20. The function f :R → R is defined by 8x - 3 2x - 7' **. f is A odd B surjective C even D injective

Q: Show that f (x) = 1 is not uni form continuous on (0,3) I-3

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 7. Let S = [0, 1] × [0, 1] and ƒ: S → R be defined by f(x, y) (2x³+y², 10, Show that f is integrable…

A: Follow the steps.

Q: Show

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Q: 8. If f is continuous and f(x) dx 10, find xf(x²) dr. %3D Give proper reasoning.

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Q: Show that F = ху, , zy) is not conservative. 2

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Q: 1. Let f(x, y) = In(x - y) then at the point (4,1), fryis equal to: %3D -1/9 O 1/7 1/9

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 3. Compute the value of F.dr if F = -yi + xj and C is a semicircle from (-1,1) to (1,-1).

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Q: If f has a critical point in the interior of a closed and bounded domain D then the minimum and…

A: Statement: If f has a critical point in the interior of a closed and bounded domain D then the…

Q: Define fi z-> 2 xZ by Ala)l (2,72t1) if xis even 18,0) if t is odd a) Is f injective 2? b) Is f…

A: We have f:Z→z×z Such that fx=x,x+1     if x is evenx,0          if x is odd

Q: Find the Wronskian for the set of functions.{x, sin x, cos x}

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Q: Use Theorem 2 to show that 3, if x <-10 2, if – 10 sxso F:R → R,F(x) = -2, if 0< x< 10 -3, if x2 10…

A: so we have to show that given function is discontinuous at 2 and -2 (a)   Discontinuous  at -2…

Q: 2. Show that 4=x i+y°j+:'k is irotational.

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Q: The interval on which f(x) = 3 – 2x – 12x² – x³ is | - concave down is: O (-4, 0) O (-∞, 4) O (4,…

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Q: Let f:R→R be defined by f(x) : [ 2x – 1, z<2 | 2x +1, 22 , then f-'(4, 7() is None of the choices O…

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: Show that the functionf (x ,y)=xy³onD: x|<2, ]y|<oodoes not satisfies Lipschitz condition.

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Q: Q1/ Discuss the continuity of : 1 x+ for x 2

A: Since, you have post multiple question. I am answering first one. Please post again for remaining…

Q: Show that x is continuous everywhere. r(x)-x-0 XX<0

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Q: 3 Suppose that e(x) and f(x) are differentiable on [0, 1] and that 0 < |e'(x)| < |f'(x)| for all x €…

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Q: 1. Find of ахду OF f(x,y) = xy (x+y-1) -x2

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Q: Verify Cauchy's MVT for f(x) and f'(x) in [4,9] where f(x) = Vx %3D

A: Cauchy's MVT : If two functions f(x) and g(x) are continues on [a, b] and differentiable on (a, b),…

Q: 15 51 :- -/- -1- :- ーによ -1- イーキーーュ ナー ートー- ー ーー III II III IL 1,0 15 15 -1 ーャー- -15 r2 + 13x + 42…

A: The given question can be solved as shown in step2.

Q: Find the Wronskian for {x, -sin x, cos x}

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Q: (b). Show that iff= u+iv is analytic in a region S and u is a constant function (i.e., independent…

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Q: Find the Wronskian for the set of functions.{x, ex, sin x, cos x}

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Q: For the IVP, y'=f(x,y), y=yo, x=xo, iff and df/dy are continuous discontinous defined undefined then…

A: Here we have to choose the correct option.

Q: If f is a function defined from R to R, is given by f(x) = 5x - 3 then f -(x) is given by %3D -- 20…

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Q: 9. Consider the function f: R → R, defined by (x²sin(1/x) ifx # 0 f(x) = if x = 0 Then a. f is not…

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Q: Show that x| is continuous everywhere. r(x)- x- 0 xX <0

A: f(x) is continuous, if LHL=RHL=f(x&gt;0), where LHL is left hand limit while RHL is right hand…

Q: 11. The function f(x) is defined on [1, o0) and satisfies VTO dt. 10 Find f(x).

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Q: how (in terms of  − δ) that a function f : R 3 → R defined by f(x, y, z) = (2x + 3y + 4z) is…

A: Solution of given problem is followed by

Q: 1. Show (in terms of  ε - δ) that a function f : R3 → R defined by f(x; y; z) = (2x + 3y + 4z) is…

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Q: 8 Examine holomorphism of given function  f(z) = |z|2

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Q: az are Let F(x, y,z) = z +x+ysin x+ xIn z = 0, where z =f(x,y), then at (0,0,1) and %3D ax equal to:…

A: We have to find the partial derivatives of given function at point

Q: Suppose that a continuous function g satisfies: | = 36 and g(x)dx | 9(2x)dr = 15. 0. : = =p(= |…

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Q: Suppose that f(1) = 2, f(4) = 8, f '(1) = 4, f '(4) = 3, and f " is continuous. Find the value of xf…

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Q: 2. Suppose that f is a measurable function satisfying m({r €R: [f(x)| 2n}) < ne N. n3' Is f…

A: Given that f is a measurable function, with the following condition satisfied. m(x∈ℝ:…

Q: Show that the converses of parts (a) and (b) of Theorem 6.2.8 are false by finding counterexamples.…

A: Theorem: Let f be a differentiable function on the interval I. Then, If f'x&gt;0 for all x∈I, then…

Q: Find aland U so that the function S 7z³ – 3x² + 7, z -2 is both continuous and differentiable. al =

A: To Determine: fins a and b so that the function is continuous and differentiable given: we have a…

Q: Suppose that f(1) = 5, ƒ(4) = -8, f'(1) = 4, f'(4) = -2, and f" is continuous. Find the value of |…

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Q: b) caleulate the lerivative of f Cx) by USing product rule flx) = (2-3x)? the

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Q: Let f(x, y, z) = In(x² + z) + y²e#². Find fzyæ-

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Q: 8. If f is conformal on a domain D which is symmetric with respect to the real axis, is f(z)…

A: Given that f is conformal on a domain D which is symmetric with respect to the real axis.

Q: Let f = f(x, y), x = s +t and y = s - t. Show that (9- ) - se se as at ax ду

A: It is given that, f=f(x,y), x=s+t and y=s-t. Show that, ∂f∂x2−∂f∂y2=∂f∂s·∂f∂t.…

Q: 1. Show (in terms of -5) that a function f: [2, 7] R be defined by f(r) V+1 is uniformly continuous.

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Q: let Peas be delimed by Xく2 3-X I5 fixo continuous V= 2 2.

A: A function is continuous at a point if it's left hand limit is equal to right hand limit and both…

Q: 15.If the Wronskian of f and g is t cos t − sin t, and if u = f + 3g, v = f − g, find the Wronskian…

A: Consider the provided information, Wf,g=fg'-gf'⇒tcost-sint ...... (1) Find the Wronskian of u and v.…

Q: yLet f(2) be analytic in {z: |2| < 1} with f(0) that |f"(0)| < 2. = 0 and |f(2)| < 1 for all z in…

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Q: 2. Suppose that f is a measurable function satisfying m{r ER: |f (x)| > n} ) < 1 nEN. n3 Is f…

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Q: 5) Suppose a path C is defined by r(t), 2 and r(8) = . If f is a differentiable function satisfying…

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.