Find the solution r(t) of the differential equation with the given initial condition: r(t) = r' (t) = (sin 9t, sin 9t, 3t), r(0) = (8,7,4) > A " "

Q: Find the solution of the following initial value problem. g'(x) = 4×x(׳ − 1); 9(1) = 1 The solution…

A: Step 1:​g′(x)=4x(x3−41​);g(1)=1g′(x)=4(x4−4x​)​Step 2:​g′(x)=4(x4−4x​)Integrate both sides with…

Q: 87. Suppose lim an = oo and an+1≥ an > 0 for all n ≥ 1. Which of the following statements must be…

A: Step 1:

Q: 9. The slope of the line tangent to the graph of y = xe* at x = ln 2 is (A) 2 In 2 (B) 2 In 2+2 (C)…

A: The slope of the tangent line to a curve at any point is equivalent to the derivative of the…

Q: Evaluate the limit, using L'Hôpital's Rule if necessary

A: As we directly applies the limit the it results in the fraction 0/0. So we use L'Hôpital's rule.To…

Q: do both parts of the problem , following each of the different directions properly and correctly,…

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Q: 1. a) show that the lines [x, y, z] and x = y-7/-8=z-1/2 lie on the plane 2x + y + 3z - 10=0 b) find…

A: a) To show that the lines [x,y,z] and 1x​=−8y−7​=2z−1​ lie on the plane 2x+y+3z−10=0, we can check…

Q: dy 13. Let y = f(x) be the solution to the differential equation = x + 2y with initial condition…

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Q: Evaluate the surface integral F(x, y, z) =xi+yj+6k F. ds for the given vector field F and the…

A: Step 1:Step 2: Step 3: Step 4:

Q: The total accumulated costs C(t) and revenues R(t) (in thousands of dollars), respectively, for a…

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Q: Expand the given logarithmic expression. Assume all variable expressions represent positive real…

A: Step 1: Step 2: Step 3: Step 4:

Q: Find Lim- 3x-6 x-2 x²-4' A. ∞o C. 34 Select one: ос O B О А B. D. +13 010

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Q: Evaluate the definite integral where the upper limit =6and the lower limit = 3and f(x)=(10x^2+6)/…

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Q: Solve the initial-value problem by separation of variables. y' - xe = 7e", y(2) = 0 y(x) = =

A: Step 1: Step 2: Step 3: Step 4:

Q: Given f(x, y) = 6x7 cos (y³), find fxy(x, y) = fyy(x, y) =

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Q: Use the formula for the sum of a geometric series to find the sum or state that the series diverges…

A: Step 1:​Given a series here:n=4∑∞​14n5n​​Step 2:​S=n=4∑∞​14n5n​S=14454​+14555​+14656​+⋯∞Using the…

Q: Three different forces act on an object. They are: F₁ = F₂ = F¾³ = Find the net force Fnet on the…

A: Net force on the object…

Q: Please use L'Hospital's rule or the method pasted in the second image to solve this pro

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Q: a. A rectangular pen is built with one side against a barn. If 1000 m of fencing are used for the…

A: Step 1:Step 2:Step 3:Step 4:Step 5:

Q: (a) Find a power series representation for f(x) = In(1 + x). f(x) = 8 n = 1 ((-1)"-1" ( − 1 ) n - 1…

A: Step 1: Step 2: Step 3: Step 4:

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Q: see pic for problem please do correctly

A: The definite integral ∫ab​g(x)dx is also defined as the area under the curve and it can sometimes be…

Q: 82. The derivative of the function ƒ is given by f'(x) = e¯*cos(x2), for all real numbers x. What is…

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Q: Calculate √3 – i. Give your answer in a + bi form. - Give the solution with smallest positive angle.

