1. For y=In2x, determine the equation of a tangent line parallel to 2x-3y+1=0.

Q: Find f. (Use C for the constant of the first antiderivative and D for the constant of the second…

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

A: We will use binomial theorem for the expansion of the function.

Q: Find the general solution of the differential equation y" – 10y' + 29y = e-*

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Q: Find the values of the trigonometric functions of 0 from the information given. 3 O in quadrant II…

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Q: 4: Show yor work. a) 1: Find the exact area of the surface obtained by rotating the curve y? +x =5,…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Suppose that a g(t) dt = v2. Find g(1) dt b. g(u) du а. [-g(x)] dx /"g(r) с. d. dr -3

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Q: ): Consider the 3 x 3 matrix -- -1 A = 3 -X where x is an unknown scalar. -1 Find the unknow x if it…

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Q: (1 point) Calculate the volume under the elliptic paraboloid z = 2x2 +3y2 and over the rectangle R =…

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Q: Find the limit or show that it does not exist. V1+4x6 (1) lim x- 2- (2) lim (V9x2-5x+3x

A: 1. limx→-∞1+4x62-x32. limx→∞9x2-5x+3x

Q: Write the vector equation for the given parametric equations: x=3+5t y=9+7t

A: Consider the parametric equation  x=3+5t  y=9+7t

Q: Determine positive integers A, B, C, D, E and F such that 9n-14 6x2 -132-5 A Bx+C Ex-F A B = C = D =…

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Q: Calculate M, for f(x) = V7x over [2, 5]. %3D (Use decimal notation. Give your answer to two decimal…

A: This is a problem related to Mid point rule of the function. Based on the general formula we will…

Q: Integration by Partial Fraction Decomposition 6х-7 7. S dx (2x+1)(4x²+1)

A: Solving the problem by finding the value of the integral.   NOTE :: As per our Expert guidelines we…

Q: Determine whether each of th or converges conditionally: 1)(-1)* ek k=1

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

Q: Given a function F(x) =xv/x+6. ) Find the intervals of increase or decrease. ) Find the local…

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Q: Find the volume of the regular hexagonal pyramid shown below, and then answer the following…

A: We have to find the perimeter of the regular hexagonal base, the measure of the apothem of the…

Q: 2. Suppose that the triangle with vertices (-1,-1), (0, 1) and (1,–1) is revolved about the y –…

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Q: 10. Find the average value of the function f (x) 1 = -x + Vx on the interval xe[0,8]. Graph on…

A: The average value of the function is given by;favg =1b-a ∫abf(x) dxTo plot the average function…

Q: a. To maximize the area of the pen, the sides perpendicular to the barn should be 625 m long and the…

A: Given query is to find the dimensions of each barn.

Q: Suppose a company's revenue function is given by R(q)= − q^3+320q^2 and its cost function is given…

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Q: (a) Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z? = 14, (1,…

A: a To find an equation of the tangent plane to the surface at the given point.x2+y2+z2=14, 1, 3, 2b…

Q: 5. USC cyllndrical coordinates. Evaluatc (k4)dv, where E IS the solid that ies betwern the cylinders…

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Q: 3 | (16t3 – 12t? + 6)dt

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Q: Graph the function and find its average value over the given interval а. g(x) %3D \x| —1 оп [-1,1]…

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Q: The height y (in feet) of a ball thrown by a child is 1 x² + 6x + 5 14 y = where x is the horizontal…

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Q: Given 0<a < 360°, find all the solutions to 2 sin? (x) = 9 sin(x) – 4. %3D

A: Given query is to find the solution of the expression.

Q: 2. Find the exact length of the fllowing curvis 1&s4 () x= Imfi-) <と

A: a) y=13xx-3 ; 1≤x≤4 Note:      Multiple questions are given, we are answer with only one question.…

Q: Draw a diagram to show that there are two tangent lines to the parabola y = x² that pass through the…

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Q: Use the graph of f(x) to determine whether the function is one-to-one. If it is, find a formula for…

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Q: In x cot x 6 ) Tim

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Q: Problem3. Solve 4 + 3log(2x) = 16. %3D

A: We can solve the equation as below using properties of log.

Q: A rectangle is inscribed with its base on the X-axis and its upper corners on the parabola y=…

A: A rectangle is inscribed with its base on the x-axis and its upper cornerson the parabola y=8-x2.

Q: Why does this work? If we have the curve in the xy-plane: F (x, y) = 0, then why is the implicit…

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Q: A contour map is shown for a function fSn the square R = |0, 4| x [0, 4| %3D (z, y)dA 4 to estimate…

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Q: Find any critical numbers for f and then use the second derivative test to decide whether the…

A: For finding critical point f'(x) = 0

Q: Find any critical numbers for f and then use the second derivative test to decide whether the…

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Q: Note: Below we are using t as the variable for angles instead of 0. 1 Consider the following…

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Q: f(x) = x² - = x + 2* – 100

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Q: Find the absolute maximum value of f(x) = x² - 2x +9 over the interval [0, 5] |

A: Given problem:- Find the absolute maximum value of f(x) = x2 - 2x + 9 over the interval [0,5]

Q: 5. Fied ť+, y= t*+t for t=-l equatin ef the lagest limye te the Cume an

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Q: Let A = 1 a. Find the matrix product A'A b. Find the determinant |A'A| c. Find the inverse (A'A)-1,…

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Q: Given sinα=0.771 and sinβ=0.716 with both angles' terminal rays in Quadrant-I, find the following:…

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Q: erify the following identities: 1-sin(x) 1-sin(x) %3D V1+sin(x) |cos(x)| sin*(x). cos?(x) = cos?(x)…

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Q: Qz: IF U=h cx,g )= Lnce+ ě).show that %3D Sy

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Q: Find the following indefinite integrals. x* – 5x dx. 2. x3

A: Answer is given below.

Q: Find the absolute maximum value of f(a) = x2- 2x +9 over the interval [0,5] The value C for the…

A: Use derivative and integration for the following question.

Q: 2 / 2 00% Find the absolute maximum and absolute minimum values of f(x) = 3x+4x - 12+1 on the given…

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Q: For the function f(x) = 4x* – 3x - 4x2 +9, find f'"(x). Then find f"(0) and f"(9). ... f"(x) =O

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Q: x Ve dx =

A: We are asked to evaluate the integral

Q: Find the centroid of the region bounded by the given curves. 20) The region enclosed by the…

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