x + 3, x < 2 - Let h(x) = 5, x = 2 1 x > 2 x - 2

Q: Let h(x) = {x^2 +3,  x2 Determine the continuity of h(x) at/over the following point/interval.…

A: To solve the following problem on comtinuity of functions

Q: Determine the intervals of continuity for the function: f(x) = over the interval of 0 < x < 2n…

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Q: 25. For the function f(x) = 45x3 - 3x5, determine the interval(s) for which f(x) decreases. O (3, 3)…

A: We will solve this question by  differentiating f(x) and then finding the intervals for which the…

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

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Q: f X1, Y1, are two positive unequal numbers and Xp = (Xn- 1+ Yn– 1) and Prove that the sequences (xn)…

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Q: Pe A- IF ax +b Continuous at x-1 %3D X+2 and Fca)=3,. Find the Value of Constant a, bER

A: Since the function is continuous at x=1, so the value of the two pieces of the piecewise fucntion…

Q: Find the constant a such that the function sin x -13 - S(x) = %3D a+ 11x, x 20 is continuous on the…

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Q: If f is continuous and ∫31 f (x) dx = 8 , show that f takes on the value 4 at least once on the…

A: Given that f is continuous and ∫31 f (x) dx = 8. We have to prove that, f takes on the value 4 at…

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 f(x, y, z) = 1 / (x2 + y2 − z) .

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

Q: 1) Find the absolute extremum values of f(x) = x? [1, 2]. 2x +24 over the interval %3D -

A: Topic - maxima minima

Q: sketch f(x)=sec x over the half-open interval -r,27). 2 1 3/% 27t 52

A: Given query is to find sketch the graph of sec(x) .

Q: For what values of a and b is ax + 2b, g(x) = {x + 3a - b, 0 2 continuous at every x?

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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: • Use the IVP to prove that r3 – 4z+2 has a zero in the interval [0, 1] • Use the IVP (and a similar…

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Q: Given f(x) = In(x² + 3x + 9), over the interval [ – 5, - 1], answer the following: %3D a) The point…

A: Given,           fx=lnx2+3x+9

Q: D. Discuss the continuity of the function g (x): 1 %3D on the interval [-1,2]. x2-4

A: Given, To discuss continuity of the function g(x)

Q: The function f(x)= (x² – 1)³, is decreasing on the interval (- 00 , – 2) U (0,2) ^O (-1,0)U (1, ∞o )…

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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: If f(x)= (x^4) + 3x + 1 and there are two roots x=a and x=b in the interval [-3,-1] with a &lt;b.…

A: The given function is,

Q: If f is continuousand ∫31f(x) dx=8, show that f takes on the value 4 at least once on the interval…

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Q: use the Laws of Continuity and Theorems 2 and 3 to show that the function is continuous f (x) = ex…

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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: 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: Use the equation ƒ(x) = ƒ(a) + ƒ′(a)(x - a) + ƒ′′(c2) /2 (x - a)2 to establish the following test.…

A: For the given function to determine its behaviour at a critical point x=a, use second derivative…

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: 2. For the given function, f, determine if the function is discontinuous at a given point. State…

A: Function is f(x)=xx a=0 We have to check whether the function is continuous or discontinuous at…

Q: S(x) = 7x* – 1x* +2. | Use interval notation to indicate where f is continuous. Domain of…

A:

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 interval(s) where f(x)= x²- 2x+3 is continuous.

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Q: . Use calculus to find the absolute maximum and minimum value of the function f(x)= x+ cos x on the…

A: Consider the function: fx=x+cosx,  0,π To calculate the derivative of the given function with…

Q: Showthat fo= x| is Continuous evalyuhore- 1x1+1

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Q: Find c such that the function 10 I C - is continuous everywhere.

A: A function f(x) is said to be continuous at a point x=a if limx→af(x)=f(a). That is, a function f(x)…

Q: 3. Apply the three conditions of continuity to determine if the function f(x) = 2x²+5x+2 x²-x-12 is…

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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: Which values of C makes r(x) (a) left-continuous, (b) right-continuous (c) continuous x2 +3 for x 2

A: If the function r(x) is left-continuous, then use limx→-1-rx=limx→-1+rx, to determine the value of…

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

A: The given function is: f(x)=2-x           0≤x&lt;121≤x&lt;23x=22x-22&lt;x≤310-2x3&lt;x≤4

Q: 3 - x, x<2 Q.No.15: Is f(x) = {+2 x22 continuous at every x € R. x+1 xs1 -.

A: Continuity of a function.

Q: Q4: Discuss the continuity of : 1 for x2

A: f(x) is continuous at a point if right hand limit and left hand limit and functional value equal at…

Q: For f(x, y), find all values of x and y such that f,(x, y)= 0 and f,(x.y)= simultaneously.

A: Please refer to the image below

Q: For what values of a and b is ax + 2b, g(x) = {x? + 3a - b, 0<xS2 3x 5, %3D - continuous at every x?

A: The given function is gx=ax+2b,        x≤0x2+3a-b,  0&lt;x≤23x-5,           x&gt;2. For the given…

Q: f(x) = 3x - 5x² 1. c = 2

A: Given: fx=3x-5x2  ; c=2   The function will be continuous at x=c when, limx→c-fx=limx→c+fx=finite…

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…

Q: For what values of h and k is h+2x , 15 x52 -2 < x<-1 2< * 2 - Continuous at every x ? 2x2 - 2x-4,…

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Q: Find values ofa and b that make B(x) both continuous and differentiable at x = 2: ax? B(x) ={ 6x + b…

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