estion # 10 Let f (x) = x² and if 0s x<1 if, x=1 -4, g(x) = Ix - 4| Determine weather f°g and g fare continuous at x = 0.

Q: (x2 -7 , 0b Is fdifferentiable at b?

A: Given that: f(x)=x2-7,       0&lt;x≤b6/x   ,        x&gt;b

Q: Iベ+g2 Let f(x y) s (x,y) = (0, 0) . ノ Is f Continuous at 10,0) ? why ?

A:

Q: Locate the absolute extrema of the function on the closed interval. g(x) = x² - 2x, [0, 9] minimum…

A: Given that      g(x) = x2 - 2x ,    [0,9]

Q: Let ƒ(x), g(x) be two continuously differentiable functions satisfying the relationships ƒ′(x) =…

A: Given,

Q: g(x) = x + 2 (2, 4) (blue line) f(x) = x² (black curve) A (-1, 1) 1-

A: From the given bounded region; Now use the double integration method to find the area between the…

Q: Examine the function for relative extrema. (If an answer does not exist, enter DNE.) f(x, у) %3D 2x2…

A:

Q: xy³ Q3: Let f(x,y)=2x² + y² 1 (x, y) = (0,0) Is f continuous at (0,0) ? Is f continuous at every…

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Q: f(x) = 'dt th (2) 3=

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Q: Please

A: Given function: Now,

Q: II. Let F(x)= ecosh z √x+1 1. Find F(0). 2. Find F'(x). sin(1-t) dt.

A: Let Fx=∫x+1cosh x sin1-t dt.1 To find F0.2 To find F'x.

Q: find the absolute extrema of thefunction on the closed interval y=x \ln (x+3),[0,3]

A: A function is usually represented as f(x) where x is the input to the function and f(x) represents…

Q: xy³ Q3: Let f(x,y)=2x²+y² 1 (x, y) = (0,0) Is f continuous at (0,0) ? Is f continuous at every point…

A:

Q: 3. Find a value of b so that the function x 1 f(x) = is continuous on (-0, 0).

A: A function is said to be continuous if Left Hand limit = Right Hand limit = f(a) In this question,…

Q: 1 x2 - х х x 2 Vx -2, Identify if the function g(x) is continuous/discontinuous at x=1. If…

A: Given: f(x)=1x2-x+1xx&lt;0-10≤x&lt;101≤x&lt;21x=2x-2x&gt;2 To determine: The given function is…

Q: - Integrate the function f orgy) =y-Vx over triangle cut from the first quadrant by Line X+y=1

A:

Q: 5.) What can you conclude when dx is changing from negative to positive? A) fis at a local minimum…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: x²-y² x²+y2 (x, y) = (0,0) For which value of "a" the function f (x,y) is continuous? (x, y) = (0,0)

A: Continuity.

Q: x² + 1, x 1 Let f(x) = Is function f continuous at x = 1? Is functionf differentiable at x = 1?

A: Given :-  f(x) = x2+1 when x&lt;1  f(x) = 4-2x when x≥ 1  To find:- Check function continuous or…

Q: Find the points of inflection and discuss the concavity of the graph of the function.

A: Find the points of inflection and discuss the concavity of the graph of the function.…

Q: Find linearizing ( L(x) ) f(x) at x=a . where f(x) = tanx and a = π a) π b)  x - π c) π - x d)…

A: SOLUTION-

Q: .Find extrema for a function y=f(x)%3D2X² - 8x on an interval [0, 6].

A: An extremum (or extreme value) of a function is a point at which a maximum or minimum value of the…

Q: V4+x-2 If f(x) = ,x*0 be continuous at x = 0, then f(0) = 1/2 1/4 3/2

A:

Q: find a non zero value for the constant k that makes the function fx={tan k(x) /x ,x0}continuous at…

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Q: x + y + 1 f(x, y) = , x ln (y² х — 1 -

A: A function f=f1, f2, ⋯, fn is said to be continuous at a if and only if the all the components f1,…

