Write the inverse of h(x) = log6x h -1( x) = 6 x h -1( x) = 6 x h -1( x) = x 6

Q: Find dy/dx by using Leibniz’s notation for the chain rule: dy/dx = (dy/du) (du/dx)  y = 6u3,u = 7x ...

A: To find dydx bu using Leibniz's notation for the chain rule: dydx=dydududxy=6u3, u=7x-4    

Q: y=(x^1/2)^7x find y'

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Q: Find the particular solution to the following equation y" + 4y' + 5y = 0 y(0) = 1; y'(0) = -3 Hint: ...

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Q: What is the derivative of f(x) = e&x + 3? a. f(x) = 8e b. f(x) = e8 C. f(x) = 8e8x+3 d. f(x) = 3e&x ...

A: We find derivative of given function.

Q: We have  P(t) =  7000 1 + 24e−kt. Since P(1) = 840, then 1 + 24e−k = ____ , and so ek =

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Q: Use a scientific calculator or unit circle to convert the polar form of the complex number to its eq...

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Q: 5. (x + 3): (5y - 2) = 1:4 and 2x + 3y = 4 6. x: y:z- 1:2:4 and x +y +z= 112 (x + y): (y - 2): 2 = 5...

A: solve the equations

Q: 2 f(x)=-2cot(x-45)+2 Period f(x) Vertical Shift Horizontal Shift Start End: Increments

A: According to question,Given function,fx = -2cotx- 45o + 2

Q: 1. Find the work done by the force F(x, y, z) = (xz, z² – x, y ), along C, the curve defined by x = ...

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Q: Find the Fourier series of the following waveform: f(t) 2 ... -T -T/2 T/2 T Which is defined as 2t f...

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Q: Consider vectors u and v. u = 4i + 2j,  v = 2i + 3j a.) Find the vector projection w = projuv of vec...

A: Us vector and scalar projection formula

Q: Graph of f 5. The graph of y = f(x) on the interval 0 < x < 5 is shown above. Which of the following...

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Q: the series using any appropriate test from this chapter. Identify t t with the p-series

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

Q: Find the phase shift of the function y = -sec(2x + T) 2 2 -2TT 2TT

A: Topic:- trigonometry 

Q: dy Find by implicit differentiation. dx 7x2 + 3xy – y? = 9 dy dx

A: Differentiation of the above function is

Q: Given f(x.y) = e X cos y, Evaluate fx(2,0) e2 cos 2 O sin 2

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Q: Determine the convergence or divergence of the series using any appropriate test from this chapter. ...

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Q: 13 The polynomial equation x4 - 6x3 + 10x2 + 2x - 15 = 0 has solution set _____. {3 + i, 2 - i, 3,...

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Q: 6. Determine the x-value(s) of the point(s) on the graph of f (x) = 3x³ – 11x – 2 where the tangent ...

A:  The function f(x)=3x3-11x-2 where the tangent line is parallel to the line 10x-2y-18=0

Q: 1. A movie theater seats 240 people. For any particular show, the amount of money the theater makes ...

A: According to question,Given,Number of people n= 240 - 12pwhere,p is the price of one tickets. 

Q: A fourth degree polynomial with constant coefficients may have (1) 4 distinct real roots. (1I) 3 dis...

A: Find your answer below 

Q: If f(x) =x² +1 and g(x) = 2x + 3, find all values of x where the derivative of fAg(x)) is equal to t...

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Q: 6. Find the exact solution of each equation, no decimals. Do not use a calculator and find the domai...

A: Given problem:-

Q: Find the exact length of the curve. 2 3/2 y = = 12, 0<xs 1

A: Given ,y=23x32Aim: To find length of curve in [0,1]We know that L=∫ab1+[f'(x)]2dxTherefore,L=∫011+dd...

Q: ld the absolute extrema if they exist, as well as all values of x where they occur, for the function...

