1.) Use the arc length formula to find the length of the curve y = 3x + 2 on the interval 0 ≤ x ≤ 3.

Q: Find the area of the region that is bounded by the given curve and lies in the specified sector.…

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Q: 4. The equation t + f(t)+h(t)x= [(t) becomes homogeneous when d²x dt² (a) f(t) and h(t) are…

A: A detailed solution is given below

Q: Verify the identity by converting the left side into sines and cosines. (Simplify at each step.) 7…

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Q: A manufacturer knows that when he charges p dollars per unit for his product, he will be able to…

A: Given :Ax=5+x50x=380-20p

Q: =) y II 131 Olim x 1 z 1 0 -1 lim 2-1 x |x-1| |x-1| x - |x-1| lim z 1 x- - 1 -5 -1 DNE UND 0.9 -1…

A: c) Given,y=|x-1|x-1 now, limx→1-11-xx-1=limx→1-1(-1)=-1

Q: The particular solution of y(x+y) dx + (x + 2y − 1) dy=0; y(0) = 2 by NEDE is A B C D x(x+y=1)=4e-x…

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Q: Given y(4) - 6y" - 36y" +216y' = t² +8+ t sint, determine a suitable form for Y(t) if the method of…

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Q: 11 7 Find Y y N 2x² + y² = 4 2

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Q: By using the substitution t² determine the convergence of = S ∞ dx (x+1)√√x*

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Q: Find all solutions of the equation in the interval [0, 2?). (Enter your answers as a comma-separated…

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Q: $fº f(x) dx = 12.5. Use this information to fill in the blanks. (Round your answer for part (f) to…

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Q: Exercise 14. Determ (a) f(x)=x" (b) f(x) = ln x 1 7-x (c) f(x) =

A: a.fx=xnDnax+bn=n!an…

Q: For each system of equations, determine if there is an intersection and classify it (point, line, or…

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Q: 5. Krypton-85 is an inert radioactive noble gas with a half-life of approximately 10.76 years. a.…

A: To find out the exponential equation to model this.

Q: Evaluate the integral. *3 7 39+x² dx

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Q: lf f(x) = 3x sin x cos x, find f'(x)= To two decimal places, Find f'(2) =

A: f(x) = 3xsinxcosx find f'(x) = ? and find f'(2) = ? here first we use formula 2sinxcosx = sin2x and…

Q: Find the volume of revolution from the region bounded by y=x, x+y=6 and y=1, being revolved around…

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Q: 3. Find the F. T. of the following periodic signal H -2 -1 2

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Q: Recall the equation for a circle with center (h, k) and radius r. At what point in the first…

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Q: Find the distance along an arc on the surface of the earth that subtends a central angle of 2…

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Q: Let y = tan(4x + 3). Find the differential dy when x = 3 and dx = 0.3 Find the differential dy when…

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Q: 1. Show that (a) Log(-ei) = 1 - ži;

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Q: The derivative of a function at each point is itself. y=kex

A: To find out the derivative of the function.

Q: Express lim Σ n → ∞i=1 3 n ( n 3i + COS 9/² 2 as a definite integral

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Q: Consider the vector function r(t) = . (a) Find the unit tangent and normal vectors of r(t).…

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Q: Consider the following equations. f(x) = x5 + 3 g(x) = x + 3

A: Given equations f(x)=x5+3g(x)=x+3First we need to find the intersection points…

Q: Find the derivative, f'(x), for f(x) = S dr 3 sinr+2 (₁²³+√7) X A f(x) = B f(x)= −sinx − 2 x²³+√√x X…

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Q: ) ㅠ S tan5 (2x) sec² (2x) dx 2

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Q: How to work out the break-even???

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Q: A jwb (b-a) [ube job A سلم) ] (b-a) e + wa a (ولم _4 ou - وسلام

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Q: Find V x F for F(x, y, z)= - -xZ + y² i+ -yz x² + y² =j+√x² + y²k.

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Q: Using the trapezoidal rule with n = 5, approximate the integral L' TO S³ give the error of…

A: Trapezoidal rule formula: ∫abf(x) dx=h2(y0+yn)+2(y1+y2+...+yn-1) Given ∫03dx16+x2 Here f(x)=116+x2…

Q: The angle between 0 and 27 in radians that is coterminal with the angle 14 5 Tin radians is

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Q: Write an equation for the transformed logarithm shown below, that passes through (3,0) and (0,3) -5…

A: Understanding of logarithmic function is required to understand this problem.

Q: Find the solution of the following initial value problem. y" + 10y' + 21y = 0_y(0) = 9, y'(0) = −55…

A: Given: The characteristics equation is m2+10m+21=0. So,                  m2+10m+21=0⇒m=-10±102-4·…

Q: Use Lagrange multipliers to minimize the function f(x,y,z) = x² + y² +z² subject to the following…

A: The given function is;  f(x,y,z)=x2+y2+z2 Constraint: x+y+z-33=0.

Q: 3 dx 00 (2²+4)³/2 es or diverges.

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Q: For each of the following functions, f(0), find f(1), ​and ​f(5).

A: Follow the procedure given below.

Q: Determine all the eigenvalues of the matrix G given below. Hence, obtain an eigenvector…

A: The understanding of Eigen value and Eigen vectors are required to solve these kinds of problems.

Q: Use the if f₁ (t) F, (w) properties of Fourier transform eat alt) JF.T = = f flt) e jwt -00 -at ejwt…

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Q: c) (n+1)2

A: We will apply Ratio-Test for converge

Q: Evaluate d -tan − ¹ (√x + 7) = dx

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Q: Determine the general solution of the given differential equation. y" - y" -y + y = 5e +6 NOTE: Use…

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Q: Consider the following equations. f(x) = x5 + 3 g(x) = x + 3

A: Here we have to plot a graph.

Q: Use matrices to solve the system of equations (if possible). Use Gaussian elimination with…

A: In this question we have to find the value of x, y and z using Gaussian Elimination with back…

Q: Find dy/dx for 2x+y³ = 2y A B D bevelled fraction numerator d y over denominator d x end fraction…

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Q: (2) √(2x³² - 4x²) -4xº)dx (b) [(72+ + ²) dx (c) [(5x² + 7e +3x+2)dx 3x

A: In this question we have to solve the Integration.

Q: The function f(x) This function has a local maximum at x = with value - with value 5 + 8x + 72x and…

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Q: Find the area of the surface generated when the indicated arc is revolved about the y-axis: a. y =…

A: Given :y=2xx=0 to x=4

Q: Compute the gradient of the following function and evaluate it at the given point P.…

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