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. Assume that x, y, and z are positive. 2 Inx-15 Iny+5lnz =

Q: Problem 4. Calculate each of the following indefinite and definite integrals. Remember that you…

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Q: dw dt = x²y = xy³, x = cos(t), y = et Find: @t= 0, when w =

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Q: A differential equation (DE) is a mathematical equation for an unknown function that relates the…

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Q: y" + 4y = sec²2x

A: Given: y'' +4y=sec22x The general solution of the corresponding homogeneous solution is y=c1 cos…

Q: 3. Verify Clairaut's Theorem on by showing fry=fyx. f(x, y) = 4 x² + y² + 2

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Q: Find the polar form for zw, z/w and 1/2 where: z = 2(1 + i), w = 3(1+√3i)

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Q: b. IF A = +²î - tj + (2+ +1) K B = (2-3)i +Ĵ-tk A. d_ (A.B) dt OBTAIN THE FOLLOWING @ t = 1

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Q: Evaluate the integral. (Use C for the constant of integration.) [sc 5 csc¹(x) cot(x) dx X

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Q: A ladder 15 ft long leans against a vertical wall. If the lower end is being moved away from the…

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Q: What is the sum of the first 50 terms of the series 10 + 85 +160 + 32

A: Given :   series 10 + 85 +160 + 325   Common Differences

Q: The cost for x Giants hats is C(x) = 500 + 10x + 100/x and revenue is R(x) = 18x Use the marginal…

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Q: Qe Evaluate the following integrals, then reverse the integration order ( a) y dx dy.

A: Consider: ∫02∫04-y2y dx dy=∫02y x04-y2 dy=∫02y 4-y2-0dy=∫024y-y3dy=2y2-y4402=222-244-202-044=8-4=4…

Q: dz Calculate for z = 4x² + 3y², x = sin(t), y = cos(t) dt

A: Topic- derivative of a function we are given, z=4x2+3y2x=sin(t),y=cos(t)we know…

Q: Find the solution of the differential equation y(t) = = 1 t sec y = 6 cos t { x + + + ² ( 1 ) x - *…

A: The given differential equation is  y'+1/5sec(t/5) y= 6cos(t/5) , y(0) = 1  where 0<t/5<

Q: Find for x³ + y²x − 3 = 0 - dx

A: To find dy/dx

Q: show complete solution

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Q: = : 0. z = x² + x − 3xy + y³ − 5, find all points(x, y) wherein zxand zy

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) √er (5 + 6e 6e)7/2 dr

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Q: If f(x) = x+3 and g(x)=x²-2, find the following. a. f(g(0)) c. f(g(x)) b. g(f(0)) d. g(f(x))

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Q: Show that xzxx + yZxy = y²Zyy if z = xy + yln(xy)

A: Given, z=xy+y ln(xy)

Q: 29. xyy' = 1 + y²; when x = 2, y = 3.

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Q: Qe Evaluate the following integrals, then reverse the integration order 2 c2x 1) (4x + 2)dy dx.

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Q: Evaluate the integral: - (6x + 14) (x - 1)(x + 1)² SE dr +C

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Q: For the function f, use composition of functions to show that f 3 1 (x) = -x + 1, f¯ ¹ (x) = = ¹(x)…

A: Topic- Functions and inverse of function We are given, f(x)=37x+1,f-1(x)=7x-73

Q: [x²-2 if x≤2] -3x+1 if x>2 Graph the function, f(x)=- x y

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Q: (D4 + 2D³ - 3D² - 4D + 4)y=0

A: (D⁴+2D³-3D²-4D+4)y=0 So, D⁴+2D³-3D²-4D+4=0

Q: Using the attatched equation 3.9, find the general solution of the following differential equation…

A: Given data:- The given differential equation is, dy+2xy-xe-x2dx=0

Q: Then (fog)(x) = (fog)-¹(x) = (f ¹ og ¹)(x) = (g-¹ of ¹)(x) = f(x)=x+4 and g(x) = 2x - 5.

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Q: (3) Consider the initial value problem zy' + y = 5x¹, find the general solution. Now, with inital…

A: Solution

Q: 2 Find and simplify the expression if f(x)=x²-3. f(4 + h) − f(4) f(4+h)-f(4)=

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Q: X-2 (a) lim x2-7x+10

A: as per the company rule we are supposed to answer only the first question and rest can be reposted.

Q: N 2 -3 EXAMPLE 5 Find an equation of the tangent line to the parabola y=x²-8x + 9 at the point (2,…

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Q: Iculate zu for z=₁₁₁x = e Z X 2u cos(3v), y = e²usin(=

A: We are given  z=2x-yx+3y, x=e2ucos3v, y=e2usin3v we have to evaluate zu=∂z∂u

Q: Given f(x, y, z) = xyz, find fyyx

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Q: find the differential equations of every families of curves given. complete solution  1. all…

A: I have solution in detail...go through the solution

Q: Find dy. y=34+ 10x²5x5 dy = (Simplify your answer.)

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Q: 2.  Evaluate the integral. 7 5 dx (x − 6)2   please hsow step by step clealry

A: Given Expression: ∫57x-62 dx

Q: Evaluate the integral. Ta dx = (x-2)(x-3)(x + 2) + C

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Q: y= Cix2 + Cze' C₂e² 2X

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Q: . Find the volume of the solid generated if the area bounded by y=x², x=2, ar x-axis. A. 32/5 cubic…

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Q: Solve (D³ − 2D² + 2D) y = 0; when x = 0, y = 0, y = 1 and y/l =

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Q: Let f(x)= -6 cos x + 6 tan x Find ‘(x) Find ‘(π/3) My results were the following: f’(x)=…

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Q: and- I need a clear answer by hand, not by keyboard | dybala Determine the general solution for the…

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Q: Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an…

A: We have to find the values using Law of sines.

Q: y = sin (x) 1+cos (x) Answer: 1 1 +cos x |

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Q: EXAMPLES Find an equation of the tangent line to the parabola y--&x+9 at the point (2.-3). SOLUTION…

A: Find equation of tangent line

Q: Let F(t)=4t^4i−2sin(3t)j+2e^(5t)k and G(t)=−2cos(2t)i+j+4/t^4k,find F(t)⋅G(t)

A: Let's find F(t)•G(t).

Q: Evaluate the integral. 5 1³w² w² In(w) dw

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Q: Find y' of tan(x²y4) = 3x + y²

A: NOTE: Refresh your page if you can't see any equations. . take derivative on both sides

Q: Solve for the partial Derivaties of each equations

A: We have to solve for partial derivatives (1) f(x, y) = x4 + 6√y - 10