Find the value of a such that the function S(«) = {** -1, x < 3 x 2 3 | f(x) = 2ах, is continuous at every x.

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

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Q: is continuous at x=3, f (-1) =6 ? + a, x # 3 3b, x 3 ontinuous at x=2? - x > 0

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Q: 3. Determine f(x) = x2 + x-2 is continuous on the given interval (-0,+0) (show graph and its table…

A: Here, the given function is: f(x)=x2+x-2 And the given interval is (-∞,∞).

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Q: Q7 Show that f is continuous on (-∞, 0) sinxif x - 4

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A: Given data: The value of function is, f(-8)=-9 The value of differentiating function  f(x)≤2

Q: : Verify Mean value theorem for the function f(z) = 4x over the interval [0, 2].

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Q: True False Suppose f(x) is continuous everywhere. Must f(x) attain an absolute maximum somewhere on…

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

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Q: verify mean value theorem for the function f(x)=4x3 over ihe interval [0,2 ]?

A: verify mean value theorem for the function f(x)=4x3 over ihe interval [0,2 ]

Q: 1. Show that the function f(x) = 3x + 2 is continuous at (-2, 3). Is it uniformly continuous?

A: As per our guidelines we are mandated to solve only one question at a time please repost the…

Q: limit as x----0 for the function (px)/(sqrt(bx+a^2))-a using L'Hopitals

A: Apply the limit.

Q: 8. If a continuous, differentiable function f is equal to 2 at x = 3 and at x = 5, what can you say…

A: Given that if a continuous, differentiable function f is equal to 2 atx=3 and at x=5, Our Aim is to…

Q: Express the limit as a definite integral on the given interval. n X;* -Дх, [1, 9] lim (x;*)² + 4 n-…

A: limn→∞∑i=1nxi*xi*2+4∆x,    1, 9 Here, fx=xx2+4, a, b=1, 9

Q: If f is continuous on (-x, ∞), what can you say about its graph?

A: If f is continuous on (-oo oo) what can you say about its graph?

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: fully continuous for all x E R by use of the product rule differentiate the function f{x} = x3e-4x

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Q: Verify Mean value theorem for the function f(x)=4x3+x+2 over t interval [0,1].

A: Prove hypothesis of mean value theorem Differentiate continuous and value of c

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Q: Suppose that fis a continuous function and that1. f(x)dx=-1 and L(x)dx = 5, find the value of…

A: suppose that f is continuous function . We have to find the following

Q: Suppose we know that f(x) is continuous and differentiable on the interval [1, 9], that f(9) = 0 and…

A: Given, f(x) is continuous and Diferentiable on interval [1,9] f(9)=0 and f'(x)≥8 We have to find :-…

Q: Express the limit as a definite integral on the given interval.

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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: The Bisection method is based on the principle that a continuous function which is positive at one…

A: Consider the provided question, We have find the value after third bisection process of the function…

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: Consider a function f that is continuous on [-2, 4] with f'(x) = 0 whenever x = 3 or x = 5. Suppose…

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Q: 4. "The function f(x)= x-1 is continuous on(-o, 00)". Is the statement true or false? If it is…

A: Hi there, i have explain that if x tends to 1 from right side the function will give +1 and while…

Q: Suppose that f hits every value between y = 0 and y = 1 on the interval [0, 1]. Must f be continuous…

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Q: 4. "The function f(x)= x-1 is continuous on(-0,0)". Is the statement true or false? If it is false,…

A: f(x) is continuous at x = a if L.H.L = R.H.L. = f(a).

Q: 4. Determine if 1 1 sec if – 1 1 x – 1 is continuous or not at x = 0 and 1. In the case of…

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Q: +4イ find the cyitical Points of fCks and the intervals on which the function is increasing de…

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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: Suppose we know that f(x) is continuous and differentiable on the interval (-7,0], that f(-7)=-3 and…

A: fx is continuous and differentiable function on the interval -7, 0, f-7=-3 &amp; f'x≤2.

Q: Suppose f is continuous on an interval containing a critical pointc and f″(c) = 0. How do you…

A: According to the second derivative test, If c= critical value. if f''(c)&lt;0, then f(x) has local…

Q: limit as x approaches infinity of (-1)x+1

A: Apply the limit.

Q: Find the value of a which makes the function below continuous on (-∞, ∞). f(t) = [a(x²/2) x < 1…

A: We will use the definition of continuity to solve this question.

Q: limit x to infinty tan(5t)sec(99t)/t

A: Lim           f∞(st) Sec(q q t )tx→∞    Here limit x→∞ But the function is in t ∴

Q: Sketch the graph of a function continuous on the given interval that satisfies the following…

A: Given, f is continuous on -∞,∞; f'(x)&lt;0 and f''(x)&lt;0 on -∞,0; f'(x)&gt;0 and f''(x)&gt;0 on…

Q: Does f(x) 1-V1-x² continuous on the interval [-1, 1]?

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Q: Verify Mean value theorem for the function f(x) = 4x° over the interval [0, 2].

A: Question - a Given function, fx=4x3 Interval : [0, 2] Conditions of Mean value theorem: 1. f(x) 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: a function is continuous at x = c, then the limit exists as x approaches c. If the domain of a…

A: a. If a function is continuous at x = c, then the limit exists as x approaches c By the definition…