Find the total income produced by a continuous income stream in the first 5 years if the rate of flow is given by the following​ function, where t is time in years. ​f(t)=2500

Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Show…

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Q: is an improper integrat. dr A True B False

A: To check : The statement "∫-121x2dx is an improper integral." is True or False ?

Q: Use Newton's method to approximate the indicated root of the equation correct to six decimal place…

A: Here, let the given function be: f(x)=x2+ex-9⇒f'(x)=2x+ex Next,…

Q: Find the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) (x² + lim x + 5…

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Q: sinh(3 In(a)) = (A) - (B) a³ – (C) 을 + 3a - (D) – 11 -18 -13 - -

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Q: Use series to evaluate lim 3x(e -2/x - 1). lim 3x (e -2/* - 1) -O X00 (Simplify your answer.)

A: We can use series to find the limit as below.

Q: 1.

A: Given,  ∫1+∞1xdx

Q: Write the sum in sigma notation. 4 3 1. +- 6. 6. 26 | ... 8. 10 12 52 3+n Ce tn an= fram T 26 26 3+n…

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Q: Find the equation of the tangent line to the curve g(x) = 5x2 - 6x +2 at the point (1, 1).

A: Use equation of  tangent line

Q: Solve the following differential equations of dy x'y-x'. = y' cos(x). dx

A: Use substitution to reduce the differential equation into linear differential equation.

Q: Use implicit differentiation to find an equation of the tangent line to the graph of the equation at…

A: tan-1(xy)=sin-1(9x+9y)differentiating w.r.t. x;   11+(xy)2ddx(xy)=11-81(x+y)2ddx(9x+9y)…

Q: sečxdx ztanx 5-9tarix ansi sin 2

A: Solution is done in step 2

Q: g=ズ, a find dy dx %3D

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Q: f (x) = x² + 1

A: Given :

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Q: dy x(2lnx+1) dx sin y + y cos y

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Q: A rectangular storage container without a lid is to have a volume of 10 m. The length of its base is…

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Q: f(x) = x-5/x+8 find the domain

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Q: Verity Gauss' theorem for the vector feld f (x,y, z)= (y,x,2) on the surface of the sechere with…

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Q: dy = 2 – y dx Find the correct direction field for the differential equation ノー\\ ババーと

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Q: III. Do as indicated showing the details of your work. Show your complete solution on the space…

A: We need to evaluate definite integral.

Q: 4) Value of gold bar is V=2500 evt and interest rate r=0.07 please find the optimal value of t to…

A: We have to find the optimal value of t to maximize the present value.

Q: Solve the following given differential equation  using the method of indeterminate coefficients

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Q: Consider the integral cot(0) · In(6 sin(@)) d0: This can be transformed into a basic integral by…

A: We have to find the integral.

Q: 19 Suppose that Ts (x) centered at 2 for f(x) is gien by. Is (X=3+5Cx-2)+8(x-2)²+2G-2)°+(x-2) (3)…

A: T5(x) centered at 2 for f(x) is given by,T5(x)=3+5(x-2)+8(x-2)2+2(x-2)3+(x-2)5

Q: sin(3x) dx 1+cos²(3x)

A: The given integral is Sin(3x)/[1+cos2(3x)].

Q: 3. Find the equation of the plane tangent to xyz + x² – 2y² +z' =14 at (5,–2,3)

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Q: Find the distance from the point to the plane. (5,7,6), 10y +z= 0 The distance is

A: We can find the distance as below.

Q: Differentiate. 9. y = e

A: As per the guidelines I am sharing the solution to the first question.

Q: Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding…

A: The solution is given below.

Q: Find the area bounded by the graphs of the indicated equations over the given interval.   y=−4x+12​;…

A: Given query is to find the are of the region.

Q: Solve the initial value problem y' = xe ; y(-1) = 3

A: We can solve the initial value problem as below.

Q: ​(A) Find the average value of the function over the indicated interval.   ​(B) Graph the function…

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Q: 5. Write an expression equal to - log. (c) · log (b) |using exactly one log. (hint: the base of the…

A: To answer the given question of logarithms.

Q: Evaluate the integral * (2* – 8)* dz, 33 by making the appropriate substitution: u = 33 NOTE: Your…

A: We need to evaluate the following integral I = ∫x3x4-833dx                         ..........1…

Q: Problem 3.4 Parameterize the following surface. Then, integrate the given function over the…

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Q: Solve the initial value problem. 1 u'(x) = – 2; u(0) = 1 x2+1

A: Explanation of the answer is as follows

Q: Н.W (1) Solve the following differential equations of dy 2 - - (1+y*)e* dx 1- ye** . dy = dx; x+y…

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Q: The acceleration function (in m/s2) and the initial velocity v(0) (in m/s) are given for a particle…

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Q: x²+x dx x2+1

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Q: -3

A: topic- definite integral

Q: 5. The denominator of a fraction is four less than the numerator. If the denominator is doubled and…

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Q: Find the divergence of the vector field F. F(x, y) = 8xe*i – 7x²y²j |

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Q: Identify the type of surface represented by the given equation. 2 O Parabolic cylinder O Ellipsoid O…

A: We know that x-h2a2+y-k2b2=1 is the ellipse standard equationGivenx27+y22=2Divide 2 on both…

Q: Find an equation of the tangent plane to R(u, v) = (e" sin u , e" cos u , e¯º ) at the point where u…

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Q: + 3x² 4)dx

A: Given query is to find the value of the integral.

Q: Calculate s f(x, y, z) dS for the given surface and function. D(r, 0) = (r cos(0), r sin(0), 0), 0<r…

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Q: Find the Maclaurin series for the function. (Use the table of power series for elementary…

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Q: uestion 19 Describe the largest set S on which it is correct to say that f is continuous. f(x, y, z)…

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Q: Solve the differential equation for general solution y' = 2x - xy; y = 5 when x = 0 %3D O y =…

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