5 - x, -1sxS 2 r² – 1, 2

Q: Find all values of c such that fis continuous on (--,-). f(x) = {7-2², c=2.193 c= 3.193 7-2²³, xse…

A: The given function,    fx=7-x2,x≤cx,x>c

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: Axample 2 3. Use the definition of continuity to prove that the function is not continuous at x =-5.…

A: Given query is to prove that function is not continues at x = -5.

Q: 2. Let f(x) = 2x²-3x+1 ,x 0.5 Determine constants A and B such that is continuous for all values of…

A:

Q: f(t) = 3 – 9 ? -6, [-3, 3]

A: To find: The continuity of the function f(t)=3-9-t2 on the interval [-3, 3]

Q: 4 if x3 to define f at x = -2 in such a way that f becomes continuous nossible what ie the velue of…

A: We have to find the following conditions according to the given information

Q: 21. Discuss the continuity of : 1 for x+- x 2 (ans.: discontinuous at x=0,2 ; continuous at x=1)

A: Given: f(x)=x+1x   for x&lt;0-x3      for 0≤x&lt;1-1       for 1≤x&lt;21          for  x=20…

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: f:(-m,m)-R, f(x)=xt cosx, (MER") function, at the point of a t (-M,m) COSX Ts this function uniform…

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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: [0,1] 6. If f is continuous on • prove that

A: We can solve an integral of some function f(x) w.r.t. x by using substituting, say, t=f(x) which…

Q: ax²-3 -,x > 1 х-1 Value of a and b that will make f (x) = continuous everywhere are .... (bx + 2,x…

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Q: lim r" use Cauchy Criteria to prove that exists and 0<r<1 n → 00

A: To Prove - Use Cauchy Criteria to prove that lim rn exists and 0 ≤ r &lt; 1 , n →∞         Theorem…

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: Let fn f, where if 0<x<! if <a<i -x if 0 <x<1 fn (x) n-2 (2 - x) 2 and f(x) %3D if x = 0 Then lim…

A: 2

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: 2-x, x#1 Domain Range 21. g(x)= 3, x = 1 Intervals of Continuity

A: Answer

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

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Q: 6. State the (ɛ, 8)-Definition for continuity of a function f : R → R at x E R.

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Q: x+4 Which will prove that f(x) = %3D x2+16 is continuous at C= -4? 1. f(-4)=0 II. lim f(x)=0 III.…

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Q: Show, using the definition of continuity from the topological point of view, that the constant…

A: See the attachment.

Q: Find numbers a and b, so that f is continuous at every point.  f(x)= 20 , x-1

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Q: *=3 is continuous on: x> 3 R-(0,3} R- {2,3} R- {3} R = (-00, 00)

A: Continuity

Q: x+4 if x2 is continuous at x= 2. Verify all three conditions of continuity and be very clear!

A:

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: x3 – 7x2 + 5x + 7 = 0, (-1, 1) Let f(x) = x3 - 7x2 + 5x + 7. f(x) is ---Select--- f(-1) = on the…

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Q: Q2. Show that F(x) = 3 – x², x € is contractive on its domain, but does not have any fixed points.…

A: To show - Show that Fx = 3 - x2, x ∈ -14, 14 is contractive on its domain, but does not have any…

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

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Q: 9. Using graph discuss continuity f(x) = *,1, -1sx< z 0 <x<1 2x,

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Q: x + 3, x 2 x - 2

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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: Let f : [0, 1] → [0, 1] be continuous. Show that there exists an element x = [0, 1] such that f(x) =…

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Q: Let f [0, 1] → [0, 1] be continuous. Show that there exists an element x = [0, 1] such that f(x) =…

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Q: Discuss the continuity of the function g(x) = 1/(x^2-4) on the interval (0, 2] and [−1, 3].

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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: Define f(x) = x² for all x. Verify the e-8 criterion for continuity at x = 2.

A: Given real valued function  f(x) = x2, ∀x We have to show that the given function is continuous at x…

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: Discuss the continuity of the function on the closed interval.                             Function…

A: The given function is said to be continuous in a closed interval [a,b] if it is continuous in (a,b)…

Q: 3. Let f [2,3] → {1,3} be a continuous function such that the equation f(x) - x = 0 has a solution a…

A: 3 Give that f:2,3→1,3 be a continuous function such that the equation fx-x=0 has a solution x in…

Q: r(x) = -is continuous at every point in its domain.

A: In any rational function of form p(x)q(x) where p(x),q(x) are polynomials giving real outputs; the…

Q: xercise 3 - Continuity: (a) Can we use the IVT to conclude that f(x) = x³ + 2x +1 passes through y =…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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: 1-x², x 2 at x = 2.

A: Given, fx=1-12x2, x&lt;23,    x=2x-2-1,   x&gt;2

Q: 3+2+x, xs7 8-Jx-3, x>7 three part definition of continuity. Is the function f(x)= continuous at x=7?…

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Q: (a). Find the values of a and b that make f continuous everywhere. x² -4 if x<2 x-2 f(x)={ax² - bx+3…

A: f(x)=x2-4x-2if x&lt;2ax2-bx+3if 2≤x&lt;32x- a+bif x≥3 Definition: Continuous functionLet f(x) be a…

Q: 2. Define f : (2,7) → R by f (x) = x³ – x + 1. Use the definition of uniformly continuity to prove…

A: Consider the given information. fx=x3-x+1 As the function is in the form of a polynomial.  Now, find…

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.