1. Find the derivative of the following functions: a. y = x² b. y=x4 c. y=- X

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: What are the coordinates of the vertex of the equation (+8)² (x+2)² 36 = 1? 25 O (-2,-2), (-2, 14) O…

A: The given equation is

Q: b) Solve the following rational equation for the indicated variable. Be sure check for extraneous…

A: To solve the following rational equation.

Q: Use the formula f'(x) = lim Z-X f(x)=x²-x+4 f'(x) = f(z)-f(x) Z-X to find the derivative of the…

A: we need to find f'(x)

Q: lim x-0+ x lim x-0-x² g. h. 2 1+x i. lim (¹+2) ² →? x-2

A: Note:-Since you asked multiple sub parts questions, according to our policy we can solve only first…

Q: A stone is dropped from the upper observation deck of a tower, 500 m above the ground. (Assume g =…

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Q: 1. Use the Limit Comparison Test to determine whether the series below converges or diverges. List…

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Q: i. x+1 lim X→∞ X-1

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

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

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Q: 15. An open rectangular box is to be made by cutting equal-sized squares from the corners of an 8"…

A: The dimensions of the box are:Length: L=15-2xWidth: W=8-2xHeight: H=x

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…

Q: b) x²-8x+15 2x²-x 1-4x² x²-x-30 X

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Q: Use Green's theorem for flux to evaluate the line integral F. û ds. F = (2xy, y² – x²) and C is the…

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Q: The marginal revenue (in thousands of dollars) from the sale of x handheld gaming devices is given…

A: The marginal revenue (in thousands of dollars) from the sale of x handheld gaming devices is given…

Q: Consider the following position function. a. Find the velocity and speed of the object. b. Find the…

A: Given,

Q: 3. Evaluate the integrals. a. b. /4 5*1*4 (sec (1))² dt [²7/x dx baxax 8x dx

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Q: 8 7 5 3 2 1 0 1 2 3 (a) The integral f's f (x) dx -f(x)- 4 5 f (x) dx. Round your answer to the…

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Q: et P(x, y) denote the point where the terminal side of angle 8 (in standard position) meets the unit…

A: The figure

Q: Find the areas of the shaded regions in

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Q: 2. Evaluate the integrals. a. b. C. L (6x - e²) dx [²₁12 +2 (2 + 2y)² dy 7T/4 3 3 sec Ꮎ tan Ꮎ ᏧᎾ

A: .

Q: A company's marginal cost function is C'(x) = 686 - 4x +0.06x² where x is the number of units, i…

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Q: 9. The angular displacement of a spinning shaft is given as = 0.7t² - 5t+3, where is in radians and…

A: Given that the angular displacement of spinning shaft is where  is in radians and t is in seconds

Q: Let (a) Evaluate det1B 2 by expanding by the second row. (b) Evaluate det1B 2 by expanding by the…

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Q: Evaluate the following definite integral. π JU OA. (( sin 8t)i + (cos 8t)j + (10t)k) dt Select the…

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Q: Find two positive numbers whose product is 100 such that the sum of the first and four times the…

A: Find two positive numbers whose product is 100 such that the sum of the first and four times the…

Q: Find ∫∫R(5x+2y)dAwhere R is the parallelogram with vertices (0,0), (-2,3), (5,-4), and (3,-1). Use…

A: We need to find the integral value of given data.

Q: 6. Find the sum of the series: 100 x5n−1 n!

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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: Σ(17)

A: ∑n=1∞(3n+7n11n)

Q: = Find fæ, fy, fxx, fyy, fay for the function f 5 x³ siny+8 y² cosx+3x+7y.

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Q: If sin(-s) = 5/13, and (a) (b) (c) (d) sin s cos(-s) COS S 3πt < s < 2π, compute the following.…

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Q: A company manufactures and sells x television sets per month. The monthly cost and price-demand…

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Q: Consider the following integral. ƒ(9e¹) e* dx By making an appropriate substitution, the above…

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Q: 5. Solve y"" - 6y" + 11y' - 6y = 0

A: The given differential equation is

Q: SX7UPET dx

A: I=∫x7x4+1dxI=∫x4(x4+1)x3dxI=14∫x4(x4+1)4x3dxSubstitute x4+1=u

Q: 1 se sec4 x tan x dx

A:

Q: The figure below shows human arterial blood pressure during the course of one heartbeat. arterial…

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Q: Find a power series representation for the function. (Give your power series representation centered…

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Q: Suppose that we're setting up a wireless data network for a small municipality. The local ISP wants…

A: The given cost function is

Q: Find the exact area of the surface obtained by rotating the given curve about the x-axis. x = a cos³…

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Q: Write in terms of sine and cosine and simplify the expression. cos A - 2 sin A cos A cos² Asin² A +…

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Q: f(x) = cos² (3x + 1) − sin² (3x +1) f(x) = ln 1-sin 2.7

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Q: S(3x+1) (3x²+2x+1)³dx

A: I=∫(3x+1)(3x2+2x+1)3dxSubstitute 3x2+2x+1=u

Q: Convert the point with cylindrical coordinates 11π 13, 5 to Cartesian coordinates. Enter your answer…

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Q: Which of the following represents the limit definition of the definite 16 integral 26 4x5 dx using a…

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Q: Match the series with the right expression. (Use the Maclaurin series.) (−1)n3−(2n+1) 2n + 1 1. 0 2.…

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Q: b) 9-x² x²+4x+4

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Q: find the limit if it exists, or show that it does not exist.  lim (x,y)→(0,0) (x^4 −y^4)/x^2+y^2

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Q: Find the following limits: lim (x² – 13) a. X--3 b. lim 8(t-5) (t - 7) t-6 2x+5 lim x-211-x³ c. C.

A: To find the following limits.

Q: 5. Use Part one of the fundamental theorem of calculus to find the derivative of the following…

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