Express as a sum or difference of logarithms without exponents. 5 4 X log c 4_7 y'z What is the equivalent sum or difference of logarithms? (Simplify your answer. Use integers or fractions for any numbers in the expression.)

Q: 0 3² 3x - 4x dx 5x

A: Basic identities of integration are used.

Q: Alternative Formula for the Derivative f'(x) = lim Z-X f(z) = f(x) Z - X

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Q: Directions: Determine whether rational equation, rational inequa solutions in your activity noteboo…

A: As per the company guidelines We can first three parts   only. Please understand. Kindly repost the…

Q: Solve the given differential equation. All solutions should be found. dy 3x² – 2y - y³ 2x + 3xy² dx…

A: Given differential equation is dydx=3x2-2y-y32x+3xy2

Q: Q3) find the soluation of differention equation 2) y' sin 2x = y cos 2x

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Q: (b) y = e, y = ²x, x=0, x= ln 2 1 (c) x = =, x = 0, y = 1, y = e Y (d) y = 5x - x², y = x (e) y =…

A: Using vertical strip

Q: 7. Determine the dimensions of a rectangular box, open at the top, having a volume of 32 ft³, and…

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Q: Which of the following is equivalent to the expression a) √√³² Ob)-20 h³ d) h² • ?

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Q: ९२ e 17 olx

A: ∫1e2(1-x)/dx2x here integration is given  ∫1e2 dx/2x - ∫1e2 dx/2 (1/2)[lnx]1e2 - [x/2]1e2 (2-ln1)/2…

Q: Use the graph below to determine that slope of the secant line on f(x) from x-1 to x-3. 5 4 3 2 y =…

A: use the graph for finding the slope of the secant line.

Q: Show that the series n=0 xn cos(nx) x² +n³ + 1 defines a differentiable function g(x) for x in [-1,…

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Q: ] Find the Taylor series expansion of f(x) = ln(3-2x) about a = 1.

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Q: 3) Use the definition of derivative (do NOT use the short cut method) to find_ƒ'(x) given that f(x)…

A: This question is based on finding slope using definition of derivative.

Q: 1) a car is slowing down at the rate 0.8 ft /sec², How the will the can move before it stops if its…

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Q: 4. y +==y² A.-4-2 5. 4x² + 4y2 = 36 A. - 6. x² + 3xy-y = 7 A. 2x-3y 3x-1 B. 3 B. 4y-2 KIA 2x+3y 3x-1…

A:

Q: 12. Calculate the area of the segment cut from the curve y = x (3-x) by the line y = x. A. 5/3 sq.…

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Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i-2j+ 2k. 1, Find the unit vector…

A: We can solve this as follows:

Q: Answer true or false? A function is not a function but is defined on a function space true Ofalse

A: Solution )  a function defined on the function space  Function space is set of function between 2…

Q: [1 if A= 2 13 23 2 1 -2 find det (A) if 3 3 -1. 6 O 38 O 16 O 18 O 48 O

A: The solution is given in the next step.

Q: Consider the initial-value problem y' + exy = f(x), y(0) = 1. Express the solution of the IVP for…

A: Given:- y'+ex y =f(x) , y(0) =1  Find:- Express the solution of the IVF for x>0 as a non…

Q: Q4:B/Simplify Moivre's theorem? [cos 30+ i sin30 15 [cos 0-i sine 1³ [cos 50+ i sin50 ] [cos 20-i…

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Q: 3) The line L: x = 3 + 2t, y = 2t, z = t intersects the plane x + 3y -z = -4 in a point P. Find the…

A: To find the coordinates of P and find the equation for the line .

Q: d²y Find for the following function. 2 dx y= (3x² +1) -5 d²y dx² =

A: On solving this we will get

Q: 16. A cup like object is made by rotating the area between y = 2x² and y = x+1 with x> 0 around the…

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Q: Find the general solution of the given differential equation, and use to determine how solutions…

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Q: Find the solution of the given initial value problem in explicit form 1 y' = (1 - 5x)y², y(0) = 9

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Q: Determine whether the differential equation (4x² − 2xy + 6) dx + (2y² − x² + 4) dy = 0 is exact. If…

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Q: termine whether the function has a vertical asymptote or a removable discontinuity at x = -3. Graph…

A: Here is the solution:

Q: 11. A hockey player, on left defense, is about to take a shot on net. The net is 1.83m wide. The…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Find the solution of the given initial value problem. π ty' + 2y = sint, y "(-) = 5, t > 0 Y ||

A: Concept: linear differential equation of the form dydx+Py=Q The general solution of the linear…

Q: 2.) Determine whether the geometric series is convergent or divergent. If it is convergent, find its…

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Q: State the order of the given ordinary differential equation. (1-x)y" - 8xy' + 3y = COS X

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Q: Rewrite the given function with a rational exponent. 7|X 8 = y In X + 8 = In x + 1 || In x + 00 8 00

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Q: The exponential function given y H(t) = 80,031.49(1.0483)', where t is the number of years after…

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Q: The dimensions of Roy and Roger's sandbox are t² meters by t5 meters. One cubic meter of the sandbox…

A: dimensions of the Roy and Roger's sandbox : length =  t2  width = t5 height = v2…

Q: Find dy dx 2 for x²exy = 5 WA/

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Q: A company can produce LCD digital alarm clocks at a cost of $6 each while fixed costs are $50.…

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Q: x-2x +x= 15; x (0) = 7, x (0) = -16 hand written plz

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Q: Which one of the following is the gradient of the tangent line at the point (6, -3) on the graph of,…

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Q: Let f be the function defined as follows. y = f(x) = √5x + 5 (a) Find the differential of f. dy = X…

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Q: Where is the function f(x) below discontinuous? if z 2 Choose all answers that apply. f(x) is…

A: This question is related to limit and continuity, we will solve it using given information.

Q: WEEK 8 LESSON 3: Finding Circumferenc 0 LEARNING TASK 1 Ma'am Rona, Reese's teacher saw Piolo and…

A: Given Diameter=4m  Radius=2m  Solve the learning task

Q: 5(c) Find the rectangle with the largest area that can be inscribed in the top half of the ellipse ²…

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Q: Solve the following system of linear equations: X₂-5x₂+x3 = 2 If the system has infinitely many…

A: The given system of equations,        x1-5x2+x3=2

Q: 3 -21 3 -1 The Cofactor Matrix is :- -3 0 [-3 0 12] 606 6] 36 ن من من IF A [-3 0 12] 606 3-6 6…

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

Q: Determine whether the differential equation (4x² - 2xy + 5) dx + (7y² − x² + 4) dy = 0 is exact. If…

A: The given differential equation is;  (4x2-2xy+5)dx+(7y2-x2+4)dy=0.

Q: x dx 2)√√√27+6x-x²

A: Given, ∫ x27+6x-x2dx

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

A: Newton’s Law of Cooling Formula The greater the difference in temperature between the system and…

Q: Q.2)(A) Find a formula for the area of the triangle in the xy-plane with vertices at A(0, 0), B(a1,…

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Q: ſº 5u³ – 3u³ – 9du

A: