28. Write the expression as a sum and/or difference of logarithms. Express powers as factors. log 2 (16x)

Q: Find the Jacobian for the indicated change of variables. x = uy -2u, y = uv О д(x,y) H(u, v) О…

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Q: (x² + y²) dx - xy dy = 0.

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Q: Find the smallest angle in the right triangle with a hypotenuse of length 175 and a leg of length…

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Q: 4

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Q: 40+ toz

A: Topic:- application of derivatives

Q: Use implicit differentiation to find an equation of the tangent line to the graph at the given…

A: The tangent is a straight line so it will be of the form y = mx +c  We can get  m  by finding the…

Q: Evaluate the integral. er HEAD ² y³ In(x) dx, y> 0 ind

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Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at…

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Q: For each of the following differential equations, write the particular solution proposed according…

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Q: If the acceleration A(t) of an object is proportional to the square root of its speed S(t); write…

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Q: 23. Find the radius of the circle inscribed in a triangle formed by the lines 7x+24y-70-0,…

A: The given equations of the lines are: 7x+24y-70=0  ..........(1)21x-20y-70=0…

Q: Evaluate the following integral using integration by parts. x¹ ln x dx

A: This question is based on integration by parts.

Q: Evaluate ff sin(9x² + 4y²) dA, over the region in the first quadrant by the ellipse 9x² + 4y² = 1.

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Q: For the following exercises, evaluate the binomial coefficient. (3) 17 25 6. 11 7- (7) 7. (200) 8.…

A: To evaluate the binomial coefficient.

Q: W Let z = x₁ + iy₁ and w = x2 + iy2. Prove = e²-w ew

A: ex × ey  = ex+y  e-x = 1/ex

Q: A dynamic system is represented by the following differential equation. y" - y' - 2 sin y = u(t),…

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Q: What is the area under the curve of the following positive function y = 10x4 + 3x² between x = -1…

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Q: The minimum value of N such that the remainder estimate given in the text guarantees that SN…

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Q: Using geometry only, find the area under the curve. Include a sketch of graph for each region. Give…

A: Given fx=∫0636-x2+9 dx

Q: Find the definite integral of ₁3 T Option 1: 4 Option 2: Option 3: Option 4: 4 2 I 6 π 3 6…

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Q: Find a Cartesian equation for the curve described by the given polar equation. r = 9sin 8 Select the…

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Q: valuate the integral using the Trigonometric Substitution metho x² (81-x²)3/²2 dx

A: Topic:- application of integration

Q: The bass population of a mountain lake was measured a year ago, and the lake was found to host 6,000…

A: This is a logarithmic problem

Q: Find the curl for the vector field at the given point. F(x, y, z)= 6xyzi+6yj+6zk (6, 7, 6) O…

A: We have to find the curl

Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

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Q: If a reflection is performed on the graph of y y = 3+1 and the equation x-1, the reflection was…

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Q: Example: Determine the volume of the solid that bounded by the parabolic cylinders y-x2 and x-y2 and…

A: Given: we have to find the volume of solid that bounded by the curve y=x2 and x=y2 and plane z=0 and…

Q: VA Find the equation of the curve that passes through the point (1, 0) and has a slope of O = y = y…

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Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (17, -18, -1)

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Q: a) fo f(x) dx d) f3f(x) dx b) √²³ƒf(x)dx c) ff(x) dx e) fºƒ(x)dx − [f(−ƒ(x))dx + f² ƒ(x)dx]

A: Note:- according to the company policy we can attempt maximum three subparts of a question so please…

Q: Questions 3. Which of the following points is an invariant point when f(x) is transformed to f-¹(x)?…

A: Solution ) f (x) and f-1(x) are symmetric about                  x = y  It means when we change the…

Q: Use Theorem 7.1.1 to find {f(t)}. (Write your answer as a function of s.) f(t) = (e² - e-t)² L{f(t)}

A: f(t)=(et-e-t)2

Q: Use implicit differentiation in finding y'. 1. x²³² +y³ =18xy

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Q: Find the following indefinite integrals. 24x² a) S -dx (3x4-8) b) c) (-2x² - 15e* + √√x³) dx…

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Q: Bob's grade in his science class is related to the number of hours he studies. The rate of change…

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

Q: dx xy dy x² + y² Ans. y² = 2x²ln (

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Q: (4) The symbol f was introduced by and is called an It is an elongated S and is chosen because an…

A: NOTE: As per our guidelines, I am supposed to solve only one question. Even though I have answered…

Q: Is the following statement true or false? Please explain and justify your reasoning. If f takes on…

A: True f takes on both positive and negative values, then the Riemann sum is the sum of the areas of…

Q: [D3 – 6D2 + 11D − 6)y = cosx sinx

A: The objective is to solve the above differential equation.

Q: A town's raccoon population is growing exponentially. The expected population can be estimated using…

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Q: First-class postage is $0.37 for a letter weighing up to one ounce and $0.24 for each additional…

A: First‐class postage is $0.37 for a letter weighing up to one ounce and $0.24 for each additional…

Q: Find the curvature of the curve r(t) =

A: This question can be solved by applying the formula for curvature.

Q: Integrate: S dx sin ³x cos6x

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Q: y y = f(x) 8

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = —, (1, 8, 8) X 10…

A: Explanation of the answer is as follows

Q: Integrate using appropriate U-Substitution. You must label u and du: (x - 1)(x + 1) 15x -5x³ S dx u…

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Q: A population of 440 bacteria is introduced into a culture and grows In number according to the…

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Q: A 20-volt electromotive force is applied to an LR-series circuit in which the inductance is 0.1…

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Q: Find the arc length of f(x) = (1+2²) from x = 0 to x = 2. Simplify your

A: Given :fx=231+x232x from 0 to 2

Q: Evaluate ff xydxdy over the square with corners (0,0), (1,1), (2,0) and (1, –−1) (u + v) (u - v) 2 2…

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