A: Let z=a+bi, where a,b∈R. Consider z2=−3−i    ⟹(a+bi)2=−3−i    ⟹(a2−b2)+i(2ab)=−3−i Comparing Real…

Q: Write the equation of the trigonometric graph. Use a positive coefficient on cosine for this…

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the interval of convergence for the power series. The series is convergent for <x< n=1 Ignore…

A: Step 1:​Given a series here:S=n=1∑∞​n!9n(x−1)n​​Step 2:​Using the Ratio Test:For the Ratio Test, we…

Q: I need help on my homework

A: Step 1: Define the variables: x: Length of the square carpets in feet. Step 2: Determine the…

Q: 2. Evaluate the given integral by changing to polar coordinates. SdA, where D is the region in the…

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Q: [S24] 7.Applications of Integra X a 침하하 + C gum…

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A: In order to find the consumer surplus (CS) and producer surplus (PS), we first need to find the…

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

A: The objective of this question is to find the average weekly sales for the first 9 weeks after…

Q: Let f (x) = ex- 1 for 0 ≤ x ≤ 9. Find the area A of the region between the graph of f and the x axis…

A: Given that, f(x)=e−x−1   for   0≤x≤9 We know that, the area of the region between the graph of f and…

Q: Please don't provide handwritten solution .....

A: To find the exact answer, let's first compute the double integral over the region ( R ) defined by…

Q: Use geometry (not Riemann sums) to evaluate the following definite integral. Sketch a graph of the…

A: Given that ∫06​f(x) dx  where f(x)={53x−1​ if x≤2 if x&gt;2​ The graph of f(x) is B For 0≤x≤2 f(x)=5…

Q: Given the vector u = (-2, −4), find the magnitude and angle in which the vector points (measured…

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Q: Please find the volume for the attached question.

A: Step 1:​Region is bounded by f(x)=cosx, the line y=1, and the line x=2π​Rotating the region about…

Q: Evaluate the outward flux of the vector field F(x,y,z) = (x, -y, z) across the surface S: x2 +y2 =4,…

A: The approach used in the solution is to first parameterize the surface S using cylindrical…

Q: QUESTION 10 Consider the infinite series below. n=1 [In(n)-In(n+1)] i. List the first 3 terms s S 1…

A: Step 1:Step 2:Step 3:Step 4:

Q: Do part C only without PMI.

A: Step 1: Part C. Without using the principle of mathematical induction (PMI). Given the…

Q: Let a = n -n+3 7n2+1 i. Evaluate lim a 818 If the limit does not exist, then write DNE 11 ii. Do the…

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Q: Given log A=3.227 and log,B=0.201, evaluate log AB. A. 3.026 OB. 16.055 O C. 0.649 OD. 3.428

A: The objective of this question is to find the value of log AB given the values of log A and log B.

Q: Determine the intervals on which the following function is concave up or concave down. Identify any…

A: The given function is:f(x)=3x4−3x3+9 First, find the points of inflection. Recall that the function…

Q: Find the inverse of the function. f(x)=7x A. f(x)=log 7x OB. f(x)=logx7 OC. f(x)= In (7x) OD. f(x)=x

A: Step 1:To find the inverse function, Let f(x) = yThen, you can rewrite the function as y=7x Step…

Q: Write the complex

A: To write a complex number in polar form, we need to find the modulus (r) and the argument (θ), also…

Q: Find all the values of x for which the given series converges. Use interval notation with exact…

A: Step 1:​Given a series here:S=n=1∑∞​7n(n2+3)(−1)nxn​​Step 2:​Using the Ratio Test:For the Ratio…

Q: When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.02 cm/min.…

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Q: on 1 Given f(x, y) = 2x-3xy³ + 4y³, find faz(x, y) = fzy(x, y) = Question Help: Video Submit…

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Q: 5. A swimming pool is circular with a 30-ft diameter. The depth is constant along east-west lines…

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Q: Determine the following indefinite integral. S7x+3) (7x+3)(1-x) dx Істx+3: (7x+3)(1-x) dx =

A: Step 1: Step 2: Step 3: Step 4:

Q: 2. R 86. Let R be the region in the first quadrant bounded by the graphs of y = 4 cos π.χ and y =…

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Q: The radius of a right circular cone is increasing at a rate of 1.9 in/s while its height is…

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