Consider the function F(x) = [*__cos(1²) dt. (a) Compute F(-√√T).

Q: Given y = f(u) and u = g(x), find - (3) ² y=9u-5, u= dy dx = f'(g(x))g'(x).

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Q: 1 7. Ση=0 (2n+1)!

A: The given series is

Q: √(x ³ ex² + 4x + ex¹ +4x) dx.

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

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Q: Find for y=cos ²(9xt-8). dy dt dy dt

A: )   Is givenWe want to find the derivative

Q: Find the critical numbers and the open intervals on which the function is increasing or decreasing.…

A: The objective of this question is to find the critical numbers and the open intervals on which the…

Q: Suppose value of [ f(x)dx 2 f(x)dx. f(x) dx = -1, [**f(x)dx = 4 and [ f(x)dx = 2. Find the

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Q: Find y as a function of a if y(1)9, y'(1) = -5. y = x²y" - 15xy' + 64y = x²,

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Q: Find the indicated term of the binomial expansion. (√2₁² +1³); second term 3 u

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Q: Let g(z) = √√23 Determine the most general antiderivative of 9. | √dz = [

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Q: The system of first order differential equations y₁ = 5y₁ + 1y2 y2 = −4y₁ + 1y2 where y₁ (0) = 4, y2…

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Q: Let A and B be the following matrices. Perform the following operations: -6A A+ 3B: 2A + 4B A 9. 5…

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Q: Consider the indefinite integral Then the integrand has partial fractions decomposition a b cx + d…

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Q: 6. Find the equation of the line tangent to the following functions ate the given points. a. y = x²…

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Q: lim n→∞ (1 + 1/2 ) ² = 2n

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Q: For answer in part "E", is the answer 1/2 ln| sqrt(x^2+4/x^2) - 2/x |+C or 1/2 ln| sqrt(x^2+4) / x^2…

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Q: The cost for producing a thousand widgets is given by C(x) = 0.06x4 - 2x³ + 14x² + 400x, 0 ≤ x ≤ 60.…

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Q: The system of first order differential equations y₁ = 5y₁ + 1y2 y₂ = −4y₁ + 1y2 where y₁ (0)= 4, y2…

A: The objective of the question is to verify if the given functions y1(t) = (4 - t)e^(3t) and y2(t) =…

Q: Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed, and…

A: Here

Q: Given f is concave down and ƒ (4) = −2 and f1 (4) = 3. What is the estimate for = 4? Is it an…

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Q: Find the limit of f(x) = lim f(x) = -5 9√x+x 3x-9 X→∞ (Simplify your answer.) as x approaches co.

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Q: a 16. If there are initially 1000 bacteria in à culture, and the number of bacteria double each…

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Q: Stoite the Fundamental Theorem of Calculus?

A: we need to write down the fundamental theorem of calculus.

Q: The graph of a one-to-one function f is given. Draw the graph of the inverse function f¹. For…

A: The graph of a​ one-to-one function  is given. To draw the graphof the inverse function .

Q: The function f(x)=x^3 - 3x^2 - 9x D. Where is the function f(x) concave up or down? E. What are…

A: The given function is

Q: 1 e e 5. If A-), then ¹-(3) = eª = 01 0 e

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Q: S dx x+7 2x-3

A: To solve the following integral.

Q: Consider the triangle below. Click on the picture to see it more clearly. If c = 4, the angle C =…

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Q: Let y = f(x). Begin by finding the derivative of f(x) = -x³ + 6x² - 3. 3 F'(x) = (x³ + 6x² − 3) d dx…

A: The objective of the question is to find the second derivative of the function f(x) = -x^3 + 6x^2 -…

Q: d. f(x) = 2 f(x)=√x e. f. f(t) = g. √√t ² f(u)= ut + u² + ¹ น

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Q: Consider the triangle below. Click on the picture to see it more clearly. If a = 8, the angle C =…

A: The given triangle has measures .The aim is to find the remaining meausres .

Q: Question Details Given VxF= 2yj, what can we say about the vector field F? (Select all that apply.)…

A: We have to use the concept of curl of vector field

Q: Find the cube roots of 125i. (Enter your answers as a comma separated list.) Sketch these roots in…

A: The given complex number is By De Morive's theorem The nth root of a complex number is

Q: 9. Linda's Bakery sells three kinds of cookies: chocolate chip cookies at 15 cents each, oatmeal…

A: We use the concept of linear equations to solve the given problem.

Q: Solve the rational inequality x²-9 x² - 49 -≤0.

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Q: A physician invests $24,000 in two bonds. If one bond yields 6% and the other yields 12%, how much…

A: Given that a physician invests 24000 dollars in two bonds , 6% and 12% , total annual income 1980…

Q: Let h(z) = 2¹/3 Determine the most general indefinite integral of h. 1/3 dz

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Q: Find the indefinite integral and check the results by differentiation S(4x²+ + 3)²dx

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Q: Evaluate the following limits algebraically. 1. lim x---> 2      {5x - 7; x = 2

A: Note:-Since you asked multiple questions according to our polcy we can answer only first question…

Q: Evaluate the integral. 3 f(x) dx where f(x) =26-x² if -4 ≤ x ≤ 0 if 0 < x≤ 3

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Q: 4. Find the function given by the power series n f(x) = Σ + ²)", x+2 when -7 < x < 3. 5 n=1/

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Q: 2 Assume that f'(2) = -9, g'(3) = g(3)=2, and y=f(g(x)). What is y' at x = 3?

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Q: A company finds that the rate at which the quantity of a product that consumers demand changes with…

A: Consider the given marginal-demand function,

Q: (−1)" (x + 15)" Σ 10" 14 n=|

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Q: Evaluate ∫∫∫E 1/(x^2+y^2+z^2 )dV where E lines between the spheres x^2+y^2+z^2=4 and x^2+y^2+z^2=16…

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Q: Question 1. Below is the velocity graph for a golf cart measured in meters per second with respect…

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Q: If f(x) = 15 to dt then f'(x) =

A: Note:-Since you asked multiple questions according to our policy we can answer only first question…

Q: Use the figure below, which shows the graph of y = f(x), to answer the following questions. Which of…

A: Area above the x-axis is considered as positive and area below the x-axis is considered as negative.

Q: Let f(x) = 3x - 6 and g(x)=x+3. Find each composite function and describe the domain of the…

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Q: Evaluate the given definite integral. 3 [(-8 -4 (-8z - 7)dz =

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