Sketch the graph of a function f that is continuous on (-o, 0) and satisfies the following set of conditions: • f"(x) > 0 on (-0, -2) • f"(-2) = 0 f'(-1) = f'(1) = 0 f"(2) = 0 • f'(3) = 0 f"(x) > 0 on (4, 0)

Q: Prove that f(x)= 2x-tan^1x-ln(x+√x^2+1) increasing on [0, infinity]

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Q: The hyperbolic cosine function, denoted cosh x, is used to model the shape of a hanging cable (a…

A: Given information:Tyhe given function is cosh(x).

Q: estimate the limit numerically to two decimal places or state that the limit does not exist

A: Given: Plugging the limit directly, we get:

Q: 7. Express the limit as a definite integral on the given interval: n lim n- 00 3 tan x; Ax , [0, 1 ]…

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Q: Determine if the function f(x)= is continuous -- sin(x) x on the interval I= (0,1).

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Q: Express the limit as a definite integral on the given interval. in lim [5(x,")3 – 2x,*]Ax, [2, 7] i…

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Q: limit x approaches 0, (xcot2x)

A: Limit x-> 0 ( x/tanx ) =1Calculating the limit of the given expression using this result:

Q: What is the limit of (sinx)/x if x approaches to 0?

A: Given: A function limx→0sin xx and x approaches to 0. Since sin xx is an intermediate form of type…

Q: Find two paths of approach from which one can conclude that the function has no limit as (z, y)…

A: Given fx,y=x4-yx4+y

Q: Sketch the graph of a function f that is continuous on [1, 5] and has the given properties.…

A: Given data: The absolute maximum at MA=5. The absolute minimum at mA=2. The local maximum at MB=3.…

Q: The function f(x) is differentiable on (0, 1) and satisfies f(0) = f(1). However, its derivative is…

A: Consider the given function: Here the objective to check whether the given function contradicting…

Q: tion f defined as xy Ax, y)=- when (x, y)#(0, 0) when (x, y)=(0, 0) =0, is continuous at the origin.

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Q: is there any linear independent functions with n – 1th continuous derivative g1, 92, ... , gn(with…

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Q: 32? And are

A: {x2                               if x<-2f(x)={x1/5                           if…

Q: Express the limit as an integral. * lim (5(x)2 - 2(x;)³)Ax over [0, 3] i = 1 dx

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Q: Suppose that a nonnegativefunction y = ƒ(x) has a continuous first derivative on [a, b] . LetC be…

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Q: Assume that f : (0, 1) → R is a differentiable function with the derivative f' increasing on (0,…

A: Given f:0,1→R is a differentiable function and derivative of f is increasing in 0,1 that is f'x>0…

Q: 1 () X. lim х+ sin X→+∞

A: The objective of the question is evaluate the limit of the given function.

Q: 1. Show that a frination fiłamb ]->1R is differentiable at xolamb) is and only if its lower and…

A: Solution: f:[a,b]→ℝ is differentiable at x0(a,b). Let us take upper derivative at x0+. Then,…

Q: Sketch the graph of a function f  that is continuouson [1, 5] and has the given properties.…

A: Sketch the graph of a function that is continuous defined on the interval [1,5] having the following…

Q: Express the limit as a definite integral on the given interval. lim n - 00 cos(x}) Дх, [2л, 5л] Xi i…

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Q: Determine whether the following function continuous at point (1, 1). Justify your answer. (x²-xy if…

A: Here we have to determine whether the given function is continuous or not.

Q: Estimate the limit numerically to two decimal places or state that the limit does not exist.

A: Given: limx→01-cos3xx2 we know that a3-b3=a-ba2+ab+b2

Q: 1. Express the limit as a definite integral on the given interval. Xi lim Ax, [1, 3] '(x;)² +13 n00

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Q: Express the limit as a definite integral on the given interval. lim -Дх, [1, 4] (x;")² + 9 i = 1 dx

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Q: Show that the function is continuous on  (∞ , -∞).

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Q: Identify the limit that represents the limit definition of the definite integral ∫39 6x3 dx using a…

A: From the given indefinite integral, observe that f (x) = 6x^3, the lower limit and upper limit is 3…

Q: Find the limit and determine if the function is continuous at the point being approached. (- lim sin…

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Q: Express the limit as a definite integral on the given interval. lim -Ax, [1, 3] (x†)² + 2 i = 1 dx

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Q: Suppose f is differentiable with continuous derivative on [a, b]. Show that lim f(x) sin(nx) dr = 0.

A: To prove the given limit

Q: Suppose /has a continuous derivative on the interval [0, 6]. Assume also that f' is increasing on…

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Q: Iff is bounded and integrable in the interval [a, b], f(x) cos nx dx=0. show that lim

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Q: Find the limit of the transcendental function. Ilm sin 7tx

A: topic- limits

Q: Find the limit.  limit as x approaches 0 sin3x/x

A: Apply the limits and find the in-determinant form.

Q: Find the absolute extrema of the function on the closed interval. TEX y = tan 16 ), [0, 4] minimum…

A: Given that, The function is y=tanπx16 on the closed interval [0, 4]. To find absolute extrema:…

Q: Estimate the limit numerically or state that the limit does not exist (DNE): lim x→0 sin(11x)/x

A: Evaluating the limit

Q: Prove: the limit as x approaches 0 1-cos(x)/x=0

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Q: Find the exact location of all the relative and absolute extrema of the function. f(x) = 2x – 2…

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Q: Let f(x) = 2x³ + 5x, and let a be a number. Compute the appropriate limit to find the instantaneous…

A: Please see the explanation below...

Q: Let ƒ be a function that is continuous on [0, 2] and đifferentiable on (0, 2). Suppose that f (0) <…

A: Yes, we will show that f' necessarily take on both positive and negative values on (0, 2). If the…

Q: If f is bounded and integrable in the interval [a, b], (x) cos nx dx3D0. show that lim

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Q: Would it be possible for a function to be continuous on [0,2) but not on [0,2]?

A: Let us consider the function f(x) =(x+4)/(x-2) .

Q: 2. Sketch a graph of a function f that is continuous on (-00, 00) and has the following properties.…

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Q: 3. What are is the absolute maximum of f (x) = sin(x) cos(x) on the interval [0, ¤]?

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Q: Give an example of a function that is integrable on the interval [−1, 1] but not continuous on [−1,…

A: Let fx=x       Greatest integer function. Now, ∫-11x dx=∫-10x dx+∫01x dx=∫-10-1 dx+∫010…

Q: Let f(x) = ln x / sin^-1 x    analyze the limit : lim x--&gt; 1- (from the left) f(x)

A: Given information:The given function is

Q: (i) Consider the function such that f(x) = 2x if 0SxS1 and f(x) = x-1 if x> 1. Is f continuous over…

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Q: Estimate the limit numerically or state that the limit does not exist (DNE): sin(7x) lim x →0

A: Given:

Q: Sketch the graph of a function f that is continuouson [1, 5] and has the given properties. Absolute…

A: Given: The function is continuous on [1,5] The absolute minimum is at 2 The absolute maximum is at 3…