2. A bushfire spreads with burning area according to the following function, A(t) = 160t – 40t² (in acres). What is the growth rate of the burning area, (the rate of change of the acreage that is burning with respect to time) when t = 1.5 hrs?

Q: n Σ=o(-1)n+1 (는) absolutely converges, conditionally converges or diverges. 12. Determine if

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. (-3)" (2n + 1) n = 0…

A: Solve the following

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A: Given query is to find the limit of the expression.

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Q: 9 =\n(VX ), find y' X43

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Q: Find the third derivative of the function f(x)=8x^7/2. Simplify so there are no negative or…

A: Given query is to find the derivative if the expression.

Q: Find the nth term of  (– 4 3 14 29 ) and (4, 5, 8, 13)

A: Sequence

Q: Let y = tan(3x + 6). Find the differential dy when x = 2 and dæ 0.2 Find the differential dy when x…

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Q: y= fix) 16 01 16 32 48 64

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Q: Use Newton's method to approximate a root of the equation 5x'+ 7x+2 =0 as follows. Let 1 = 3 be the…

A: For Newtons Method we have to calculate xn+1=xn-fxnf'xn  for n=1,2,3,.....

Q: Evaluate the following integral. 2x +5 dx - 2 Le 2x+5 dx = (Type an exact answer.) - 2

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Q: » / 13t – 41º + 4 dt = 6. (а) 1 - 5 Jū du: (b) dx = 4x3 (c)

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Q: 1 7. Determine by the ratio test if n- converges or diverges. п! -

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Q: Find the limit. lim (arctan(6t), e-4t In(t)

A: See the details solution in below

Q: Solve the initial value problem. dy + 9xy = 4x, y(0) = - 3 dx

A: This question is related to differential equations, we will solve it using given information.

Q: A car travels down a highway at 25 m/s. An observer stands 200 m from the highway. (a) How fast is…

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Q: A roctangular tonk uith a cauaro boco and a volumo of 2.016 e3 dimoncions of tho tank that hac 1o…

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Q: Use the Laws of Logarithms to expand the expression. 4x7 In (x + 3)8

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Q: Given the curve y = x' and the line y = 2 – x . M. Find the moment of R with respect to the x-axis…

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Q: If y = a + b/x , then the linear form of the following equation is In y = a + b y = a + b x y = a +…

A: Given query is to find the linear firm of the equation.

Q: Use the Laws of Logarithms to combine the expression. 3 In(2) + 5 In(x) - - In(x + 7)

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Q: Find the function F that satisfies the following differential equations and initial conditions.…

A: We will find the function.

Q: 1 Determine by the direct comparison test if Ln=1 2n+1 converges or diverges .

A: We have to find convergence test

Q: The linear approximation at z = 0 to sin(8x) is A + Bx where A is: %3D and where Bis:

A: Given : The linear approximation at x=0 to sin(8x) is Ax + B   To Find : Value of A and B

Q: Complete the table. (Use C for the constant of integration.) Original Integral Rewrite Integrate…

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Q: Express the integral as a limit of right endpoint Riemann sums. Do not evaluate the limit. 8 + x2 dx

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Q: | (6+xvF)dx

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Q: 1 11. Use the alternate series test to determine if E=1(-1)"+1, converges or diverges.

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Q: Find the following using the table below. 1 2 3 4 f(x) f'(2) g(x) 2 4 1 3 1 4 3 2 4 3 1 1 3 4 (x),6…

A: Given,

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A: A plane perpendicular to a vector and through a point In vector form, a plane's equation is…

Q: Evaluate the integral using integration by parts. 5x dx= %xp

A: solving by integration by parts

Q: dx x3 4. Зх2 + dy y+1 -8(у + 1) %3D 0

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Q: Calculate 5x*dx, given the following. Pdx= 93 (Type an integer or a simplified fraction.)

A: We need to evaluate integral.

Q: a multi-part problem. If F(t) = + 4t² 412 – t+ 9, find F'(t). 3 This is F'(t) = |

A: Given query is to find the derivative of the expression.

Q: 4 -4 -3 -2 -1 1 2 3 4 5 -2 -3 -4 -5 The plot above is created with the parametric equations Sæ(t)…

A: From the graph we can see that in horizontal direction the maximum value is 6 so, a=6. From the…

Q: 2. Find the limit or show that it does not exist: lim (2,y)→(0,0) 2x6 + y?

A: We have to find limit

Q: A region is enclosed by the equations below. y = 8, 3 x = 1 z + 4' Find the volume of the solid…

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Q: f(x) dx

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Q: Let F(x) = f(f(x)) and G(x) = (F(x)). You also know that f(7) = 3, f(3) = 3, f'(3) = 3, f'(7) = 10…

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Q: plve the equation: u = a u, Uxx 0 0 (x, 0) = f(x), u(0,t) = u(L, t) = 0

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Q: The sum 5 x) dx + -1, fx) dx can be written as a single integral in the form f(x) dx Determine a and…

A: Given query is to find the single integral fir the expression.

Q: Sketch the region that is bounded by y = 8 - x² and y = 2 – x. Then, find the coordinates of the…

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Q: 5. Determine the horizontal asymptote. x³ +2x² -6 а. У- x? x* +3x° +x² –7 b. y: x* - 3x³ +8

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Q: A graph of y = y = f'(x) over the interval [ - 4, 4]. f(x) is shown. In the same coordinate system,…

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Q: Express the integrand as a sum of partial fractions and evaluate the integral. 9 y dy 6 У - 2у - 3…

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Q: Find polar coordinates to represent (-2, -2) with r >0 and 0 <0< 2T.

A: Cartesian to polar conversion (x,y)→(r,θ) where r=x2+y2 θ=tan-1yx

Q: answer

A: We will find the particular solution.

Q: Given the two polar curves, r = 2 sin 0 and r =1- cos? 0, find the following. A) Sketch the graph of…

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