Suppose f: (0,00) → (0, ∞) and g: (0, ∞o) → (0, ∞o) are continuous functions. True or false: If g and fog are differentiable, then f must be differentiable too. True False

Q: Oil is being pumped into a tank at a rate of r(t) liters per minute, where t is in minutes. Selected…

A: t r(t) 0 3.5 4 3.2 8 2.5 12 1.1

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Q: inates. coordin (b) by symmetry considerations, without . 5. Given F= xi + yj + (z² − 1)k, find ff…

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Q: 8. Al needs to borrow $15,000 to buy a car. He can borrow at 4.5% annual interest rate. a. How much…

A: Compound interest formula A=P1+rnnt and formula for the continuous compounding is  A=P0ert where P…

Q: Cn Cn+1 ists (or if the ratio properly diverges to ∞, in which case we say that R = ∞), then the…

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Q: Waterfall Heights The data show the heights in feet of waterfalls in Europe and in Asia. Find the…

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Q: 1. Graph a) lim f(x) = I >0 b) lim f(x) = I >1 d) lim f(x) = I 3+ e) lim f(x) = - I >3

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Q: -1+ <+16y=0 d²y dy dt² dt d²y dy e)2- + dt² dt d²y +9y=0 dt² i) +16y=1/ cos 4t d²y dt² po -2+ +5. +…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: 1 = √√√₁₂² xy dA, where D is the triangular region with vertices (0, 0), (6, 0), (0, 1). Evaluate…

A: To Evaluate: I=∬Dxy dA where the D is the triangular region with vertices (0,0), (6,0), and (0,1).

Q: Consider the following curve. x = sin(6t), y = -cos(6t), z = 18t Using the given parametric…

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Q: 5) Find the flux of F = (-2y, -x) on the circle of radius 2 centered at the origin. Use the vector…

A: When the field vectors are going the same direction as the vectors normal to the surface, the flux…

Q: Exercise 2: Induction Prove by induction that for all n E N 2²-(₂) = Σ k= k=1 2 k .

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Q: The State Government have built a new express transport system to connect the CBD to the town of…

A: The given transition matrix is T=0.90.10.30.7 The share matrix is S=01.   The steady state vector of…

Q: . Let s (0, ∞) → R be the usual square root defined on the nonnegative reals: s(x) is the unique…

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Q: Find the vectors T, N, and B at the given point. T = N = B = r(t) = (4 cos(t), 4 sin(t), 4…

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Q: Determine the truth values of each of these statements if the domain for all variables consists of…

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Q: Twenty children are selected from a group of twenty-eight boys and twenty-two girls. Set up the…

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Q: Estimate the area of the region under the curve y = In(x) for 1 ≤ x ≤ 5. Use the left-hand rule with…

A: Here, the given equation is y=ln x ; 1≤x≤5. To Find: The area of the region.

Q: Here is the region of integration of the integral a. dy dz dx b. dy dx dz c. dx dy dz d. dx dz dy e.…

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Q: Exercise 4.11.22 You are doing experiments and have obtained the ordered pairs, (0, 1), (1,2),…

A: Solution :-

Q: The rest of my solutions, D-F, were not given/solved.

A: The domain of csc-1x is ℝ-(-1,1) and it has a horizontal asymptotes in this domain but no vertical…

Q: 3. Prove the following statement. If (sn), (tn) are sequences of real numbers such that then (Sn) is…

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Q: Write the uncoded row matrices for the message. Message: SELL CONSOLIDATED Row Matrix Size: 1x3…

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Q: Solve the initial value problem below using the method of Laplace transforms y" + 36y=144t² - 36t+…

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Q: Graph the curve with parametric equations  x = sin(t), y = 3 sin(2t), z = sin(3t). Find the total…

A: x=sint, y=3 sin2t, z=sin3t We have to find the total length of the curve.

Q: (ez²-1-7²) Sin³z

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Q: Express the function below using window and step functions and compute its Laplace transform. g(t)…

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Q: 2. Determine whether each of the following relations is a function. If it is not a function, explain…

A: Let A and B be two non-empty sets. A function f from A to B is a rule that assigns to each element a…

Q: Solve the following linear program using the general formulas z = -2x1-x2 x1 + x₂ ≤ 5 2x1 + 3x2 ≤ 12…

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Q: Consider the linear transformation T: Rn→Rn whose matrix A relative to the standard basis is given.…

A: Given matrix of a linear transformation

Q: 4. The graph of y = −3x + 5 is translated 6 units to the left. State the defining equation of the…

A: We have to find equation of new graph using given information. Graph of f(x+a) is obtained by…

Q: (a) Decide whether the matrix A = -1 2 -4 2 6 -3 3 is diagonalizable, and diagonalize it if so.…

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Q: Suppose f: IR→ R and g: R → R and h: R→ R are continuous functions such that h(x) = f(x)g(x) for…

A: Using given information we have to tell that whether the  given statement is true or false.

Q: 1. Graph a) lim f(x) = x-0 b) lim f(x) = c) lim f(x) = x-2 - per d) lim f(x) = 1+3+ e) lim f(x) =…

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Q: (a) We consider an investment problem with 1 riskfree asset (with return rf) and N risky assets (N >…

A: Advance maths

Q: Given y = x² + 10x + k, for what value of k will the graph of the relation ve only one x-intercept?

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Q: Consider the following three simple statements: o: The oven is on. c: Some cookies are baking. s:…

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Q: - If X is a vector space and if X= MN, where M and N are subspaces, prove that N is isomorphic to…

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Q: (c) and Y2(t) 7. The functions Y₁(t) = t and Y₂(t) = tet form a fundamental pair of solutions to the…

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Q: 1) a) Find the zeros and their order for the following functions: 2) cos (2³) 3) Coset Sinh (2) 3 1)…

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Q: 1. Use the Laplace transform definition to find L(f(t) (-1, 0≤t 1 a. f(t) = {¹ b. f(t) = te4t c.…

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Q: 6. Consider the series [ª a and ¹b. where a > 0 and b² > 0 for n ≥ 1. If [ª converges, which of the…

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Q: 1. Show that if the Wronskian of Y₁ and Y₂ is nonzero then so is the Wronskian of 2Y₁ and Y₁ + Y₂. 2…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: 1. Solve the initial value problem x'(t) = [11]x(t) + [] x(0) : -=[7]. - [8 Ste³+8e³-10e 4te³ +2e³…

A: Given that, the initial value problem is- x't = 1411xt + e3t0, x0 = -27 Firstly, solve the matrix…

Q: The population of a certain country was approximately 75 million in 1900, 175 million in 1950, and…

A: We have to find quadratic equation and population in 2050

Q: A function f(x) is (g(x)) if and only if there are positive constants k, C₁, and C₂ such that…

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Q: Given that live]) = 2₁ |1v1l = 4 and 11u till = 5 (@) Calculate i. v 1) determine cosin of the angle…

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Q: You need a $12,000 loan to buy a good used car. Your bank offers a 3-year loan with an APR of 5% and…

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Q: Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the…

A: The given function is 7t sin27t. The Laplace of 7t sin27t is obtained using: L(tnf(t))=-1ndndsnf(s)…

Q: If h(x) = and f(1) =2, f(1) =3. g (1)=-3, g'(1) = -2, compute h'(1) f (x) g(x) B h'(1) -- 54 54…

A: Given that the function hx=fxgx   and f1=2 , f'1=3 , g1=-3 , g'1=-2   .