Find a value of k making h(x) continuous on [0, 5]. kx , 0 < x < 1 h(x) = x +3, 1

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Q: For a continuous function f(x) on the set 2 [- 5,2], the net area Tx)dx must be -5 always positive…

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Q: Suppose f is continuous on the closed interval l-1,3] if Fis an antiderivative of f, which of the…

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A: In these question , we can check where the function is continuous . Check where the function is…

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Q: Express the limit as a definite integral on the given interval. lim n → ∞  n [2 − 5(xi*)2 + 6(xi*)4]…

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Q: Find all values of c such that f is continuous on (-o, 0). { 7- r, /(r) – (smaller value) (larger…

A: f(x)=7-x2,x≤cx,x&gt;c

Q: Let f and g be continuous on the closed interval L0,5]. suppose that J s(x)dx=A, / f(x) dr=B, The…

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Q: Suppose f is a real continuous function on R', f.(t)=f(nt) for n=1, 2, 3, ..., and {S} is…

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Q: Find all values of c such that f is continuous on (-0, 0). 1- x2, f(z) = { – x², x. C = (smaller…

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A: Consider the provided definite integral, ∫02 2-x2dx Evaluate the provided integration using limit of…

Q: 1. Consider the function f defined on [0, 0), f (x) = {x* sin- x + 0 x = 0 where r > 0. Determine…

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Q: Explain why or why not f(x) is continuous or not continuous at x = 1 using the ideas of the delta…

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Q: Let x > 1, f be continuous and g be a Lipschitz function with constant L satisfying g(1) = 0 defined…

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Q: 3 Let fand g be continuous on the closed interval [0,5]. suppose that / f(x)dx=A, / f(x)dx =B,…

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Q: The function g is continuous on the interval [a, b] and is differentiable on (a, b).Suppose that…

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Q: Let f and g be continuous on the closed interval [0, 5]. Suppose that J f(x)dx = A, f(x)dx = B, and…

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Q: Consider the function f that is continuous on the interval [-5, 5] and for which 5 f(x)dx = 4.…

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Q: Suppose f is a continuous function defined on (-e, e) for some e > 0 and assume that f(0) = 0 and…

A: Since function f(x) is continuous at x=0. Also given that limx→0f(x)x=C

Q: Suppose f(x) is continuous on [0, 1], with f(0) = 2 and f(1) = 0. Then there must be a value x in…

A: Here given that f(x) is continues.

Q: S [[x+1]], Determine iF f(x) = if x ≤ -1 2 tanh (H), ip-IxO (x+1), < <) In [cash (x+1) + sinh…

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Q: II. Determine if [x+1]. if x < -1 S x + 1 f(x) = 2 tanh (x+¹) if 1<x< 1 1-x In [cosh (x + 1) + sinh…

A: It is solved whether f(x) is continuous or not.

Q: Find a value of k making h(x) continuous on [0, 5]. 0 <x < 2 x +1, 2<x < 5 eka, h(x)

A: Givenh(x)=ekx    0≤x&lt;2          x+1  2≤x≤5To find a value k when h is continuous on…

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Q: Let f and g be continuous on the closed interval [0, 5]. Suppose that f(x)dx = A, ] f(x)dx =B, and…

A: Since f and g are continous we used the properties and got answer as D

Q: Let f and g be continuous on the closed interval [0, 5]. Suppose that f(x)dx = A, / f(x)dæ = B , &nd…

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Q: 2. Let f (x) = cos-. Show that f is NOT uniformly continuous on (0,1).

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Q: Assume that J is continuous on [0, 3 and differentiable on (0, 3) with f (z) > 6 for each z in (0,…

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Q: If f is continuous on [-1, 1] and ', f(x)dr = 0, then f(x) = 0 for every r E [-1, 1]. %3D

A: Solution-

Q: Let f and g be continuous on the closed interval [0, 5]. Suppose that | f(æ)dx = A, f(x)dx = B…

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Q: Let f(x) be continuous on [0, oo) and twice differentiable on (0, co). If f'(x) > 0 and f"(x) 1,…

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Q: Consider the sequence of functions {fn} defined on the interval (1, 0), where fn (x) 1 Vx E (1, 0),…

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Q: Estimate f(x) dx given that f is a continuous function containing (-2,8), (–1,0), (4, 125) , and…

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Q: Determine where h(x) = sin(x- Sx + 2) is continuous. %3D h is continuous on the interval [0, co). h…

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Q: give an example where f is not derivable at [0, ∞), but is uniformly continuous

A: give an example where f is not derivable at [0, ∞), but is uniformly continuous

Q: lim n→∞  n xi ln(1 + xi2) Δx, [0, 2]   i = 1  2   0     dx

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Q: Suppose  f is continuous on [0, ∞) and limx→∞ f (x) = 1 . Is itpossible that  ∫ 0∞f (x) dx is…

A: Consider a function f(x) which is continuous on [0, ∞) with limx→∞f(x)=1. The objective is to…