Use the properties of natural logarithms to simplify the function. f(x) = In(13x) - In(13) f(x) = || X

Q: n= 1 (2n)!

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Q: How did you go from x^5 to x^10 on the denominator? You divided everything by x^5 and then just the…

A: Limx-infinity(x3-3x5+5)/sqrt(x4+12x10+1).

Q: 2. Newton's law of cooling states that the temperature of an object changes at a rate proportional…

A: If the temperature of the object is T and the temperature of the surroundings is T' then by newtons…

Q: Liner algebra

A: We will find the required.

Q: Find the EXACT limit. Show your work or explain how you determined the limit lim, arctan r

A: Here we have to find the limit.

Q: If the function j is represented by j(x)= 2x²-3 then which of the following statements is true? 5x+2…

A: Here we have to find the limits.

Q: Find the value of a so that f(x) = - 3 B 2 C) 6 x²-9 x-3 a xisnotequalto 3 x=3 is continuous at 3.

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Q: For the differential equation given below, variable. d²x dr2 + kx=Acost is the independent variable…

A: Given :d2xdt2+kx=Acost

Q: Let limf(x)=L(Lbeanyrealnumber) andnbe apositive integer. X→C Whichof the givenstatementsis/are…

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Q: Use the graph of f(x) = log 1/3x to graph the function f(x) = log 1/3(x-5). Then give the domain and…

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

Q: arctan(r)dx 1+x² Evaluate an

A: Solve the integration

Q: Forms used: y-y1=m(x-x1) M= y2-y1/x2-x1 Y=mx+b I was supposed to write an equation for these…

A: There is a little calculation mistake. The whole solution has been given here. Assuming the question…

Q: The function f is defined for all in the interval 3 < x < 6. Which of the following statements, if…

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Q: The table gives values of a temperature T(t) of an object at time t. Using the Midpoint Rule…

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Q: ex 3-4e2x 21) f dx

A: Given expression:  ∫ex3-4e2xdx

Q: 4 Solve for y(x) y"-y-16=0

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Q: 19. y = tanh(e*)

A: Given; y=tanh(ex).

Q: IF YOU BORROW MONEY FROM YOUR FRIEND WITH SIMPLE INTEREST OF 12%, FIND THE PRESENT WORTH OF P50,000,…

A: Here we have to find the principal.

Q: The following function expresses an income tax that is 20% for incomes below $5000, and otherwise is…

A: To find out the taxes

Q: Determine the value of ksuchthatf (x)= kx2 ifx ≤ 2 2x+k ifx>2 iscontinuouseverywhere.Then, kerk

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Q: 10. Find the amplitude (a) and period (T) of the following function f(t)=2cos(720xt-6)

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Q: For x > 0, the horizontal line y = 2 is an asymptote for the graph of the function f(x). Which of…

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Q: PROBLEM 3 [COMPOSITE AND INVERSE FUNCTIONS]: Two functions p(x) and q (x) are inverses of each other…

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Q: For the curve: f(x) = 3x^2- 12 : i. determine the x and y intercepts.  ii. locate the stationary…

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Q: x-L^=(x) 8

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Q: x" √n2n has radius of conver- 2. Use the Ratio Test to show that n= gence R=2. Then determine…

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Q: 5. Solve the initial value problem and find the interval of existence. dy 1 dt 2y + 1' y (0) = 1. 6.…

A: I have to solve differential equations in this question.

Q: sin 3x cos 3x (cos 3x + 1)² dx 19) fa 22) fex√3-4e2x dx

A: Note: We are entitled to solve only one question at a time. As the specified one is not mentioned,…

Q: Eliminate the arbitrary constants in the equation defined by y = ax^2 + bx. Which of the following…

A: The given equation has two arbitrary constants so it has to be differentiated twice for elimination…

Q: √√x+1 x²-3x+2 h(x)=-

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Q: n=3 3n+ 5 n(n − 1)(n − 2)

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Q: - 2 to The region bounded by the line 2x + 3y = 6 and the x and y axes is rotated around the line y…

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Q: Evaluate the definite integral: [ 2√5x-2 dx =

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

Q: 27. Show that n=1 n! nn converges. Hint: Use lim n→∞ n (₁ + ²)² = n e.

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Q: A ball is thrown directly upward from the edge of a cliff and travels in such a way that t seconds…

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Q: Zim x²-3x³ +5 X-700 X²4 +12X10+ 5

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Q: Is it possible to use the fundamental theorem of calc to find the area between the graph of f(x) = |…

A: calc to find the area between the graph of f(x) = | x | -1/2 and the x axis, for all x between -1…

Q: If lim g(x) = 6and lim- X-4 A B C D 3 6 √√3 √f(x)-1_√2 g(x) √6 ,whatisthe limf (x)?

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Q: Rewrite the vector equation r(t) = (−4 − 3t)i + (3 − 2t)j + (−1 − 5t)k as the corresponding…

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Q: Find the general solution of the Differential Equations: dy dx 3)(x+1). 3x · y = e³x (x + 1)²

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Q: 11x3:3=5, then y is о-ух 0 ху -ху 0 Ух

A: Given that x3y3=5To find : y'solution :x3y3=53x2y3+3y2y'x3=03y2y'x3=-3x2y3y'x=-y

Q: A rich uncle wants to make you a millionaire. How much money must he deposit in a trust fund paying…

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Q: 23. f(x) = (1+x)¹/4

A: Concept: The Maclaurin series is given by f(x)=∑k=0∞f(k)(a)k!xk In this case…

Q: Evaluate lim (z,y) → (0,0) 1 - cos(xy) x²y²( −3+ y)

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Q: Using the Laplace transform and showing the details, solve 1. 9y" - 6y + y = 0, y(0) = 3, y'(0) = 1

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Q: Determine the slope of the line passing through the given points. (8,5) and (7, -1)

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Q: M8 n- = n2 n n+n 5

A: Given:        ∑n=1∞n2-nn5+n taking n as common   =∑n=1∞nn-1nn4+1     =∑n=1∞n-1n4+1

Q: Letf (x)=- 2x+9 ifx1 ffisnotcontinuousatx=1, Determine whetherf (x) iscontinuousordiscontinuousatx =…

A: NOTE: Refresh your page if you can't see any equations. . . the function is not defined for x=1  so…

Q: How much work is done lifting a 20 pound object from the ground to the top of a 60 foot building if…

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Q: Refer to the graph of y = f(x) = x² + x shown. a) Find the slope of the secant line joining (-2,…

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