Let f : Z+ → N be the floor function f(x) = [(x – 1)/2].

Q: Find c such that the function x2 – 9 x с is continuous everywhere. - С —

A: f(x) will be continuous at x=c. when value of the function at c , left hand limit of f(x) at c  and…

Q: Q2 (A) At what points f(x, y, z) in which the function f(x, y, z) = -√x²+y² is Z- continuous?

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Q: Find the funchion f Such that F(x) xf (x)-x and fo) 2

A: Convert the given problem to a simple differential equation and solve the same.

Q: Let f(x, y) = - 4xy² – 2x² + 8y². Find and classify the critical points of f.

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Q: Differentiate fx) with respect to g(x) of yx= xsiny

A: To find the derivative

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

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Q: Use the chain rule to show that for any differentiable function f(x), [e/(e) = f(x)e/(=),

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Q: Let z = f(x, y) = 5x – x³ + 2xy – y². - Find and classify all the critical point(s) of this…

A: Differentiate the function fx,y=5x-x3+2xy-y2 partially with respect to x and y, to obtain fx and fy.…

Q: Define the function f(x, v) = 4x³-x³y-4y5 3x5-3y5 at the origin so that it becomes continuous there.

A: A function is said to be continuous at (a,b) if the the value of function at (a,b) is equal to…

Q: Determine the set of points at which the function is continuous. a) f(x,y) = ln (x² + y² – 4)

A: According to question given thatf(x,y)=ln (x2+y2-4)

Q: Find the linearization L(x) of f(x)=tan x at x=3pie/4.

A: Given

Q: Find the minimum and maximum of A over a particular interval [0,6]. A(x) = f(t) dt

A: The solution is given below in the next step: I

Q: Find the linearization L(x) of f (x) = tan x at a =

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Q: Explain why f (x) = sin (x² + 3r + 1) is a continuous function for all c € R. %3D

A: Let us assume that: g(x)=sin(x)and h(x)=(x2+3x+1)So,…

Q: Decide whether or not the real function In (eon 2) I+0, = (1) 1= 0, is continuous at r = 0.

A: The given function is fx=ln cos2x2x2     if  x≠0-1                if  x=0. Compute the limit…

Q: Consider the function xy f(x, y) x²+xy+y² k if (x, y) = (0,0) if (x, y) = (0,0) State, with…

A: Given :  f(x, y) = xyx2+xy+y2if (x, y)≠(0, 0)kif (x, y) = (0, 0) To find : The value of k if it…

Q: Let F = 1) Find the divergence of F. V•F = 1+ 1/xz + In(y)

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Q: Use the Second Fundamental Theorem of Calculus to find F′(x).

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Q: Let f(x) =esin 3x + 2x a. find the linearization of f(x)=esin3x+2x at x=0. b. Use your linearizato…

A: a). Given f(x) =esin 3x + 2x f(x) ≈ L(x) = f(a)+f′(a)(x−a). where the function L(x) is called the…

Q: Let f(x, y) = ln (3x + y2). Show that fxy = fyx

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Q: the function f (2) = z Cos z ̟has a zero of order

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Q: Let f(z) (x-iy)e- ) Determine the points at which exist, and find r(2) at these points.

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Q: Show that the limit of the function f(x,y) = at (0,0) does not exist. (x+y)² x² + y²

A: Limit of a Function: Like a single-variable function, a multi-variable function can also have limit.…

Q: Find the linearization f(x) = √x, L(x) = L(x) of the function at a. a=4

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Q: attached

A: Linearization of f(x) at x=a is given by

Q: Find the linearization L(x) of f(x) at x=a. f(x)=x/2x+9 a=0

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Q: Determine whether the function f (z)= Įz² – e3z I0

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Q: Find the linearization L(x) of f(x) = cot x at x = 4 %3D -

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Q: C. Is the function define by g(x) = x² – sin x + 5 continuous at x = n?

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Q: Find the best linear approximation, g, to f on the interval [0, 1]. (x) = 2/x g(x) %3D

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Q: Determine the maximum value of f (x) = 5x – e5x [T:3] on the interval [-1,1] %3D

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Q: Find the best linear approximation to f on  the interval [-1,1].                        f(x) = x2

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Q: Find the Wronskian for the set of functions.{ex, e−x}

A: Given set of functions ,f1=ex & f2=e-x

Q: Let f be a continuous function with f(x) > 0 for all æ € R. Define r(z²+1)" g(r) = e" f(t)dt.

A: Let f be a continuous function with fx>0 ∀x∈ℝ. A function g is defined by  gx=∫0x2+1xexftdt…

Q: Find c such that the function 10 I C - is continuous everywhere.

A: A function f(x) is said to be continuous at a point x=a if limx→af(x)=f(a). That is, a function f(x)…

Q: Q1. (a) Find the points (x ,y, z) in space, where the function f(x, y,z) = /x² +y² -1 Is continuous.

A: Given :- The points x,y,z in space , where the function f x,y,z = x2 +y2 -1 is continuous.

Q: Find the linearization L(x)of the function at a .

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Q: A continuous real-valued function f (x) with f (a) ƒ (b) < 0 , has at least one root in [a, b]

A: This question is related to Real Analysis.

Q: Use the Second Fundamental Theorem of Calculus to find F′(x).

A: It is given that,Fx=∫-2xt2-2tdt We have to use the Second Fundamental Theorem of Calculus to find…

Q: Let g(u) be a differentiable function and let f(x, y) = g(x² + y²), find the direction of maximal…

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Q: Let L(r) be the linearization of f(x) = sin x + 1 at the point x = . Find L(π/2).

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Q: Find the linearization L(x) of f(x) at x = a. f(x) = a = 0 4x +3

A: topic - linearization of a function

Q: Estimate the global maximum value for the function F on the interval [-2,1] if F(x)= || dt . t2 +1

A: The given function is: F(x)=∫-2x tt2+1 dt

Q: | For what value of a is Sx² – 1, x< 3 |2ax, f(x) = continuous at every x?

A: Let f is continuous at x = 3 then left and right limit are equal.

Q: Find the linearization L(x) of f(x) at x = a. f(x) = sin x, a = 0 O L(x) = 3x + 1 O L(x) = 0 O L(x)…

A: L(x) = f(a) + f '(a) (x - a) where, L(x) is the linear approximation of f(x) at x = a. f '(a) is…

Q: Let f(x) = 2 cosh(4x) – e4x %3D Find the absolute maximum of f(x) on the interval [0, In 3].

A: The given function is                                         f(x)=2 cosh(4x)-e-4x We know that…

Q: Use the e-d definition to prove that f(x) = x³ + 3 is continuous at xo = 3.

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Q: Find the Wronskian of the set of functions {e*,e® sin(x)}.

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Q: Let f be the function from R to R with f (x) = x2. Is f invertible?

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