Suppose that the functions h and g are defined as follows. h (x) =x+4 g (x) = (x+1)(x+2) )(-3). (a) Find h (b) Find all values that are NOT in the domain of -. If there is more than one value, separate them with commas.

Q: Verify that the Mean Value Theorem applies to the function f(x) = √25-x2 on the interval [-3, 4] and…

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Q: Find critical number of f(x) = 5x^2-8x+1

A: Given,          fx=5x2-8x+1

Q: Show that f(x) = x3 - 2x - 1 has a real zero between 1 and 2.

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Q: Discuss the continuity of f(x) = 2x + 3 at x = −4.

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Q: Find the constant a such that the function is continuous on the entire real line. 7sin x if x < 0…

A: Here we find the value of constant a

Q: Discuss the continuity of the function on the closed interval.                              g(x) =…

A: We can not have a negative value under the square root.  So,

Q: Discuss the continuity of the function h(x) = }" (x2 + 7х -5, x3 – 2x2 + 1, x < 3 x 2 3 on the…

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Q: Verify the Mean value Theorem for the function f(x) = 2x2 - 8z +6 on [1, 3]

A: f(x)=2x2-8x+6  on [1,3] conditions of mean value theorem: i) f(x) is continuous at (a,b) ii) f(x) is…

Q: Suppose that f(x) = βx2 − 3     if x ≤ 2                                βx + 2       if x &gt; 2…

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Q: If the function f (x) is continuous for all real numbers and if f (x) x²-4 when x + -2, then x+2 f…

A: f(-2) = -4

Q: Suppose that y is a function of x. Find if 2x°y 3 2y + 5. - -

A: We will find out the required value.

Q: Verify that f(x)=x3- 3x + 2 satisfies the hypotheses of the Mean Value Theorem on the interval…

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Q: is the function continuous at x=5 if f(x)={x2-4x-5/x-5,     x5

A: Given: f(x)=x2-4x-5x-5  ,   x&lt;5x+1            ,  x≥5

Q: Use intermediate value theorem to show that f(x) = -x3 + x2 + x + 1 must have at least one zero on…

A: Given: fx=-x3+x2+x+1 &amp; interval 0,2 To show: The given function must have at least one zero on…

Q: Discuss the continuity of the function on the closed interval.

A: Given: f(x)=x2-1x+1 The function is continuous at a point if the function returns a unique value…

Q: Find the constant a, such that the function is continuous on the entire real line. f(x) = {2x2,…

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Q: Find critical number of f(x) = x^2 - 6x + 8

A: To find critical number of f(x) = x^2 - 6x + 8

Q: Find the constant a such that the function is continuous on the entire real line. 7sin x if x <0…

A: For a function to be continuous at x = a, it must satisfy the following condition:

Q: Find the derivative of f(x) = 2² +8-2³ + 5z³. 0 (2) - 1/2 +8-235-24 + 152² O f(2)=1/22-²5 2¹ +152²…

A: The given function is; f(x)=x2/4 +8 - 5x5/3 +5x3.

Q: Prove that a function of the form:is an even function.

A: The given function is  y=a2nx2n+a2n-2x2n-2+...+a2x2+a0

Q: The functions f, (x) = 3x2 – 1 and f2(x) = 5x³ – 3x are orthogonal on the interval [-1,1] True/False…

A:

Q: x -4x +5 - Prove that: f' x x-2

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 1. prove that if x is real number then ,[2x] =[x] +[x +1/2] when [x] denote the greatest integer…

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Q: prove using the IVT. √2 exists. Hint: Consider f (x) = x2.

A: we have to show √2 exists. Now let

Q: . If f : (0, 3) → R is continuous, must its range be an open (possibly infinite) interval?

A: See the detailed solution below.

Q: Discuss the continuity of the function f(x) = {x2 − 3x if x &lt; 2 2x + 4 if x ≥ 2 on the open…

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Q: Find the constant a such that the function is continuous on the entire real line. 8sin x If x < 0 if…

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Q: Find the constant a such that the function is continuous on the entire real line. 8sin x if x < 0…

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Q: Q1) check the continuity of fX) at X- -1, 0,1.23 -1<x<1 2x-1, 3x-2 25x53 2, x=3

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Q: Oz(-@) and Ør(@) are conjugate functions. That is, Px(-@) =Øx°(@) %3D and Oz"(-@) = , (@)

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Q: Find the constant a such that the function is continuous on the entire real line. 3sin x if x < 0…

A:

Q: Check the continuity of the function f(x) at x = -2 f(x) = - 6r + 3x l-6x if xs-2 if x>-2

A: Given,         The function fx at x=-2.           fx=x2+3xif x≤-2x3-6xif x&gt;-2

Q: Suppose that f(x) = βx2-3     if x≤2                                   βx+2       if x &gt; 2…

A:

Q: If f : [0, 3] → R is continuous, must its range be a closed interval?

A: Given data: The expression for the function is f : [0,3]→R. The continuous image of the open bounded…

Q: Find the are under the graph of f(x) = 4-x2  on the interval (-2,1)

A: Given, f(x) =4-x2  we have to find the area under the curve on the interval (-2,1)

Q: Q1) check the continuity of fX) at X--1, 0,1.2,3 -1<x<1 f(x) = 2x-1, 3x-2 2SxS3 2, 1=3

A: As per the answering guidelines we need to answer only first question so please repost the other…

Q: 5. Show that the functions x,x? -,x³ -x x are mutually orthogonal in the interval [-1,1].

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Q: Find a function for which f'(x) exists for all real numbers but f"(x) doesn't exist for all real…

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Q: Show that the function g(x)  =x| x has an inflection pointat (0, 0) but g"(0) does not exist

A: Given: The function g(x)= x |x| For x&lt;0, |x|=-x, thus g(x)=x(-x)=-x2 Also for x≥0, |x|=x, thus…

Q: Discuss the continuity of the function on the closed interval.                        Function g(x)…

A: Givengx=1x2−4  Interval [-1,2]

Q: Find all critical points of the function f(x) = x³ + 3x² them in descending order and separate them…

A: Find all critical points of the function f(x) = x³ + 3x² - 5x + 9.

Q: 4) Show that and are eventually fixed points for the function : 8 4x Osx< 2- 4x sx< f(x) = - 1 4x –…

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Q: The domain of function x) = In(2– x) is %3D

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Q: - Find all critical numbers of f(x) = 3x* + 20x – 36x²

A:

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.