=== =+ = ²x² 6 2x Find the arc length given: y = - on the interval [1,2]

Q: Q1: If y=sint and t= sin x, then at x = a) 0 b) c) cosl dx² d) -cosl e) others

A: I have stated the used properties in the solution

Q: 1. Given the function f(x) = 20 √7-x find f (-9). "

A: The given function is: fx=207-x    ...1

Q: A bacteria culture starts with 500 bacteria and doubles in size every half hour. (c) How many…

A: Topic:- exponential growth function

Q: Ex: Expand fit) = +² o<t <2π in a Fourier Series expansion : Sol: 2 L = 2 T /// L = π -411 -27 2 tr…

A: I am attaching image so that you understand each and every step.

Q: Q4: Let y = √t and t= x² then y(") = 0 if n= a) 2 b) 3 c) 4 d)5 e) others

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Q: Q2: The equation of the tangent line to the graph of y=t² and t = 4x² at t = 1 is (not that x is…

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Q: Use Laws of Exponents to rewrite and simplify each expression. (b) (2x-2)-³x-3 x3.xn xn+1 (c)

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Q: Enclosed by x² + 4y² = 16

A: We have to find area bounded by given curves.

Q: Find the volume generated by revolving the area bounded by y = 1 - x³, OX and OY about the x-axis.

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Q: 3 Safin designed and launched an app. One week after he launched the app, it had 8 400 users. Four…

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Q: Solve for the non-homogenous linear differential equation: y''+4y=cos^2(x)

A: Given; y''+4y=cos^2(x)

Q: Find the vectors T, N, and B at the given point. r(t) ) =(2², ²32²³, t), (4,- 15, -2) N = B =

A: This question can be solved by applying the formula of T,N,B

Q: Q. Solve the following Initial Value Problem (IVP): y + 3y + 2y = 6e-t at y(0)=1 and y (0)=2

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Q: 1) How many 5 digit numbers can be made using the digits 5, 6, 1, 4, 9, 3, 2 if no digits can be…

A: According to our guidelines, we can answer only one question or three subparts of a question.

Q: Problem 2: Use the definition of the Laplace transform to find the transform of the piecewise…

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Q: Given f(x,y) = x²y-3xy³. Evaluate O 14y-27y³ 6 + C O -6y³ +8y/3+C O 6x²-45x + C 4 O 2x²-12x+ C 2 f²f…

A: Please see the answer below.

Q: 26/ Given the triangle 39° 11 answer to 4 decimal places. x = x find the length of side x using the…

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Q: 3. Carry out the following mathematical operations and report your final answer in the correct…

A: The objective is to solve the mathematical expressions.

Q: Scotch is looking to make a larger size roll of duct tape. The current roll is shown in the photo.…

A: First finding the volume of original roll

Q: 12) Consider the following exponential function f, Given that f(x) = -616, what is the value of x?…

A: exponential function

Q: Identify the conic section whose equation in standard form is y 2 + 8y - 10y - 34 = 0. ellipse…

A: Topic = Geometry parabola

Q: 21 = 106 55 104 102 ܐ

A: We have to find the sum of the series.

Q: JC LUDJE SH 31 Exercises 4.4 Use Laplace transforms to solve the given different d²y dy 1. 3- + dx²…

A: Topic:- application of integration

Q: Use the second fundamental theorem of calculus to evaluate the following: 1 1 + 1 + sin 0 5) de 1 -…

A: Value of definite integration is given.

Q: Q5: If y=tant and x = cost then at t= is (not that these functions in N) dx a) -1 b) 0 c) d) 1 e)…

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Q: A. Given that f(x)=2x-3 and g(x) = 6x-1. calculate the value of f(5). derive an expression for…

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Q: HOME ASSIGNMENT #01 cosec cosec² x - 2009 A(X) 73. If -dx = - 2009 COS X (B(x)) 20 [0, 2лs (where…

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Q: Identify the conic section whose equation in standard form is x 2 + 2y 2 - 3x + 8y = 10. ellipse…

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Q: 12. (a) Use the alternating series test to show that the series converge [(-1)*+¹/ k k=1

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Q: Find the average value of f(x) = sin³ x cos³x on the interval [0,1].

A: We need to find average value.

Q: Question Find the volume of the solid whose base is a triangle with vertices (0, 0), (0, 2), and (3,…

A: Given problem:- Find the volume of the solid whose base is a triangle with vertices (0, 0), (0, 2),…

Q: Find the volume of the solid obtained by rotating about the y-axis the region bounded by the curves…

A: Cylindrical shell Method : If th eregion between the two curves y=f(x) and y=g(x) and f(x)≥g(x) is…

Q: Suppose ƒ be a function such that fo f(x) dx = 3. Then ² t² f(t³)dt: 9 [Select] Select] 103

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Q: 6. show that the complex Fourier series of the function; f.(.t.) = t ..。. st.s.1. is...:. i2nt e j…

A: Fourier series of function is given.

Q: What is the amount of work done on a spring when it is compressed from its natural length of 1 meter…

A: Compress from the natural length through 1-0.8= 0.2 meter spring constant 'k'=16 N/m

Q: A 5-pound monkey is attached to the end of a 30-foot hanging rope that weighs 0.2 pound/foot. The…

A: Given problem:- A 5-pound monkey is attached to the end of a 30-foot hanging rope that weighs 0.2…

Q: Let f(x,y) = 3x4 - 4x³y + 2x2y2-y. Let f, be the partial derivative of f(x, y) with respect to x.…

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Q: Find the solution of the following differential equation. (x² - 1) + 2y (x + 1)² dy dx 1.

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Q: Consider the equation y' - 2y = te State the integrating factor u(t) and find the general solution…

A: This question can be solved using the concept of linear differential equation.

Q: Write the equation for each requested curve a) Cosine curve with vertical compression of a factor of…

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Q: i. Given that log x=12, log, y = 15 and log, z = 18. Consider the following four logarithmic…

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Q: 3. Evaluate the following integrals. For each integral, briefly explain what method you are using…

A: Please see the answer below.

Q: Given the function F(x) = 2x 3 - 6, find the value F(-1). 10 -8 -4

A: Solution is done in step 2

Q: (9x-4y+4)dx-(2x-y+1)dy=0

A:

Q: (d) The set of points in space equidistant from the origin and the point (0,2,0). (e) The set of…

A: Question d and e has been solved as per the request of the student.

Q: y = x², y = 0, x = 1, and x = √5

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Q: J udv = uv J to Explain why the substitutions below are inappropriate. Let U = eª and 1. Suppose we…

A: lets here we use integration by parts rule  ∫xexdx here lets u = x v = ex  is good to substitute…

Q: 14 Find the slope of the function ƒ(x) = -x - 1, by the definition of a limit. Slope =

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Q: Problem 1: Determine centroid Y-bar with respect to the x-axis. A = 1.6 m B-3.9 m V A A B B

A: We have to find the centroid.

Q: Exponential and Logarithmic Functions 11. Use the properties of logarithms to fully expand the…

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