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Q: Given that the acceleration vector is a(t)= the initial velocity is v(0)=, and the initial position…

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Q: Analyze the following problems then solve. Show necessary solutions. 1. A three-sided fence is to be…

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Q: The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing (in…

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Q: f(x) = 10/10x³ + 6x*

A: Follow the procedure given below.

Q: Xingqiu has 420 feet of fencing material and uses it to start a kernel by building 5 identical…

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Q: The result of the following double integral is 2 2 у ST (6 x² y - 5 e)dxdy= ? 0. -2 y 909 -20e? +…

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Q: 25) Show that the curve with parametric equations x = tcos(t) , y = tsin(t), lz = t ies on the cone…

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Q: x =r' +1, y=r -t = t° a) Find dy/dx Show all your work.

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Q: 1 a) r(t) = ( In(7t), Vi + 4, V17 - t b) r(t) = ( Vi – 3, sin(81), ² ) t 3t 1/3 c) r(t) = /2 – 64 -

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Q: 1 4 9 16 25 0, 2'3'4' - 5' 6 an Enter your answer here Or write it out and upload: Please select…

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan 2, (1, 0,…

A: Given

Q: A company determines that its weekly online sales, S(t), in hundreds of dollars, t weeks after…

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Q: TC Find all solutions of the equation in the interval 0, 2n). cosx V 1+sinx Write your answer(s) in…

A: We know, sin2x+cos2x=1 for all real x sinx=0 implies x=nπ, for all integer n sinx=1 implies…

Q: (b) C x*y dx dy a, О а. 3/8 ОБ. 28/3 O b. Ос. 7/2 O d. 27/2

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Q: 5. harmonic oscillator is The initial value problem which describes the motion of a certain undamped…

A: We have to solve the problem and find the amplitude and period.

Q: Given the triangle below, find the angle 0. 4 Give your answer in degrees rounded to the nearest…

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Q: Find the radius of convergence, R, of the series. R = Find the interval, I, of convergence of the…

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Q: EXERCISES 4:Find the tangent line at the given point 1. Xy = -4, (2, –2)

A: Equation of tangent line of a curve y=f(x) at P(a,b) is given by, y-b=dydx(a,b)(x-a) Implicit…

Q: if x1 -1 For what value(s) of x is the function f(x) = x+1 (x² +x+1 NOT continuous? A. x 1 Select…

A: We have to choose correct option

Q: If the function y = A sin z + B cos a satisfies the differential equation y" + y – 2y = sin z for…

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Q: | sin rdr 3.

A: Here we have to solve the given integration by using integration by parts.

Q: Given the differential equation y' = 4y2 + 7 Take the Implicit Derivative of this function 2 times…

A: Consider the equation  y'=4y2+7

Q: Sketch the graph and show all relative extrema and inflection points. y = 12x - x3

A: Topic:- function and application of derivatives

Q: O b. 5/6

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Q: If we are integrating by parts and we have u = x² and dv = cos xdx, what are du and v?

A: given u=x2 and dv=cosxdx

Q: Differentiate the function. s(t) = 2t – 4(2t4 + 3)3 %3D

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Q: (a) Use differentiation to find a power series representation for fx) = (3 + x)2" Σ 00 n = 0 What is…

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Q: rapidly at Po, Then find the derivatives of the functions in these directions f(x, y) = x²y + e" sin…

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Q: b. ydy 1

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Q: n y = -5e0.

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Q: Evaluate the integral. (11 - t)/e dt

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Q: /2 x cos xdx

A: The integration of the integral is x2cosx, Iimit from 0 to pi/2.

Q: A scientist has discovered a new strain of bacteria. The bacteria culture initially contained 1,000…

A: Given problem:- A scientist has discovered a new strain of bacteria. The bacteria culture initially…

Q: Solve the exponential equation algebraically. Approximate the result to three decimal places. (Enter…

A: The given equation is: 5x2=61-x   As we know that; logaxb=b·logax ; x≥0

Q: A small metal bar, whose initial temperature was 20° C, is dropped into a large container of boiling…

A: Newton law of cooling : dT/dt = k(T - Ta) and T = Cekt + Ta Boiling Temperature of water is 100° C…

Q: f(x) = 12x + x - x°, g(x) = 0 ... The area is (Type an integer or a simplified fraction)

A: Given query is to find the area of the shades region.

Q: y" + 6y' + 8.96y = 0 y" + 2ny' + 7²y = 0 y" + 4.5y' = 0

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Q: A -r = COs(U) TC Ex: Replace P(r, 0) → P(x, y) and graph. rcos (0-) = 3. (H.W %3D

A: The given equation is: rcosθ-π3=3

Q: Determine all critical points for the function. f(x) = (x - 4)³

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Q: Hiwin If Z=R Cxxy)and u=x-y V=x-y show that %3D

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Q: fxcos 73 x cos 4xcos 2xdx π ſcos(nx)dx 75 ーπ 77 xsin(nx)dx

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Q: In a certain bacteria culture the rate of increase in a number of bacteria proportional to the…

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Q: Given the differential equation y' = x2 + y? Take the Implicit Derivative of this function 2 times…

A: Given, the differential equation                                    y'=x2+y2 then take the implicit…

Q: 3. Suppose f(x) dx = 8 , f (x) dx = -2, g(x) dx = 3 Evaluate the following integrals: a) 3f(x) dx =…

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Q: Differentiate the function. 5V1 - x y = y' =

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Q: 2. Find the derivative. Simplify where possible. (b) у %3 tanh-1(г3)

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Q: The integral 5x – y dA =49 if R R={(x,y): 2<x< 4, 5< y < 6 } Select one: O True O False

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Q: Evaluate the integral. 5 cosh(t) dt

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Q: y=3 13 x-3-y 3

A: V = 2π∫ yf(y)dy f(y) = 3 -(3-y2) f(y) = y2 +3 -3 now limit from 0 to 3  V = 2π∫03 yf(y)dy V = 2π∫03…

Q: 3. As the biologist for a certain crocodile farm, you know that its carrying capacity is 20,000…

A: Let's find.