A: Topic:- application of derivatives

Q: 1 -1 -2 -2 -1 0 1 2 3 2 3 4 4 -2 -1 4. FIGURE 6.1.12. Spiral point (-2, 1) and saddle point (2,-1). ...

A:   Given the systemdxdt=2x-2y-4 anddydt=x+4y+3 To find critical point we take dxdt=0 anddydt=0  

Q: Please include solutions, for me to understand it more. Thank you

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Q: The vector describing a particular particle is given by F (t) = Rcos (wt) î + R sin (wt) ĵ, where R ...

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Q: If z = y + f(x^2-y^2), where f is differentiable, show that y(∂z/∂x) + x (∂z/∂y) = x.

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Q: 2x – x3 da. = |- In(x – 1) + | Ftan-1(x)| + с Given: + J (x – 1)²(x² + 1)' 2(х-1) 2 2x – x3 determin...

A: Find your answer below 

Q: Choose the correct graph by clicking on it. X + 3 f(x) = x2 - 9

A: Question is solved.

Q: Given f(x,y) = eX cos y, Evaluate fy(2,0) O cos 2 O sin 2

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Q: If y = (2x2 – 1) then what is y'? а. у %3 4x (2x2 -1) -12 b. у - 2x (2x2 - 1) 2 с. У 3 2x (2х- 1) % ...

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Q: Find the slope of the line through (-1, -1) and (-1, 3). undefined -1/2 0 -4

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Q: A given partial fraction Cx +D x² +1 2x A + X+4 (x-1)(x+4)(x² +1) X-a A can be evaluated as: O 15 2/...

A: Given that partial fraction 2xx-1x+4x2+1=Ax-1+Bx+4+Cx+Dx2+1To find : value of ASolution:2xx-1x+4x2+1...

Q: Which of the following functions is differentiable for all values of x? a. fAx) = 2r' + 5x² b. f(x)=...

A: Given problem:-

Q: Find the solution of the differential equation that satisfies the given initial condition. dy y(0) =...

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Q: Find lim   x3 + 3x2 + 3x + 1      x - 1    2x3 + 3x2 - 1

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Q: Which of the following functions is differentiable for all values of x? a. flx) = 2r° + 5x? b. f(x) ...

A: Function which is differentiable for every value of x is

Q: 1+ cosx + sinx sinx 1+cos x 2sec x 2csc x 2csc 2x 2sec 2x X.

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Q: 2π ||미 = 4, ||v|| = 16, 0 = 3 %3D %3D %3D

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Q: Solve the following equation by factoring. -5x2 - x = -4

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Q: 1. Find the domain of the function: f (x) = log2 Show a sign table. %3D Intervals: Test Value: Sign ...

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Q: (a) Ifx + y = 25, find dy/dx. b) Find an equntio

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Q: ders n = 0,1,2,3, and 4 about x = %3D X0, and then find th

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Q: Case 4: repeated quadratic factor (very hard!) 8dx • Example 1: r(r2+2)2

A: To evaluate: I=∫8 dxx(x2+2)2 Substitute x2+2=u⇒2x dx=du⇒dx=12xdu So, I=∫8 x(u2)du2x=4∫1x2u2du=4∫1(u-...

Q: ii. find the equation of the tangent line to f at x = a. (a) f(x)=3-4x, a=2. (b) ƒ(x)=x² +x, a = 2.

A: We have to determine the equation of tangent line 

Q: Example 19: (a) If x +y = 25, find dy/dx. (b) Find an equation of the tangent to the circle x +y = 2...

A: As asked we can find the necessary answers as below 

Q: This question has several parts that must be completed sequentially. If you skip a part of the quest...

A: NOTE: Refresh your page if you can't see any equations. . here we have 

Q: a . Use separation of variables to find the general implicit solution to the differential equation. ...

A: Answer: As per guidelines we can do only 1 question at a time so post other question separately , th...