Which of the following is continuous at x=1? @ f(x)=Tx-1)² B None of the above © s(x)=/x- O f(x)=| 2-x, x21 x-2 E f(x)= x²– 2x + 1

Q: Suppose that Xis a continuous unknown with 5< X< 5 and having PDF denoted fsatisfying f ( x ) = c (…

A: Given: fx=c×25-x2                  -5&lt;x&lt;5

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: Where is the function f(x) is continuous, such that f (x) : In(1-2x)+sin (x 4x+3 %3D [-1, ] – (-) O…

A: We know, ln(x) is defined for x&gt;0. sin-1(x) is defined for x∈-1, 1. f(x)g(x) is defined if…

Q: 1. Write the improper integral which is represented by the following limit. lim C2" 2x dx x2-4 2.…

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Q: Suppose that a PDF for a continuous variable X is given by if 0 x)=3/4

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Q: 2. If f(x) = cos2x, find f(0), f(--).f),f(-x) 3. If f(x) = x(x+1), show that f(x+h)– f(x)= h(2x +1+…

A: 2. f(x) = cos2x , find f(0) , f(-π/4), f(7π/8) ,                                         f(-x). f(0)…

Q: Express the limit as a definite integral on the given interval. [9(x†)3 – 4xj]Ax, [2,9] lim n- 00 i…

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

Q: Conclude on the convergence or divergence of sin x dx cos x

A: Since function is not continous at x=pi/2. Hence we break the limit of integral at x=pi/2. This…

Q: Show that the function is continuous. (x) = 3x cos 3x

A: Show that the function is continuous. (x) = 3x cos 3x

Q: ( 2x -. Is g(x) continuous at 2?

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Q: Express the limit as a definite integral on the given interval. n eši -Ax 4 + X; lim [0, 2] i = 1

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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: Express the limit as a definite integral on the given interval. lim [9(x;")³ – 4x;]Ax, [2, 8] i = 1…

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Q: Only one of these calculations is correct to evaluate the definite integral Inx dx Select one: Inx…

A: Integral test:  Integrals convergent if the associated limit exists and is a finite number (i.e.…

Q: Suppose that f is an integrable function on R (real numbers).  How do you show that the integral  of…

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Q: Express the limit as a definite integral on the given interval. lim [4 – 3(x¡*)² + 6(x¡*)>] Ax, [0,…

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Q: Only one of these calculations is correct to evaluate the definite integral Inx dx Select one: 1 Inx…

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

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Q: Express the limit as a definite integral on the given interval. [2 - 5(x,")2 + 6(x,)³] Ax, [4, 8] n-…

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Q: 6 Jlgul sin (nx +3) 1,(x) =- is convergent point wise to zero function. n-1 ylgn O Ihi O

A: Calculate limn→∞fn:  limn→∞fn=limn→∞sinnx+3n-1             =0

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

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Q: Suppose f(t)dt = 2 + x' + 3x°- cos(x'). Find f(x) for x > 0. %3D O f(x) = 1 + 6x² + sin(x²) O f(x) =…

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Q: Express the limit as a definite integral on the given interval. x; In(1 + x3) Ax, [2, 3] lim 3 dx

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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: Express the limit as a definite integral on the given interval. cos(x) Дх, [2л, Зл] X; lim Зл dx 27

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Q: Show if x, is convergent or divergent T.3 'n sin(x) dx 1+x S'

A: Introduction: The convergence or divergence of an infinite series depends upon the sum of the…

Q: Explain why the improper integral (x + 3) sin(x) dx L. (x² + 1)(x² + 4)² is convergent. 8

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Q: Please show all work:  Is f(x)= x2+3 continuous at x=1? Why or why not? (A rigorous mathematical…

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Q: | de P8- メレー Oe dedx

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Q: 29- For uhat values of a and b is ax+2b x+3a-b くXS2 3X-5 Continuous at every X

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: b) Determine whether the improper integral 1+ sin x 1+ x2 converges or diverges.

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Q: The improper integral f(x)dx can be written as lim f(x)dx + lim_ f" f(x)dx . w--00 w+00 If f(x) =…

A: use the above definition of improper integral

Q: calculate the limit of ln(x) - (e)^x  x goes to + infinite

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Q: Use the Intermediate Value Theorem to show that 2x – 3 - if – 3 0 has a zero on the interval [-2,…

A: First compute the function if they are continuous then apply the intermediate value theorem.

Q: 3:Use Gamma & Beta properties to evaluate : f (In x)³ dx

A: The gamma function is Γ(z)=∫0∞e-ttz-1dṭ The Gamma function is a non-integer generalization of the…

Q: find the limit as x approaches 0. 12sin(3x)/1-cos(3x) = as x approaches 0

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Q: Find a nonzero value for the constant k that makes th tan(kx) x 0 Continuous at x = 0.

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Q: Express the limit as a definite integral on the given interval. n -Ax, (x;")2 + 6 [1, 5] lim i = 1 5…

A: Given query is to express the limit as definiye integral.

Q: .2 x+15 dx Jx* +3 1

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Q: 55. Show that dx J+4 converges by comparing with x³ + xdx. -3 dx. х

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Q: Give a formula of a continuous function that is differentiable except at 0.

A: Consider the provided question, For a function to be continuous at a point x=a, we say that the same…

Q: Express the limit as a definite integral on the given interval. cos Xi lim Ax, [3π, 5π] 818 5m 3m dx

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Q: Express the limit as a definite integral on the given interval. cos X Дх, [Зя, бя] lim 6x X dx 3x

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Q: Express the limit as a definite integral on the given interval. x;* -Ax, (x;')² + 2 lim n- co [1, 6]…

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Q: If 5х + 3,х <2 { h(x) = 2x2 + 5,2 < x < 4 Is h(x) continuous at (x=2)?

A: We use definition of contunity

Q: Express the limit as a definite integral on the given interval. lim 8x; + (x;)² Ax, [3, 8] dx

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Express the limit as a definite integral on the given interval. lim (4(x")3 – 3x;]Ax, [2, 6] n- 00 i…

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Q: b) Determine whether the improper integral `1+ sin r -dx 1+x² converges or diverges.

A: Comparison test :  Suppose for x&gt;a  . If converges then also converges . If diverges then…

Q: EA H.w : Does. fcz)= Continuous at cis

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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…