02Check the continuityof the functionfir) at x-0,1,2,3, and 4, Where:(25 degrees) 12- 2 f(x) =3 2x-2 Osx<1 1sx< 2 x= 2 2

Q: Test the continuity of the following functions at the indicated points of each x < 1 (1) f(x) = { 3x…

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Q: B. Use the properties of continuity to determine where each function is continuous. 1. f(x) = 2x-x3…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

Q: Q5: State and prove the theorem of (continuity-differentiability), then find the value(s) of x that…

A: As per the policy, we are solving first question. Please repost the question and specify which…

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: Discuss the continuity of f(x, y, z) = 1 / (x2 + y2 − z) .

A: Here The function is discontinuous when the denominator is zero. Thus, That implies

Q: Test the continuity of the following functions at the indicated points of each x+ 1, 3x - 1, 1 < x <…

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Q: Discuss the continuity of the function. f(x, y, z) = 1/(√x2 + y2 + z2)

A: Given rational function is

Q: Check the differentiability of the function f(x, y) = √xy | at the point (0,0). Also check the…

A: As per the question we are give a bivariate function : f(x,y) = √|xy| And we have to check for its…

Q: 1. For what value of k is the function h(x) continuous on the whole real line? HINT: Use definition…

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Q: 6. Use definition of continuity to determine the value(s) of k such that the 2х + 5, х< 3 function f…

A: Topic : Continuity

Q: Let f(x)=x² -x² +x + 1 and g(x)= 3-х max{f(t):0sx; for 0 s x s 1} for 1 < x s 2 Discuss the…

A: Topic:- Functions

Q: Determine the whether the function is continuous at x=-2. Justify your answer 2x+7 if xS-2 using the…

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Q: check the continuity of f (x) at x 0, 1, 2, 3 and 4 2- x, 0sx <1 2, 3, 2x - 2, 2<x 53 (10-2x, 3<x S4…

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Q: 1. f(x) = x2- 6x + 3 is continuous on the interval [- 3,2].

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 5 - x, -1 sx 2 r - 1, 2 <xs 3 Discuss the continuity of g(x) = %3D

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Q: Q2:Check the continuityof the functionf(x) at x-0,1,2,3, and 4, Where:(25 degrees) 2- x 2 f(x) = | 3…

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Q: 1. X) = 3x -5x2 C = 2 2. f(x) = V3x - 1 C = 1 %3D f(x) 3. -3x+2 %3D x-1 C = 2 +4x-5 f(x) 4. %3D x+5…

A: NOTE: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: b. Test the continuity of the following function 1, V1-x,0sIs1, at x = 0,1 (x-2, x<0 x21

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Q: Discuss the continuity of the function g(x). 1 +- x 2 Vx- 2, Identify if the function g(x) is…

A: To check the continuity at x=1 we will find limx→1-g(x) and limx→1+g(x).…

Q: 2. Test continuity at x = 0 and x = 3 for the function (3 + 2x; - 3 3

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Q: (x² + 1 if x -1

A: For function g(x) to be continuous on -1 limx→-1-g(x)=limx→-1+g(x)=g(-1)…

Q: B. Use the properties of continuity to determine where each function is continuous. 1. f(x) = 2x*- x…

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Q: 5. State the Sequential Definition for continuity of a function ƒ :R → R at x e R.

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Q: Find the values of a and b that make f continuous everywhere. x2 - 4 if x < 2 X - 2 ax2 - bx + 1 4x…

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Q: How many functions f:R→R  exists such that : 2f(x)+2f(y)=f(x+y)+f(x−y)+2y holds for all real x and…

A: By choosing x=y=0. Also by choosing x=y we can see f(2x)=4f(x).  Moreover choose x=0 and use f(0)=0,…

Q: b. Test the continuity of the following function 1, x< 0 V1-x, 0sxs1 ,atx 0,1 x- 2, x21

A: We have to check the continuity of f(x) at x=0, 1

Q: Q1) Using the definition of continuity prove that the functions are continuous 1 fox)=x²³² +1 it x=2…

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Q: Q2) Discuss the continuity at x=2. When: x> 2 x = 2 3x + 1 f(x) : x² + 3 %3D 2x + 1 x< 2

A: The given functionf(x)=3x+1x&gt;2x2+3x=22x+1x&lt;2to check continuity at x=2

Q: 7. Find a and b such that f is differentiable everywhere. f(x) = {+b, S ax³, lx² + b, x 4

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Q: Determine the continuity of the function at the given points. f(x) = [1, x-2, for x=1 at x = 1 and x…

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Q: Q5: State and prove the theorem of (continuity-differentiability), then find the value(s) of x that…

A: Given That : i) y  =x                x≥0-x             x&lt;0ii)y  =(x-2)2      x&lt;1,x&gt;4x…

Q: Cx) = *-2r+2 a-1 c = 2

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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…

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Q: (2х + 6, хS \x² + 3, x > Finition of continuity. f(x) =

A: Given,                  f(x) = 2x+6x≤0x2+3x&gt;0Now,                LHL = 6 And        RHL = 3Here,…

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: Find the constant a such that the function is continuous on the entire real line. Ssin x g(x) = if x…

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Q: (c) Simplify the function f(x) = |x - 1|+ |x + 1|. Test the continuity of this function at x 1. At…

A: f(x)=|x-1|+|x+1|, for all x∈ R, It can be written as f(x)=-(x+1)-(x-1),       x&lt;-1(x+1)-(x-1),…

Q: B. Use the properties of continuity to determine where each function is continuous. 1. f(x) = 2x*x…

A: Let's find.

Q: Use the definition of continuity and the properties oflimits to show that the function…

A: Consider the given function as fx=x16-x2

Q: Q No 5)If y=(sinx}° prove that (1-x³)y2=xy:-2=o AND ALSO FIND Discuss the continuity of F(x) at x=1…

A: Given function is: y=sin-1x2 Differentiating with respect to x we get, y1=2…

Q: Q2) Discuss the continuity at x=2. When: x> 2 X = 2 x< 2 Зх + 1 f(x) = } x? + 3 %3D 2х + 1

A: Our objective is to discuss the continuity at x=2.

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: Analyze continuity of the function.

A: Before going to the continuity, we will be finding the domain of the given function. Note that the…

Q: Ql:a) check the continuity of f(x) at x = 1,2, 3 and 4 Osx s1 2-x 2 f(x) ={3 2x - 2 10-2x x= 2 2<x…

A: The given function is f(x)=2-x0≤x≤121≤x≤23x=22x-22&lt;x≤310-2x3&lt;x≤4

Q: Find the values of a and b that make f continuous everywhere. x² – 4 х — 2 ax2 – bx + 3 4х — а + b…

A: The given function is: f(x)=x2-4x-2            if  x&lt;2ax2-bx+3if  2≤x&lt;34x-a+bif…

Q: Q3: Choose A or B (one only) if xs-2 if x>-2 A) Check the continuity of the function f(x) at x = -2…

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Q: Suppose f(x) = 2=*_ 3z-2 Which piecewise function redefines f(x) as a continuous function? %3D I-2…

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Q: 6. Discuss the continuity for the following functions x+y a) f(x,y) = 4x2-y2-4 x+y b) f(x, y) = %3D…

A: The objective is to discuss the continuity of the functions.

Q: Q) check the continuity of X) at X-1, 0,1.23 (x²-1, 2x, -1<x<0 -2x +4. 1<x<2 0, 2<x<3

A: Continuous function: Let A⊆ℝ be a subset of real number, define a function f: A→ℝ be a real valued…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.