Q: 1. Is a function f(x)=√x differentiable at a) X = 1 b) X = 0 c) X = -1

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: x-1, -1 sx< 0 0<x <1 x = 1 1<x< 2 2 <x<3 2r, f(x) = 1, -2r + 4, 0, Is f(x) is continuous at x = 1…

A: Given: f(x)=x2−1,−1≤x&lt;02x,0&lt;x&lt;11,x=1−2x+4,1&lt;x&lt;20,2&lt;x&lt;3 A function f(x) is…

Q: (x+1, l-x +1, x >0 Is f(x) continuous at x = 0? x30 Suppose f(x) =

A: We find the left-hand limit, right-hand limit and the value of f(x) at x=0

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: x2- 1 -1Sx<0 1- If f(x) 1 x=0 is it continuous at x=0 %3D 2х 0<x<1

A: Here the given function is  f(x)=x2-1if -1≤x&lt;01if x=02xif 0&lt;x≤1 We need to find weather the…

Q: Vx – 2 v(x) = X – 2 at x = 2 Select the correct response: Continuous Discontinuous

A:

Q: Find the maximum and minimum values of the function f(z, g) ry subject to 3z+ 2y = 18 Maximum value:…

A: Given : f(x, y) = x²y subject to 3x² + 2y² = 18

Q: True or False Suppose f is differentiable everywhere. Then the chain rule assures that d/dxf(f(x)) =…

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Q: xY 10.3.5. Can the function f(x, y) be extended to a continuous function on R²? |x|+ \y]|

A: Here, the given function is: f(x,y)=xy|x|+|y| which is not continuous at (0,0). To extend it on ℝ2…

Q: Solve this attachment.

A: Given:fx,y=xy2-x2-y

Q: 3. (10 points) Determine the value of C such that if r +0 f(r) := V16 + 3x – 4 if r = 0 will be a…

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Q: 2. Let f(x,y)= xe" and find a) fu. fy» fy

A: Please refer the attached image for complete solution.

Q: ew Choose the definition for the function. S-x+2 x > 1 lx+1 a. y = { {-x+ 2 x 1 b. y = {x+1 1-x +2…

A: Since function is not continuous at x=1 because graph of function is break at x=1 so, right and left…

Q: A function y(t) satisfies th

A: Given, the differential equation                       dydt=-y4-3y3+4y2

Q: Find the absolute extrema of the function on the closed interval. f(x) = cos TX, [] minimum (x, y) =…

A:

Q: Examine the function for relative extrema. (If an answer does not exist, enter DNE.) f(x, y) = 9x² +…

A: Discriminant of the functionif we have fxx,fyy,fxythen D=fxxfyy-fxy2if D&gt;0 at (x,y)  anf fxx&gt;0…

Q: Let f(x), g(x) be two continuously differentiable functions satisfying the relationships f'(x) =…

A: Introduction :

Q: Find the absolute extrema of the function on the closed interval. f(x) = cos 7EX, = COS 0, minimum…

A:

Q: Sketch the graph of a differentiable function y = ƒ(x) through the point (1, 1) if ƒ′(1) = 0 and a.…

A: We need to Sketch the graph of a differentiable function y = ƒ(x) through the point (1, 1) if ƒ′(1)…

Q: 2. i) Give an example of a nonzero continuous function f on [0,1] such that f(x)dx = 0.

A: We have to give an example of a nonzero continuous function f  on [0,1] such that  ∫01f(x)dx = 0

Q: If a pdf of Y is ƒ(y)={1-|>| ||S1' />1 find and graph F(y).

A: Given, f(y)=0  y&gt;1 From the above expression, Thus, the function is zero (f(y)=0) in the…

Q: x-1 for x 1 x -1 show that flx) is continuous at x = 1 !3! for x 1,

A:

Q: mx – 11 if x – 4 If f(r) is a function which is continuous everywhere, then we must have Preview

A: A function f(x) is continuous at a point x=a, if, limx→af(x)=f(a).

Q: Find f'(x) if f(x) = arcsin ve 0 f(x) = 2√1-2² 2√√√1-e 0 f(x)=√√² E² 21-e 1

A: Topic = Derivative

Q: Determine unknown constants a and b for which g(x) is continuous at x=1. [5x - 2 x 1

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Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.