Use properties of logarithms to condense the logarithmic expression below. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. 2 In x+4 Iny-3 Inz 2 In x+4 Iny-3 Inz =

Q: Find the area between the curves y = e Area - 0.7x and y = 1.3x + 1 from x=0 to x=2

A: The area between the curves y=e-0.7x and y=1.3x+1 on interval 0, 2.

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) (2³²₁ -j+e-6tk lim t0 e³ti+…

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Q: 7) .  Use separation of variables to find the general solution. (Use C for the constant of…

A: answer is in next step. please give a like !!

Q: Evaluate the indefinite integral by using the given substitution to reduce the integral to standard…

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Q: Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the…

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Q: Evaluate the definite integral (a) ľ² _l+ x +24 dx, (b) [¹² (x² + 3) (2x + 1)dx, (c) [¹ x²e²¹dx -1…

A: ∫-11 xdx1+x2+x4

Q: 3 7 Given sin A 25 in Column 1 with its exact value in Column 2. Column 1 and sin B sin (A - B) tan…

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Q: 6 13 Find the critical points of the function f(1) = 26x7 +17. Enter your answers in increasing…

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Q: Find the component form of v given its magnitude and the angle it makes with the positive x-axis.…

A: Given: |v|=4, θ=3.1°

Q: Consider the parametric curve given by (a) Find dy/dx and d²y/dx² in terms of t. dy/dx = |d²y/dx² =…

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Q: Find the limit. 4 Ilm x3 52 5

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Q: Find the following for the given equation. r(t) = (e-t, 8t², 3 tan(t)) (a)_r'(t) = (b) r"(t) = (c)…

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Q: Assume that the rate of evaporation for water is proportional to the amount of water in a bowl. Jill…

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Q: Exercise 2 In this exercise you're going to find the linear approximation (or tangent plane, if you…

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Q: 6 5 + x²' a. Find the slope of the line tangent to its inverse function at the point P(1, 1): For…

A: We can answer the question as below.

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

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Q: A Sliding Ladder A 26 ft ladder leaning against a wall begins to slide. How fast is the top of the…

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Q: dy Find for y = dr dy dr || r J√3 + 0 3 + 4t2 dt.

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Q: A. Find the roots of the following differential equations and match with their complete solution.…

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Q: (f) If F¹(x, y) = 5y sin(xy)i + 5x sin(xy)j, then f(x, y) =

A: Given vector field F→(x,y)=5ysin(xy) i→ +5xsin(xy) j→ we need to find function f(x,y) such that…

Q: Determine whether each of the following vector fields F is path independent (conservative) or not.…

A: use partial derivative for finding the potential function.

Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary Integer…

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Q: 1) .  Solve the initial-value problem with the initial condition y0 = 0. dy dt = y + 3 y =    graph…

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Q: 3 The point P is on the unit circle. If the y-coordinate of Pis and P is in quadrant II, then 8 x =

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Q: t Find the Taylor series centered at c = -1. 7 3x-2 f(x) = Identify the correct expansion. Σ -(x -…

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Q: A vector v has magnitude |v| = 4 and has direction = 60°. Write in terms of i and j. O a) v =…

A: Vector with magnitude 'r' and direction 'θ' in terms of I and j is given by V=r(icos(θ)+jsin(θ))

Q: Solve the given differential equation. ex²dy=x√/10-y dx Choose the correct answer below. OA. 4√/10-y…

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Q: If investment A has an annual return of 4% with continuously compounded interest, and Jane has $500…

A: Given: Interest rate, r = 4% =4/100=0.04 Final amount, A = $500 Number of years, t = 4

Q: Evaluate the integral using an appropriate method. T/3 x sin(3x) dx

A: ∫0π3x sin(x)dx

Q: Find the area of the "triangular" region in the first quadrant that is bounded X X 4 4 above by the…

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Q: Find any Intercepts. y = x² + 4x - 5 (x, y) = y-Intercept: x-Intercepts: (x, y) = (x, y) = (smaller…

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Q: Find the limit. (If an answer does not exist, enter DNE.) (x²+2x-8) Ilm x-2 (x²-4)

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Q: Find all real numbers in the interval [0,2x) that satisfy the equation. 2 9 cos y + 29 cos y + 20 =…

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Q: Find the limit. Ilm x-1x²+3

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Q: 1. For what values of h (if any) does the differential equation have equilibria? dy (y- 5)(y-6) - h…

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Q: Draw the given optimization problem and solve. Find the dimensions of the closed cylinder volume…

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Q: Sketch the plane curve. r(t) = tr + t2j, [01] y 1.0 0.8 0.6 0.4 0.2 y 1.0 0.8 0.6 0.4 0.2 0.2 0.2…

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Q: Graph the integrand and use known area formulas to evaluate the integral. 4 ja S (10-|x) dx -4 Use…

A: Topic = Area

Q: Tutorial Exercise Find lim Ax-0 f(x + Ax) = f(x) Ax f(x) = 3x²-3x Step 1 Find f(x + Ax) by…

A: We will find the required limit.

Q: Find the gradient of the function at the w = x tan(y + 2), (10, 8, -3 Vw(10, 8, -3) =

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Q: an the graph of f(x), determine the domain off-(x). [10,-) [2.-) - f(x)

A: Topic:- function and it's inverse

Q: The table below gives selected values for the differentiable and increasing function f and its…

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Q: < rev The demand for a product is given by D(x) = 170e-002, where x is the number of units sold each…

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Q: Evaluate the following integrals: 1. dx 2. f6²+1²+6 dr 3. (3x - 5)(2x²-x+5)dx 4. Solve the initial…

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Q: Suppose that over a certain region of space the electrical potential V is given by the following…

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Q: nd the one-sided DNE lim_(x². +x+5) x--5- exists). (If an answer does not exist, enter DNE. Submit…

A: Topic:- limits

Q: Find an equation for the graph sketched below -5 -4 -3 -2 -1 f(x) = 8 6 5 3 2 1 -1 -2 -3 -4 -5 -6…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: For the line, x(t) = y(t): Find parametric equations for the tangent line at t = 3 for the motion of…

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Q: Given surface A: 4x² - 9y² = 9(z² + 4) 1. Find an equation of the trace of A on each of the…

A: answer is in next step.

Q: Given the functions f(x) = 2* and g(x) = log(1-x), determine the domain of the combined function…

A: We have to choose the correct option from the given options according to the given information