(x) differentiable on R?

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Q: III. Let f(x) = e2 sinz 2. Find the absolute extremum values of f on the interval [

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Q: lim f (x) = 4 f(x) has a HA at y=4 418 O True O False

A: From the given problem: limx→∞fx=4 As we know that; To calculate the horizontal asymptotes, solve…

Q: The range of the finction f(x, y) = In(-x² -+1) is %3D None of these O (00:0] O [0; +0) O [0;1]

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Q: (c) Does there necessarily exist a differentiable function h with 0 < h(x) <1 and E = {x : h(x) = 0}…

A: Sol:in the given question we have to tell about the differentiable function f(x)s.t whose range is…

Q: Q3) For what values of a and b are ax + 2b , y = {x? + 3a -b, (3x-5 , 0 2 Continuous at every x ?

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Q: Q3) For what values of a and b are (-x² + a , y = { xsin-+1, 0 < xs: bx³ + 2 , Continuous at every x…

A: See the attachment

Q: Jx?, x is rational 1o, x is irrational. Let f(x) Show that f is differentiable at x = 0.

A: Given, We know that, fx=px     , x is rationalqx     , x is irrational  is differentiable only at…

Q: Consider the function f(x) = 9x° + 9x' – 10a? – 4. An antiderivative of f(x) is F(x) = Ax" + Bxm +…

A: Given: fx=9x8+9x7-10x2-4

Q: 9. 3x2 Let g(x) = -2x2 r<0 (b) Prove that q is not differentiable at 0.

A:

Q: Suppose that f: R→R is a differentiable function, satisfying f(4)=3 and f(x) dx=6.

A: Given data: The first condition given is f(4)=3. The second condition given is ∫04f(x)dx=6. The…

Q: Q2 Let f(x) = 2x3 – 0.0064x² – 1.5x + Ia (a) Indicate that f(x) = 0 has a root in the interval [-3,…

A: let fx=2x3-0.0064x2-1.5x+Id where Id=0.55 (a) indicate that fx=0 has a root in the interval -3,0…

Q: The range of the finction f(x, y) = In(-x2-+1) is %3D None of these O (-00:0] O [0; +0) O [0;1]

A:

Q: Find a point zo where the function f (2) = (z – 8 – 10i) (z– 8 – 10i)differentiable. What is the…

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Q: Consider the function f(x) — 6ӕ* — 9a? + 10х — 9. - An antiderivative of f(x) is F(x) = Ax* + Bx³ +…

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Q: The abetute uinian value of f(r)--3r 12 on the closed interval -2, 4ceurs at aM (A) 1 (B) -1 (C) 0…

A: Given:   f(x)=x3-3x2+12   in interval [-2,4]To find absolute minimum applying first derivative test…

Q: H.W:- Prave.that.he.Maclaurinsevi.of.f(x).=-C0JA 3. (い (2n)! 2 i 5... f.(x)..co3.X.1. メ n=0

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Q: Q3) For what values of a and b are ax + 2b , y = x2 + 3a -b, 3x-5, 0 2 Continuous at every x ?

A: We will check continuity at breaking points of the function. For continuity , left hand limit and…

Q: y y =x – x12 1 Rogawski et al., Calculus: Early Transcendentals, 4e, © 2019 W. H. Freeman and…

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Q: Find the largest domain (in R²) for the function 1+ Vx + Vy x² + y? f(x, y) =

A: The domain are those values of x,y; such that f(x,y) is well defined. Well defined means that the…

Q: 0If z-x"f), show that xZ+JZy=mZ.

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Q: The function f(x) = x³ – 3x² + 5 is concave upward on the interval O (-∞, 1) (1, co) (-∞0, ∞0) O…

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Q: Q3) For what values of a and b are -x² + a , x Continuous at every x ?

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Q: O De fine fG) in a way that extends g8) = X -3 to be continuows at x=3

A: It is continous function  problem.