Prove that the inverse hyperbolic function can be written in terms of logarithms: cosh¹x = ln(x+√x²-1) for xz1

Q: (c) [*e*dz = e² dr (d) [₁ 2³ d dr

A: Let's solve given integral.

Q: Identify the equation of each of the following graphs. W 7/2 37/2 7.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Solve the given LDE using the method of variation of parameters. D²+1|y=cscx

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Q: Sketch the graph that possesses the characteristics listed below. f'(4)=0, f'(4) 0, f(0) = -5; f'(2)…

A: Given query is to find the correct graph.

Q: Consider the following. 1 -, g(x) = 7x + 5 X f(x) = (a) Find the function f o g. (fog)(x) = = Find…

A: As per your demand we solve part a and d due X mark Given function:- fx=1x ,gx=7x+5

Q: 4. y = -2 sin(x) 5. y = = sin(2x) 1 2 6. y = cos(4x) cos(4x)

A: Here we have to find period, amplitude and frequency.

Q: Alarger household produces more garbage, on average, than a smaller household. If we know the amount…

A: We use system of linear equations to solve the given problem.

Q: Consider the following parametric curve. Answer parts a and b. x=t+ 1 dy dx - 7 1 y=t-it=1 a.…

A: dtndt=ntn-1dydx=dydtdxdt

Q: Find the magnitude of each vector. Then write each vector as the sum of unit vectors.

A: We need to find magnitude and sum.

Q: (a) Estimate the area under the graph of the function f(x) = endpoints. Round your answer to four…

A: Let's find area under the curve  by using right and left endpoints.

Q: F = Vo represents the where is a and F is a choose one of the following answers to fill in the…

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Q: 3x √e³x dx = 0 (Type an integer or decimal rounded to the nearest thousandth as needed.)

A: ∫eaxdx=eaxa+c

Q: Compute the average value of f(x) = √4x + 1 on the interval [0,2]. Average value =

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Q: Calculate the indicated Riemann sum S3 for the function f(x)=x²-8x - 33. Partition [0,6] into three…

A: Let's find Riemann sum S3.

Q: 3. Evaluate the double integral. 2-1 (coey) dA where D is the regiou bounded by y-0. y -a², and

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: Determine a vector equation for a line that goes through the following points: (-8, 7, 8) and (-10,…

A: Determine a vector equation for a line that goes through the following points: (-8, 7, 8) and (-10,…

Q: Use the divergence theorem to find the total flux out of the solid x² + y² ≤ 4, 0≤z≤1, given that…

A: use divergence theorem and cylindrical coordinates for finding flux.

Q: lim (2x² - 6x - 3). x-3

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Q: Find the critical point and the interval on which the given function is increasing or decreasing,…

A: dxndx=nxn-1f(x)=5x2+4for critical points put f'(x)=0

Q: Find the equation of the line tangent to y = -3x² + 3x + 2 at x = -1. Oy=9x−1 y=-62-5 Oy=9z+5 y =…

A: given y=-3x2+3x+2 at x=-1standard form is  y=mx+cwhere m is slope of line m=dydxdxndx=nxn-1

Q: 5 6 (Type an integer or a simplified fraction.)

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Q: 2) Solve for x : a) e* = 80 b) 3¹-* = 9²x g2x

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Q: 2y y² dxdy Evaluate SS2¹ 4y²+x² O π/12 O π/16 O π/2 O π/6

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Q: Suppose that 103 Σ ai = 19 and i=1 103 i=1 b₁ = 18. Compute the sum.

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Q: 1. Evaluate the following definite integrals: 1 1.- J (20-1 0 1 [ (1³ / 2. 3. (2t - 1)'dt (t³ + t²)…

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Q: A Sno-Cone at the carnival has the shape of a hemisphere on top of an inverted cone. What is the…

A: To find the volume of sno cone.

Q: Find f'(5), if f(z) = (4z² + 5x) (2x² - 8)

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Q: Find the surface area and volume of the figure below. 7 in 7 in Surface Area = Volume = 7 in Q…

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Q: Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for ſ x(t)…

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Q: Two variable quantities A and B are found to be related by the equation given below. What is the…

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Q: Approximate the area under the curve graphed below from x = 1 to x = = 5 using a Left Endpoint…

A: The formula to calculate the approximate value of the area under the curve is, Area ≈ ∑i=1nf(ci)∆x…

Q: Use the Fundamental Theorem to evaluate the definite integral exactly. 1 [₁ (18x² + 3) dx Enter the…

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Q: Find the exact value of each expression. (a) log3(60) - log 3 (20) (b) log5 (6) log5 (2) - log5 (75)…

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Q: Find the differential dy when x = 1 and dx = 0.3 Find the differential dy when x = 1 and dx = 0.6…

A: Given query is to find differential at indicated points.

Q: Use the Fundamental Theorem to evaluate the definite integral exactly. 1," 16 5 Enter the exact…

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Q: Use the Quotient Rule to find the derivative of the given function. b) Find the derivative by…

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Q: Verify that the hypotheses of the Mean-Value Theorem are satisfied on the given interval and find…

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Q: Expand the expression using the binomial theorem (2+4)*

A: As we know from the binomial theorem: x+yn=C0nxn+C1nxn-1y+C2nxn-2y2+....+Cn-1nxyn-1+Cnnyn   To…

Q: 35. For m = (-5, -6) and = (6, −9) find the sum of the vector three times the magnitude of m and the…

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Q: 1. Sketch the graph of each function, labeling any intercepts with their coordinates and any…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Given the information below, estimate the total distance travelled during these 6 seconds using a…

A: We need to perform left endpoint approximation.

Q: ). Find the Taylor polynomial of degree two approximating the given function centered at the given…

A: Given function:- fx=x Taylor series is given by fx=∑k=0∞fkak!x-ak

Q: Determine whether the series is convergent or divergent. In(n) ₂2 n = 2 convergent divergent

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the complete solution of the linear system, or show that it is inconsistent. (If the system has…

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Q: If f(x) = x² + x and g(x)=x-9, find f(g(x)) and g(f(x)). f(g(x)) g(f(x))

A: Given query is to find indicated composite function.

Q: Evaluate. 5 -1 -1 (4x²-3x+5) dx (4x²-3x+5) dx = (Type an exact answer in simplified form.) ***

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Q: Determine the area of the triangle with the following vertices: (-3, 7, -1), (-10, -2, -1) and (5,…

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Q: A sports ball has a diameter of 27 cm. Find the volume of the ball. Round your answer to 2 decimal…

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Q: Which of the following conditions will make the equation equation of a sphere in xyz-space Oa>b>c…

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Q: Let f(x) = {5² (52–3, 2x, x > 1, x < 1, Does lim f(x) exist? Why or why not? x 3 1. Yes because you…

A: To determine whether the given limit exists or not