Use the properties of natural logarithms to simplify the function. f(x)=ln(x/6)+ln(6)

Q: Find the angle of inclination of the tangent to the curve of the follow: y = 16x² at x = 2.

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Q: 2000 388.44 a)Stonne (Round to two decimal places as needed.) 2001 615.79 2002 565.33 The price of…

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Q: 7x+2 8- Find S dx (Using substitution method). √7x-3

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Q: If f(x) = x² - 2x +3 when x > 1, and f(x) = x when x ≤ 1, then f(2) + f(0) = 1 Do 3 -1 2

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

Q: Calculate the iterated integral. 13 3 2 LI (6x2y – 5x) dy dx /1

A: To evaluate the given double integral

Q: Suppose you deposit $6000 at 6% interest compounded continuously. Find the average value of your…

A: Given: Deposit Amount = $6000 Interest rate = 6%

Q: fferentiate the function and find the slope of the tangent line at the given value of the…

A: Given query is to find the slope of the tangent.

Q: Find an equation of the normal line to the curve y = In x that is parallel to the line x + 2y 1 = 0.

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Q: + 3 2 1 1 -1 -2 -3 2 3 4 5 6 7 V = = 00 S The graph above shows the base of an object. Compute the…

A: Given that a graph and we find volume of this object. We know that area of a triangle is given as -…

Q: A homeowner wants to build, along his driveway, a garden surrounded by a fence. A rectangular garden…

A: Given: The side along the driveway is labeled "$6 per foot" . The remaining three sides are labeled…

Q: Solve the initial value problem using the method of Separation of Variables. y' - x³y=0; y(0) = 2

A: Given query is to find the solution of the differential equation.

Q: Find the number or limit approached by the entire function as h approaches 0: 3h² a. lim h→0 h Find…

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Q: 5. Convert from Polar to Rectangular Coordinates: (r,0) → (x, y) (-2,-5)

A: in polar  coordinate  x=rcosθ  and y=rsinθgiven  r=-2 and θ=π3

Q: Find the equation of the tangent line to the curve at the given point using implicit…

A: NOTE: Refresh your page if you can't see any equations. . the given function is  and the given…

Q: 4 Find the equation of each graph after the given transformation. a y = 3x² after a stretch parallel…

A: Let's find equation of each graph after the given transformation.

Q: 2. Find the tangent line at the given point c(t) = (4t, In (t)); t = 1

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Q: equation, find  dy/dx  evaluated at the given values. x2y + y2x = 0  at  x = −4, y =

A: Given query is to find derivative.

Q: Integrate the indefinite integral. Se-2 da

A: ∫eaxdx=eaxa+c

Q: (a) Use a graphing utility to graph f(x) = x - 4x + 2 on the interval [-2,2] and approximate any…

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Q: A forest fire is found at midnight. It covers 1200 acres then. It is spreading at a rate of f(t) =…

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Q: Find dy/dx if y=sin ¹(7x). Answer:

A: As per guideline only one question is allowed to solve if multiple question is asked is single…

Q: Evaluate the cylindrical coordinate integral * 0/2* 3+26r² SS S dz r dr dº 00 0

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Q: Find the following antiderivatives: 2 In²(x²) √= 1.) x + x ln(x²) dx

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Q: Find the derivative: y X Lanx+ 4 COSA x4+ sinx cosx + In 59x

A: Solve the following

Q: Find the numbers b such that the average value of f(x) = 3 + 8x − 6x2 on the interval [0, b] is…

A: formula for average value is  favg=1b-a∫abf(x)dx∫xndx=xn+1n+1+c

Q: Write an equation describing the relationship of the given variables. y varies inversely as the cube…

A: Given y varies inversly as the cube root of x when x = 64 , y = 4

Q: Find the area inside one leaf of the rose: r = 5 sin (30) The area is

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Q: When solving a triangle which is not drawn, you must consider several scenarios: (1) No triangle is…

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Q: (a. f(a)) is a relative extrema of a function f. When xa, f'(a)>0. (a,f(a)) is O maximum point…

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Q: solution

A: Please refer to the image below

Q: Find dy/dt. 13) y = (1 + sin 12t)-3

A: Given, y=1+sin 12t-3

Q: A patient's temperature is 101 degrees Fahrenheit and is changing at the rate of  t2 − 3t  degrees…

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Q: (19) Find the solution of the separable equations a) the general solution: b) the unique solution…

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Q: An airline finds that if it prices a cross-country ticket at $200, it will sell 400 tickets per day.…

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Q: Evaluate (2xy³ − y² cosx) dx + (1 – 2ysinx + 3x²y² )dy y² from (0,0) to (ñ/2, 1) along the parabola…

A: According to question,Given Integral,∫c2xy3-y2 cos x dx + 1-2y sin x + 3x2y2 dy

Q: You want a linearization that will rep subsequent work as simple as possib which the function and…

A: Take x = a = 4

Q: Find a unit vector in the same direction as v = (-8,-6).

A: Given  v = <-8, -6> To find the unit vector in the same direction as a vector we divide it by…

Q: You are designing a 1152 cm³ right circular cylindrical can whose manufacture will take waste into…

A: Given that volume of teh right circular cylinder is 1152cm3.And the total alumonium used up by the…

Q: Find the average value fave of the function f on the given interval. f(0) = 5 sec²(0/4), [0, π] fave

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Q: Given vectors u = (-2, 23) and v = Provide your answer below: (-2, 26), find vector u — v.

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Q: If the objective/target function is a function of more than one input variable, then what should we…

A: To determine the next step of a maximization or minimization problem.

Q: -X. cos(2x); dy = ? е 17) y = e

A: Given function  y=e-xcos2x

Q: α. C Bl b = 6 a. Triangle above. IF C= √61, 6=6 Find a, d and B.

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Q: The Maclaurin series for sinx can be written as ...? a) Oa) O b) Oc) o d) 18-00 (-1)'+1x2r+1 (2r+1)!…

A: To determine the Maclaurin series for sin x.

Q: The function s = f(t) gives the position of a body moving on a coordinate line, with s in meters and…

A: dtndt=ntn-1formula is speed =dsdtaccelaration=d2sdt2

Q: In which of the relations represented by the tables below is the output a function of the input?…

A: We have to solve given Questions

Q: Suppose f(x, y) = 5y - 9x Find an equation for the level curve of f that passes through the point…

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Q: x)= = ·[²² h(x) = 2 In(t) dt

A: Given query is to find the derivative.

Q: (a) What does it mean for a series to be absolutely convergent? dn is absolutely convergent if an…

A: We have to discuss about absolute convergent and conditionally convergent.

Q: find the cos(t) and sin(t) of t=3pi/4

A: