Given z = x + y6, x = ue", y = ve". Find (Use symbolic notation and fractions where needed.) du дz and using Chain Rule II. du

Q: Find the area of the region bounded by the curve y = f(x) = x³ - 4x + 1 and the tangent line to the…

A: First we need to find the equation of tangent line at point (-1,4)

Q: Estimate the area under the graph of F(X)=X2 +6X+11  over the interval [0,8] using four…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the derivative of y = x²ª dy/dx =

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Q: Use the graph of the derivative f' of a continuous function f is shown. (Assume f' continues to ∞.)…

A: Use the graph of the derivative f'(x) of a continuous function f is shown .

Q: ΣΕ k=0

A: Given query is to find series converges or diverges.

Q: Create a third and fourth degree polynomial of the form p(x)=ax^3and p(x)=ax^4. Choose a to be any…

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Q: 1. Solve the unknown. Show your neat and correct solution (if applicable). 1. If y=x²-5x³ + 3x² - 2x…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: class of fourth graders walks to a park on a field trip. The function y = f(t) graphed below gives…

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Q: Consider the following function. ∞ f(x) = Σ n=0 a. Find the full power series of f(x) centered at x…

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Q: The engine in a tank has a power curve approximated by x² 40x Y + 30 25000 46 where x is the RPM and…

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Q: In order to approximate the area under f(x) = e²² from x = 5 to x = 22 using 20 rectangles and the…

A: We need to approximate the area under f(x)=e-x2 from x=5 to x=22. So, here, a=5 and b=22.

Q: In Seattle on September 30, the temperature (in °F) thours after midnight was given by the function…

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Q: Find exactly the vector oppositely directed to v = (3) and half the length of v.

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Q: What is the general solution to the differential equation A B C y = arcsin (esin 2) + C y =…

A: The given differential equation is:dydx=cos(x) esin xcos(y)

Q: A circle is growing, its radius increasing by 3 mm per second. Find the rate at which the area is…

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Q: Find the values of x for which the series converges. (Enter your answer using interval notation.) 8…

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Q: Write a polynomial f(x) that satisfies the given conditions. Polynomial of lowest degree with zeros…

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Q: 4. (a) Show that the function f(x) = Σ Σ (b) Show that f(x) = e*. m! is a solution of the…

A: (a) The given data is: Show that the function fx=∑n=0∞xnn!  is a solution of differential equation…

Q: Find the volume of the solid bounded by the paraboloids z=-6+2x² + 2y² and z=8-2x² - 2y². Round your…

A: Given that , z=-6+2x2+2y2 and z=8-2x2-2y2 find the volume of the solid.

Q: Revenue and Marginal Revenue Functions) Suppose the unit price p in dostars for a uantity x demanded…

A: We need to find out the revenue function, the marginal revenue function and also the marginal…

Q: Find an equation of the line tangent to the curve defined by a³ + 5xy + y = 7 at the point (1, 1). Y

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Q: Find the dimensions of the rectangle of the greatest possible area that can be inscribed in the…

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Q: Suppose the point (4, -7) is on the graph of y = f(x). Find the corresponding point on the following…

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Q: Find f'(x) if f(x) = x cos (x²) dy inddx _y=²csc(√x) b) Find

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Q: The form of the partial fraction decomposition of a rational function is given below. A = B = C =…

A: Given : A = 4  B = -3 C = 0

Q: Consider the function f(x, y) = 2ye7 and the region R = {(x, y)|0 ≤ x ≤ 1, 0 ≤ y ≤ x³}. (a) Find the…

A: The solution is shown below-

Q: Model the data using an exponential function f(x) = Abx. x 0 1 2 f(x) 600 1,200 2,400 f(x) =

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Q: Problem 3. Find all points (x, y) on the graph of x² + y²/3 = 8 (see diagram) where lines tangent to…

A: To find the points where the tangent line has a slope of -1, we need to take the derivative of the…

Q: 2. [x5√x³ + 1 dx

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Q: Consider the following function. f(x) = ln(5 + 7x) a. Find the full power series of f(x) centered at…

A: The solution is shown below-

Q: A company produces very unusual CD's for which the variable cost is $12 per CD and the fixed costs…

A: x is the number of CDs produced The variable cost is $12 per CD and the fixed costs are $40,000.…

Q: here are 8 toll of carpet. Each roll of carpet is 6 yards long. How long are the 8 rolls of carpet…

A: Given, total no. of carpet  rolls= 8 units Length of each roll = 6yards

Q: R/4 4. ST¹ x sin 2x dx

A: To Find : ∫0π4xsin2x dx

Q: 10. f x¹ In x dx

A: To find the integration of ln(x).x^n

Q: Your monthly profit (in dollars) from selling magazines is given by P = 6x + 6x + 10 , where…

A: The solution is shown below-

Q: In the first six months of an outbreak in 2014, the total number of reported cases was increasing at…

A: Given model:- Ct=Aert⇒Ct=Number of cases t months after April 2014⇒A=initial number of cases⇒r=rate…

Q: Evaluate the integral. 3x/4 S x/4 3 csc 0 cot 0 de

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Q: Let f(x) xAr = Use logarithmic differentiation to determine the derivative. f'(x) =

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Q: Differentiate the following function: f' (t) = f(t) = √t – .

A: f(t)=t6-1t6d dt(tn)=ntn-1we know ba=(b)1a

Q: Determine whether the series is convergent or divergent by expressing 5, as a telescoping sum (as in…

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Q: Hale College predicts that in 18 years it will take $200,000 to attend the college for four years.…

A: Given

Q: Consider the region bounded by the graph of f(x)= 3 1 + x² and the x-axis between x = 0 and x = 1.

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Q: Show that these planes intersect in a point for all values of a, b, and c. x + y + z = a x + 2y +…

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Q: 7. Find d when 5x² +3x³y -3y³ = 44. Write an equation of the tangent line at the point (2,2).

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Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by…

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Q: evaluate using integration by parts

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Q: For each function a) find the critical points/numbers, b) intervals of increasing/decreasing, c)…

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Q: Below is a graph of two curves: x = y³ - 3y (the S-shaped one in blue) and x = 5-y (in red). Which…

A: area

Q: Consider the function f(x) = 3x³ - 4x on the interval [-3, 3]. Find the average or mean slope of the…

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Q: Consider the following. g(x) = 3x² + 39x11; g(x) = 193 With the function indicate whether an input…

A: Here is the solution: