5. Let f(z) = { 150 (a) Find f'(z) and f"(x) . Graph all three functions. (c) Is f(z) differetiable? Is fr(z) continuous? (d) Is fr(z) differentiable? Is f"(z) contimuous? (c) Is g'(z) continuous? Prove your answer correct. (d) Is f uniformly continuous? I>0.

Q: et [a, b] be a real interva b]→X is continuous, the is continuously differentia

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

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

A: The solution is given below

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A: Given that limh→0sinh3-h3cosh2h=0. The rate of convergence can be calculated by evaluating the…

Q: Suppose that Xis a continuous unknown with -4< X< 4  having PDF denoted fsatisfying f ( x ) = c (…

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Q: Express the limit as a definite integral on the given interval. n lim x, In(2 + x;²) Ax, [0, 3] j=1…

A: Given: The limit limn→∞ ∑i=1nxiln2+xi2∆x on interval 0,3 To determine: The interval notation of…

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.

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Q: Express the limit as a definite integral. n 7 lim 2 3x Ax: [2,7] Ax,0 k= 1 O A. 3x' dx 2 о в. 3x'd…

A: We have to express the given series as a definite integral.

Q: Consider the function fcX) = Vx+8 Part A: us.ng a limit, s how thut f'l1)=- Part B: Find the…

A: Using definition of derivatives (limit form)

Q: Express the limit as a definite integral on the given interval. n lim x, In(2 + x,-) Ax, [0, 4] i =…

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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: Is f(x) = ln(x) uniformly continuous on (0, 1)? Justify your response.

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Q: If the derivative of y=f(x) does not exist at X = a then y f(x) is not continuous at X = A) True B)…

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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: Express the limit as a definite integral on the given interva lim [2(xf)³ – 5x¡]Ax, [2, 5] n- 00 i =…

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Q: The pdf of a continuous RVX is given by f(x) = 3x²,where 0 < c < 1. o2 =

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

A: Here, to evaluate: ∫35(f(x)-g(x)) dx

Q: Find the derivative of f(x) at r = 0 using the definition of the derivative as a limit. %3D Va +I

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Q: Suppose that X1,..., Xn are i.i.d. following pdf given by f(x; 0) = že-5, where both x and O are in…

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Q: Express the limit as a definite integral on the given interval. n X;* lim -Ax, [1, 9] (x;*)2 + 8 i =…

A:

Q: Where is the function defined by f(x) = In (x) increasing? Where is f(x) decreasing? Where is the…

A: Given a function: f(x)= ln(x) and the function is defined in the domain x∈(0, ∞)Then, f'(x)=1x

Q: Express the limit as a definite integral on the given interval. -Дх, +7 [1, 6] lim dx J1

A: The following limit is expressed in the definite integral as shown below

Q: Fill in the blank/s:

A: We have to fill in the blank.

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

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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: Below is a table of valucs for a continuous function f . X -1 -0.5 (),5 f(x) | 2.0 | 1.5 -1.0 0.5…

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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: Prove that if the function f : I → R has a bounded derivative on I, then f is uniformly continuous…

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Q: Express the limit as a definite integral on the given interval. lim x; In(1 + x?) Ax, [0, 1] dx

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

A:

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: Let (s n(x-y) |x|+ly\ = 0 f(x, y)={ |x|+|y]| (0, (x, y) = (0,0) Is f continuous at the origin? Why?

A: The continuity of the function can be checked by checking the limits of the function at the point.…

Q: Express the limit as a definite integral on the given interval. x, In(2 + x) Ax, [0, 2] lim dx

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Express the limit as a definite integral on t lim n-oLX; In(1 + x;²) Ax, i=1

A: Given that: 1. limn→∞∑i=1nxiln(1+xi2)∆x, [0, 1]2. ∫13(x-4lnx)dx

Q: Express the limit as a definite integral on the given interval. lim Σ Σ x;* -ΔΧ, [1,4] 0-700 (x;*)2…

A: To express the given limit as a definite integral.

Q: Suppose that X is a continuous unknown with -2 < S2 with PDF denoted f satisfying $ (2) = c (4 –…

A: i) we know that the total probability should be one means the area under the PDF should be one.…

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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: Express the limit as a definite integral on the given interval. cos(x;) lim n-0 i = 1 Дх, [2л, 5л]…

A: Given limn→∞∑i=1ncos(xi)xi∆xi in the interval [2π,5π]We need to express the limit as a  definite…

Q: Consider a two-dimensional circular metal plate of radius R and let u be its temperature…

A: The solution is given below

Q: 7) Use a tangent line approximation with the function g(x)= Jx to estimate V9.2

A:

Q: Express the limit as a definite integral on the given interval. n x* lim (xF)2 + 2 Ax, [1, 7] (x*)2…

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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: Does fn converges to L1 and L2 i.e the distance between fn and f goes to 0

A: By the theorem: A metric  on BE is the uniform metric du  . A sequence of bounded functions fn:E→ℝ…

Q: Express the limit as a definite integral on the given interval. n lim x; In(1 + x}) Ax, [0, 1] i = 1…

A: Given: To convert the limit function to integral function, the following expression is used.

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

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.