Question Find the domain and range of f(x) = = Express your answer in interval notation using exact values. 8x-5 7x-6'

Q: Use linear approximation, i.e. the tangent line, to approximate √49.4 as follows: Let f(x)=√x. Find…

A: For function, f  the linear approximation at a is given by L(x)=f(a)+f'(a)(x-a)   ...............(1)…

Q: Proof Prove that if A is an orthogonal matrix, then so are AT and A-1.

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Q: valuate the integral 1₁ To xy”ddy. o 25 4 105 4 ) 15 4 D 135 4

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Q: *7. Draw the region whose area is given by the definite integral. S₁₁7 = dx Which graph shows the…

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Q: Determine whether the vector field F(x, y) = 5y² (yi+2xj) is conservative. F is not conservative F…

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Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 550…

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Q: ate the following integral using integration by parts. 4x sin x cos x dx u=4x sin x. Use the…

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Q: Let A(x) represent the area bounded by the graph, the horizontal axis, and the vertical lines at t =…

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Q: Explain why if a runner completes a 6.2-mi race in 33 min, then he must have been running at exactly…

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Q: Question Find the linear approximation L(x) of the function f(x) = -5x³ - 5x²-3x - 1 at a = -4.…

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Q: The decay equation for a radioactive substance is known to be y = y₀e⁽⁻.⁰⁵⁴⁺), t in days. About how…

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Q: If the series un is convergent, n=1 then the series (−1)ª un is also convergent. n=1

A: Given first statement is true and second statement is false.

Q: Find the Cartesian equation for the curve represented by the polar equation, r = 2 sin 0. O x² + y²…

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Q: Evaluate the following integral using integration by parts. 4x sin 4x sin x cos x dx Let u=4x sin x.…

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Q: Consider the function f(x) this interval. 1 on the interval [5, 11]. Find the average or mean slope…

A: Given, f(x)=1/x

Q: The function f(x)=√x² + 7x has an oblique asymptote y = mx + b at +∞. Find the values of m and b.…

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Q: f(x) = 2x^3 − 3x^2 − 18x − 8 Factor f(x) into linear factors. Don’t forget to include the leading…

A: Please see the below picture for detailed solution.

Q: Solve the differential equation: dy = A - By. Find the general solution to the dx differential…

A: We need to find out the general solution and particular solution for the given differential…

Q: Question Find the change in surface area dA if the radius of a sphere changes from 11 cm to 10.8 cm.…

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Q: 1. A) Express 0 1 4 1+x dx as a power series.

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Q: 2 The current domestic demand for steel is P = 150 - 2Q and the current supply is given by P = 30 +…

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Q: xydx + (x^2+y2)dy = 0 Prove that it is a Homogenous DE using homegeneity test (degree n)and solve…

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Q: Which of the following equations is/are exact? □ 3x²y² dx + (2x³y + 4y³) dy = 0 (3x²y-x²) dx + e³ dy…

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Q: n=1 n! n - (x − 3)" 2n

A: The series is given by ∑n=1∞n!2nx-3n To determine:  The radius of convergence. The interval of…

Q: The triangle with side length a=6 cm and angles measures angle B= 45° and angle C= 120° is given.…

A: Given data:- Side length of the triangle, a=6 cm ∠B=45°∠C=120°

Q: Solve the differential equation y'=1+5y subject to the initial condition y(0)=1. From your solution,…

A: Here we have to solve the differential equation.

Q: Evaluate 09 9121IN N OC 2 01 2 1 2 I -1²-2 dydx.

A: Given query is to find the value of the integral.

Q: Estimate the area under the graph of f(x) = approximating rectangles and right endpoints. R₂ = x + 2…

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Q: √ √x dx W|N 3 x2 + N/W N/W + C + C 2/3 + C

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Q: If f(x) = 7x² f'(2) = f''(x) = f''(2) = 8e, find:

A: The given function is fx=7x2-8ex

Q: in changing variables to polar coordinates, the dA in [[ f(x, y) dA R becomes r² dr do. True False

A: For conversion of Cartesian coordinates to polar coordinates put  x= rcos(thita) and y= rsin(thita)

Q: How many different 9-digit phone numbers do not contain the digit 9? Assume that any digit in the…

A: Given data÷ How many different 9-digit phone numbers do not contain the digit 9. Assume that any…

Q: If f(x) = 2ln(8 + x), f'(x) = f'(3) =

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Q: - Find the radius of convergence, R., for the power series (-1)n n²(x − 1)" 2n.n! OR=∞ OR=0 O R 8 -…

A: NOTE: Refresh your page if you can't see any equations. . here we have substitute n+1 for n

Q: lim-(In(5n³-n+1)-in(7n³n+1)) 3 3

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Q: x dy-y dx = x3 dx y" Answer: 4x + x4y + x¹y = Cy.

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Q: Use the Pythagorean Theorem to find the length of the missing side of the right triangle. Then find…

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Q: Question 3 A dilution tank initially contained 100L of fresh water. Then water which contained…

A: As per our guidelines answer first three subpart of a multipart question. So please resubmit the…

Q: Set up a triple integral using spherical coordinates that finds the volume of the solid bounded…

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Q: Let f(x) = |x-1 (a) Make tables of the values of f at values of x that approach x = -1 from above…

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Q: Calculate the vector area of the helicoid parameterised as follows: F(t, s) = (t cos s, t sin s, s)…

A: Please see the below pictures for detailed solution.

Q: Which do you think will be larger, the average value of f(x, y) = xy over the square 0 ≤ x ≤ 1,0 ≤ y…

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Q: dy dv 2 Find for y = = [ √3 +4 dt. 0

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Q: Let R be the solid enclosed by the surfaces z = 3x² + y² and z = 8 – x² - y². Fill in the missing…

A: To find the missing limits of integration.

Q: Use integration by parts to evaluate the definite integral fr² ln x dr

A: Topic- integration by parts

Q: (c) Determine whether the series (2n)! Σ 7"-¹ (n!)² n=1 converges or diverges. (d) Show that series…

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Q: Sxex² dx O 2+x²²/²/2/ HI HIN 6 1 2 HIN ex²+ + C + C + C

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Q: Find the solution of the given differential equation. dx 1 y²-6y+13 dy = 0 Express your answer…

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Q: Calculate the gradient, the divergence and the curl for the following fields, when possible: ₁ = e/y…

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Q: Using the following graph of the function f, evaluate the limits (a) through (i). 10 8 Ay 2- of X 10…

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