Suppose that f hits every value between y = 0 and y = 1 on the interval [0, 1]. Must f be continuous on that interval?

Q: is uniformly continuous by definition on the interval (-1,1) . 4 - * Show that f(x) =

A: A function fx defined on an open intervala,b is uniformly continuous on a,b iff  i fx is continuous…

Q: If f is differentiable at a, then f is continuous at a.

A: If a function fx is differentiable at x=a then function must be continuous at x=a. But a function…

Q: If f is continuous at a number, x, then f is differentiable at x. True

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Q: Is the function continuous on the interval (0, T COS x O no O yes O cannot be determined

A: Given problem:- Is the function ex/cosx continuous on the interval [0, π] ?

Q: Determine if = f(x)=Vxis uniformly continous on the interval I [0, +)

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Q: b) Suppose that f(x) 1 if x is negative. Can ƒ be continuous at x = 0?

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Q: Determine the interval(s) where f(x) = is continuous. 1- In(1/r)

A: It is given that, f(x)=11-ln1/x   A function is said to continuous in an interval in which it is…

Q: If f is differentiable at a number, x, then f is continuous at x.

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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: If f is continuous at a number, x, then f is differentiable at x. True False

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Q: If f(x) is continuous at x=a , then f(x) is also differentiable at x=a.

A: " If F(x) is continuous at x=a then f(x) is differentiable at x=a." The condition for the function…

Q: What is the definition of f(x) is continuous at x = a? ||

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Q: Let F(x) be the function defined as follows: F(x)= (1+ In(t))*dt What is the value of F'(e) ?

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Q: What does it mean for f to be differentiable at a ?

A: we have to define that what we mean by the f is differentiable at a.

Q: State the interval(s) over which the function f(x) = V16 – x² is continuous.

A: Given, fx = 16-x2   We have to state the interval over which the function is continuous.

Q: Determine if the function f(x)= are uniform X continuous on the interval I= [0,1]

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Q: Clarify that f f :(0,1) →R defined by f(x): not uniformly continuous. =-

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Q: Find the values of a and b that make f continuous everywhere.

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Q: Prove thait if y=f(x) f(x)=0 when x is a rotional number, then f(x)=0 for all x € R. is continuous…

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Q: define the function at 5 so that it becomes continuous at 5.

A: First, we rationalize the function, so that it becomes continuous at 5 which is shown on the board

Q: H(x) = L, [At) +A-1) ]dt

A: Question derivative of function.

Q: Let f(x) = CX– 2, x > I lx+ 8, x < 1 For what value of c is f(x) continuous on (-00, 0)

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Q: Use limits to determine if f(x) = 1 is continuous at x = 0. (z+2)?

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Q: Show that the function is continuous. f(x) = cos(x 2)

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Q: Set f(x) = xª for x ≥ 0 and f(x) = 0 for x < 0. For which values of a is f continuous at 0, and for…

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Q: Let f: RR be a function satisfying f(x + y) = f(x) + f(y) for all x, ye R. If the function f(x) is…

A: Note :   Let r&gt;0 and c∈R ,then vr(c)={x∈R : x-c&lt;r }=(c-r ,c+r) ,which is called r…

Q: Let f be the function defined by: sin x, x 2 - For what values of x is f NOT continuous?

A: Given function is: fx=sinxx&lt;0x20≤x&lt;12−x1≤x&lt;2x−3x≥2

Q: Use the definition to show that the function f(x) = → is continuous on the interval [c, o), %3D…

A: The given function is f(x)=1x2 .we have to show that f(x) is continuous on the intervel [c,∞)…

Q: Which of the following interval is f(x) = O (2, +∞0) O [2, +∞0) 0 (-∞0, +∞0) ○ (0, +∞) 1 Vx…

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Q: show that f,given by f(x) x +0 )is continuous on R-{0}

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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: Where is f(a) not continuous?

A: Given:

Q: Show that the function f(x) = csc(x) is not uniformly continuous on (0, pi/2]

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Q: Let f be a continuous function such that f (x) dx 5 and 6° | f(x) dx = 3. What is the value of |…

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Q: Determined where the function f(x) is continuous

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Q: Find the value/s of a such that the function f is continuous everywhere.

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Q: Show that f(x)= |x| is not differentiable at x = 0.

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Q: Is f(x) = √x continuous at x = 0?

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Q: Show that the function f(x) = 1 – I - x² is continuous on the interval [-1, 1].

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Q: If f is differentiable at a ,then f is continuous at a

A: Every differentiable function is continuous.

Q: If f(z) is continuous at z then it must be differenttiable at z, 0.

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Q: Prove that the function f(x)=sinπ|x| is continuous at x = 0 but not differntiable at the same point.

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Q: Determine if f(x)=x² is uniformly continous on the interval I = (-∞, +)

A: See the attachment.

Q: Suppose f ≤ 0 , f is continuous on [a, b] and ∫ab f dx= 0. Prove f(x) = 0, ∀ x ∈ [a, b].

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Q: what condition when present are sufficient to conclude that a function f(x) is continuous at x=a

A: To show a sufficient condition to conclude that a function f(x) is continuous at x=a.

Q: Prove: f(x)=5x y is continuous at x=2

A: A function fx is continuous at a point x=a, if limx→afx=fa Given function is

Q: Find the value of fa) which makes f(x) continuous at x = a (if exists) where X - x f(x) a =

A: Given function is fx=x-xx Find the value of fa=0.

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.