t or points for each ase portrait on this page. dx = 2x – 2y – 4 and- = x+ 4y +3 dt dt GURE 6.1.

Q: 240 2 s7 17(s-1)8

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Q: 4. sec 4x tan 4x dx

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Q: 8. Given 8. dx = 16 and f(x) C g(x) dx = -5, evaluate the following. %3D (a) [F(x) + g(x)] dx (b)…

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

Q: 4. Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

A: We have to calculate indefinite integral ∫{(3x2+6) /(x3+6x) }dx Let us say  I = ∫ {(3x2+6) /(x3+6x)}…

Q: Evaluate 2x(x2 + 2)*dx

A: First I have used  a substitution and made integral easy and then solved it.This is the process.

Q: Use De Moivre's theorem to solve for z given z = 3 – 2i. Write your answers in rectangular form. Use…

A: Given: z5 = 3-2iz   = 3-2i15                                     1-------------------De-Moivre's…

Q: Q2) Convert the polar function r tan20 to cartesian. %3D

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Q: Evaluate the integral. HINT: [Use a shortcut.] e 8x - 1 dx

A: Using substitution ,

Q: I. Find the antiderivatives of the following functions using the substitution rule. Write your…

A: According to our guidelines we can answer only one question or 3 subparts of a question, other…

Q: The concentration of a drug in a patient's bloodstream, measured in mg/L, t minutes after being…

A: We need to find average concentration.

Q: Determine the value of 3A+1OB if 14x2 + 33x + 9 Cx + B %3D (x – 1)(x+ 1)2 x - 1 (x + 1)2 Answer:

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Q: The series 1 k ln k k=2 converges. Choose an option: ()Real ()False

A: Integral Test : Suppose that f(x) is a continuous , positive and decreasing function on the interval…

Q: Differentiate the following functions: i. v = 15/7(12/7+ 3t) (2x – 9) f(x) = x + 4 ii. iii. y =…

A: We can solve this as follows:

Q: | (2x - y) dx + (x + 9y) dy. Ic Evaluate C: x-axis from (0, 0) to (0, -9) and (0, -9) to (5, -9)

A: We can solve as follows

Q: Find the net signed area between the graph of the function f(r) = -x-4 and the x-axis over the…

A: To find the area between the line and x axis.

Q: Problem: At time t = 0 there are 10 person in a community of 1,000 people who has the flu.…

A: Required formula:  Logistic growth model: Nt=K1+K-N0N0e-rt Where,  r = Exponential growth rate…

Q: Find the position function s(t) given acceleration a(t) = 2t if v(2) = 0 and s(2)=1.

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Q: 64 8 If f is continuous and f(x) dx = 18, find xf(x²) dx.

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Q: (c) in the tank to a height of 1 m above its top. Give a definite integral that computes the total…

A: answer is in next step

Q: The discontinuities of the function f(x) =D 4x-9 are: x²-2x-15 Select one: O 5,3 -5, -3 -5,3 O 5,-3

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Q: Find the area of the blue region. It is the area under the curve. 8 y = 3 x + 1 4 y =7– x 2 4 6 8.

A: This question can be solved using the concept of area under curve.

Q: Lnx sin 2x dx

A: Use the properties of definite integral and solve the question.

Q: Use Newton's method to approximate a root of the equation +x + 4 =0 as follows. Let 1 = - 1 be the…

A: The given equation,    x3+x+4=0

Q: 9- If a person with O'Micron virus coughs, It will spread the virus in a spherical form, determine…

A:

Q: (6) At the start, an experiment records 1 gram of bacterial culture, and the culture's weight is…

A:

Q: 7- Use the limit definition to compute f' (x) and find equation of the tangent line at r = 3. f (z)…

A: topic - derivative of a function using limits

Q: x³y' – y? – x²y = 0

A: We have to integrate the above expression

Q: 10 Consider the function f(x) Let F(r) be the antiderivative of f(z) with F(1) - 0. Then F(z)

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Q: Determine whether the integral is improper (x-4) -'dx A Improper B Not improper

A: Given data÷

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

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Q: y = 2 ||

A: We have to find the derivative of the function y = 1-x2ex2

Q: d²y Find the second derivative, dx2 a. x = t² + 1 and y = t³ t2 b. x = 2 · + 2 and y = sin(t + 1)

A: This question can be solved using the concept of second order derivative.

Q: Use an appropriate definition to prove the following limits. x³ – 16x* = 1 I+0 r°+ 4x² x +2 V9x2 + 4…

A: This is a problem of limit . Based on the formula and concept we will answer the question.

Q: dy + 2(t + 1)y? = 0 dt b) Solve ;y(0) 8

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Q: Dix) is the price, in dollars per unit, that consumers are willing to pay for x units of an item,…

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Q: A 4-pound weight stretches a spring 2 feet. The weight is released from rest 20 inches above the…

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Q: In constructing an open rectangular box from 48 ftf of material, what dimensions will result in a…

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Q: 4. Below is a photograph of the Eiffel Tower in France. On it there is a red parabola and purple…

A: the pair of equations can be x2=-8(y+30)      ... Parabolax236-y2169=1    ........ Hyperbola

Q: Calculate the derivative (implicit derivative): y + 19xy = Cos(7x – 5y) %3D |

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Q: 16. Interpretations of Integrals Determine the position function, s(t), of an object if the…

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Q: Find the arc length L of the graph of r(t). 1 rt) - i+t j+Vor k, 2<1<5 2 <t< 5

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Q: Find the arc length of the graph of r(t) = ev2ti+ e¯v2tj+ 2tk, 0<t< v2 In 5 NOTE: Enter the exact…

A: Let's find.

Q: Evaluate the limit, using L'HÔpital's Rule if necessary. sin 3x 1. lim x→0 tan 8x In x5 2. lim x7 –…

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Q: Evaluate the integral. 3 if -2 < x< 0 f(x) dx where f(x) | 4 – x² if 0 <x< 3

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Q: 2x + 6 Consider the function f(x) = . For this function there are two important intervals: (– ∞, A)…

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Q: Q15. Find the Maclaurin series representation for each of the following functions. For each series:…

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Q: f(x,y) = 25 - x^2 - y^2 at the point P(3, 4). Use the Partial Limit Dervatives

A: Given problem:- f(x,y) = 25 - x2 - y2 at the point P(3, 4). Use the Partial Limit Derivatives

Q: The total sales of a company (in millions of dollars) t months from now are given by S(t) = 0.02t° +…

A: This question can be solved using the concept of interpretation of a function and its derivative at…

Q: Evaluate the indefinite integral. x2 dx 0.2x3 + 2.7 + 2.7

A: topic - indefinite integral

Q: Find Duf at P. f(x, y, z) = 6x°y°z*; P(1, – 2, 1); u = i %3D Duf = i

A: