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

Q: 'he function f: E → R is uniformly continuous if

A: We have to find the answer using the definition of uniform continuity.

Q: #46

A: We need to find the value of b such that the function g(x) is continuous at every x,

Q: Find c such that the function ( a2 – 4 x c 4x – 8 x > c is continuous everywhere. c =

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Q: Define h(2) in a way that extends h(t) = (t2 + 3t - 10)/(t - 2) to be continuous at t = 2.

A: Consider the given the function,

Q: Find a constant c such that x² – c2 if x 4 g(x) ={ is continuous everywhere.

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Q: Determine the value of m such that the function *- y - 2 E + 2 vỹ VI – Vy ; z +y f(x, y) = is…

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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: Let f be a continuous function such that 5 √ (f(x) — 2) dx? What is the value of f(x) dx = -2 and…

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Q: Is f(x) = -3 A. Yes B. Does Not Exist continuous at x = 3? C. No D. Cannot be determined

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Q: f(x)={x^2−9x≤c, 2x−10 x>c } i

A: Consider function f(x)=x2-9           x≤c2x-10        x>c Now  limx→c+ f(x)=limx→c+…

Q: Consider the following function of two variables: xy g(x, y) = x² + y? Prove that the above function…

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Q: The function f is a composite of two continuous functions: y = cos x and y = x 2, so f is continuous…

A: The function fx is a composition of functions y=cosx and y=x2and it is a continuous function.

Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2]

A: Consider the given function fx,y=3x2-2xy+y2-8y First, find the partial derivatives of the function…

Q: Assume that the function f is such that f(3) = 1, ſ f(x) dx = 5, and f'(x) is continuous on [0, 3].…

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Q: Explain why f (x) = sin (x² + 3r + 1) is a continuous function for all c € R. %3D

A: Let us assume that: g(x)=sin(x)and h(x)=(x2+3x+1)So,…

Q: Suppose f is a continuous function such that Si f(t)dt = e® In(x) for all x > 0. What is the value…

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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: Use the Intermediate Value Theorem to show that f(x) = cos^−1 (x) − e^x has a zero in the interval…

A: The Intermediate Value Theorem: If f is a function which is continuous at every point of the…

Q: Decide whether or not the real function In (eon 2) I+0, = (1) 1= 0, is continuous at r = 0.

A: The given function is fx=ln cos2x2x2     if  x≠0-1                if  x=0. Compute the limit…

Q: 2. If f is a continuous function such that S(t)dt = cos(2x)e* - [e s(t)dt for all x, find an…

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Q: iii. is continuous at a provided g(a) # 0.

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Q: Consider the function xy f(x, y) x²+xy+y² k if (x, y) = (0,0) if (x, y) = (0,0) State, with…

A: Given :  f(x, y) = xyx2+xy+y2if (x, y)≠(0, 0)kif (x, y) = (0, 0) To find : The value of k if it…

Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2].

A: We have f(x, y)=3x2-2xy+y2-8y find critical points ∂f∂x=6x-2y=0 ... (1)∂f∂y=-2x+2y-8=0  ...(2)solve…

Q: What is the absolute minimum value of f(x) = æ + sin a on the interval ,

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Q: . Explain why f (x) = sin (x² + 3r + 1) is a continuous function for all c eR.

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Q: For what value of b is Sx, g(x) bx?, x 2 -2 X<-2 continuous at every x?

A: The given function is gx=x,x&lt;-2bx2x≥-2. Assume that g is continuous function.

Q: Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x ≥ 0…

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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: What value of c makes the following function continuous at (0, 0)? f(x) = с, x + y² + 5, (x, y) #…

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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: x + y + 1 f(x, y) = , x ln (y² х — 1 -

A: A function f=f1, f2, ⋯, fn is said to be continuous at a if and only if the all the components f1,…

Q: b) Show that the function sin for æ e (0, 1] { f (x) = for æ = 0 is absolutely continuous on [0, 1].

A: Function is called continuous function if the left and right hand limit values at each and every…

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: Let g be a continuous function. Using the substitution u = 3x – 1, the integral (g (3x – 1)) dx is…

A: We can use the concept of method of substitution in order to solve the given problem.

Q: If f is continuous on [0, 1], prove that f₁¹ f(x) dx = f₁¹ ƒ(1 − x)dx.

A: This question can be solved using properties of definite integrals.

Q: f is continuous and f(x) dx = 8, find xfc

A: we have to find

Q: Find the value of a so that the function is continuous everywhere x2 + ax – 2, x 1 O 1 O 2 O 3 O 4 O…

A: Given:   f(x) = x2+ ax - 2  when x≤ 1     f(x) = x + 3 when x &gt; 1

Q: Q: Which c.d.f. F is of X is continuous at x=0?

A: If F(0) = F(0-) then F(x) is said to be continuous at x = 0

Q: 4. Let f € L'(R). Prove that the function F(x) = S f(t)dt is continuous.

A: Let, f∈L1ℝ. Since,  L1=f:ℝ→ℂ∫ℝftdt&lt;∞∫ℝftdt≤∫ℝftdt&lt;∞Therefore,∫ℝftdt&lt;∞ ∫ℝftdt is a finite…

Q: For the function f(x, y) = xy((x2 − y2) /( x2 + y2) ) define f(0, 0) such that f is continuous at…

A: A function f is continuous at the origin, the function value at the origin must be equal to the…

Q: x3 B- If f(x) = ;, Find A? is continuous at x = %3D (Ax² x 2 1/N IN V

A: Given: f(x)=x3x&lt;12Ax2x≥12 Since f(x) is continuous at x=12. limx→12-f(x)=limx→12+f(x)

Q: Determine the value of m such that the function x- y - 5 E + 5 VI - Vỹ f(x, y) = is continuous at…

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Q: Determine the set of points at which the function is continuous. a) f(x,y) = ln (a²² + y² – 4)

A: Given function is                                                              f(x, y)=ln(x2+y2-4)…

Q: Give a formula for f(x) given that f is continuous and 2 x +x* + 2 = f (t) dt t+ 2

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Q: Prove f (x) 1+ mx is continuous at x = 1, where m e R

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Q: if (x, y) # (0,0) (1 if (x,y) (0,0) x+y (a) Prove that the function f(x, y) =2x+y is not continuous…

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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.

Q: For all continuous function f: [0, +o] → R, a > 0 we need to prove that 2*f) dx = [ xfw)dx

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.