(4t³ – e') dt

Q: Consider the discrete time dynamical system 5x1 . This DTDS has 3 fixed points. Choose the correct…

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Q: A circle with centre C has equation x² +y² – 6x+4y+4 = 0. (a) Find (i) the coordinates of C, (ii)…

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Q: n(-8)" Use the ratio test to determine whether converges or diverges. п! n=25 (a) Find the ratio of…

A: Here we have to use the ratio test.

Q: evaluate indkfinite intersal

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Q: 32 2 f is continuous and | f(t) dt = 6, find the integral / t* f(t) dt.

A: Given problem:-

Q: Work Problem 1 (With integrity statement] ( Let R be the region bounded by y-x+2, y=0, and x=2. Draw…

A: Given; I=∫∫R-2ydA And y=x+2, y=0, x=2   As we know that; The Power rule: ∫ax+bndx=ax+bn+1an+1+C And…

Q: Evaluate: (9 - 22) -1 x- V9- x sin A f (z) = %3D V9-2 None of the above a+V9-r sin ©f(z) = V9-7 9-…

A: We have to choose the correct option from the given options according to the given information

Q: Solve the system of equations. If the system does not have one unique solution, determine the number…

A: In this question , we can solve the system of equation by eliminating the variables .

Q: Three pens of the same size are to be built along an existing fence. If 480 feet of fencing is…

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Q: The position of a particle in the xy-plane t time t is r(t) = (e') i+ i. Find an equation in x and y…

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Q: 4" converges or diverges. (7n)2 Use the ratio test to determine whether n=6 (a) Find the ratio of…

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Q: Consider / sin'x cos²x dx. jf we let " =cos x , the integrand can be transformed to , O J(- 2u?- u*…

A: The given integral,    ∫sin5x cos2x dx

Q: cos(x) 1- cos(x) by miscellaneous substitution, the substitution z=tan In solving the antiderivative…

A: Here we have to use the subsitution.

Q: The radius r of a sphere is increasing at a rate of 2 inches per minute. (a) Find the rate of change…

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Q: x² + 64 Using trigonometric substitution, given dx, the simplified form of the integral is: […

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Q: In solving the antiderivative of (x)= sin(x) + 3cos(x) + 3 by miscellaneous substitution, the…

A: The given function,        fx=1sinx+3cosx+3

Q: Consider the region bounded by F(x)=10x3 +7x2 -7x +6 and g(x)= 9x3 +8x2 - x +6. Find the area, in…

A: Given query is to find the area bounded by the curves for the given intererval.

Q: x² + 64 Using trigonometric substitution, given - dx, the simplified form of the integral is: (sec…

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Q: S sin°x cos³x dx 1 2 1 sin'x +sin°x - sin'"x + C sin'a +sin'x +sin"x +c B 1 sin'

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Q: Let A = (1, -2) and B = (6, 2). Solve for projyA. %3D

A: projBA  implies projection of A on the vector B. projBA =A·BB2 B  ............(1) A·B is dot product…

Q: Find the derivative of the function f)= [sec() 6 sec-1 xVx2-9 1 sec x Vx2 -9 O 3 sec-G) 3. xVx2 -9 3…

A: In this question we have to find the derivative of the given function.

Q: (Continue) An astronaut drops a hammer from rest a vertical distance of 2.0 meters above the surface…

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Q: Find the volume of the solid obtained by rotating the region under the graph of the function f(x) =…

A: The function f(x)=ex revolved about the x-axis over the interval 0,5

Q: 00 n8" Use the ratio test to determine whether>. converges or diverges. (n + 1)! n=7 (a) Find the…

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Q: An astronaut drops a hammer from rest a vertical distance of 2.0 meters above the surface of the…

A: Initial velocity of the hammer, u = 0 m/s Vertical distance above the surface of the moon from which…

Q: Determine the equation in slope intercept form explain in detail how to do Slope = 2 and passes…

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Q: 3 Fin %3D tan (X?y) tanx 2.y=(1+x)

A: 1) ln(x2+y) =tan-1(x2y)  2)y=(1+x2)tan^(-1)(x).

Q: Find the derivative. 8) y = (x + 1)2(x2 + 1)-3 dy dx dy = -2(x + 1)(x2 + 1)-4(2x2 + 3x – 1) A) B) Y…

A: We can find the correct answer as below.

Q: S sin®xdx

A: ∫sin6x dx       We have sin2 x=1-cos2x2 Then ∫sin6x dx=∫sin2 x3dx                  =∫1-cos 2x23dx…

Q: Give an appropriate response. 3) Find the limit of f(x) as x approaches 2 from the left. (-3 if x3…

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Q: x² + 64 Using trigonometric substitution, given -dx, the simplified form of the integral is: x2 sec³…

A: Given: ∫x2+6464dx

Q: 25-x2 In dx , if we letu=V25-x² , then udu= – xdx.

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Q: Rewrite the expression in terms of exponentials and simplify the results. 29) sinh (5 ln x) A) 2x B)

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Q: dx J Evaluate: (x-4)(x-1) A None of the given choices 1 B x-1 +C X-4 (c) x-1 3ln X-4 + C 1 D X-4 + C…

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Q: Differentiate the function:  k(x) = 4 ln (x) + 2 cos x + x^2 k'(x) =

A: k(x)=4ln(x)+2cosx+x2Differentiate with respect to xk'(x)=(4×1x)+2-sinx+2xk'(x)=4x-2sinx+2x

Q: Finding the Slope of a Graph In Exercises 23–26, find the slope of the graph of the function at the…

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Q: 1 2. (33.6) Use the building block > a", |r| < 1, to find a power series representation 1–x n=0 for…

A: Solve the following

Q: S(3x2 + 4x – 5) dx

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

Q: Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on. 6s +…

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Q: d d Calculate [ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: Use the properties of limits to help decide whether the limit exists. If the limit exists, find its…

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Q: Evaluate the integral. (Use C for the constant of integration.) 10 dx 5x + x/x

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Q: The issue of convergence or divergence of some series can be answered by several different…

A: NOTE:- AS PER BARTLEBY GUIDELINES, WE WILL ANSWER ONLY FIRST THREE PART OF THE QUESTIONS.

Q: For the function y In (6x) on the interval [1, 9], answer the following questions. (a) Give the…

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Q: Consider / sinºx cos?x dx. |f we let u=cos x , the integrand can be transformed to A / (u²+ 2u+ +…

A: topic - indefinite integral

Q: Use the method of Lagrange multipliers to find the maximum and minimum of f(x,y) = 5xy subject to x…

A: We have to find the maximum value.

Q: The graph of a function f is given. (Let a = 1.) 0 1 8. (a) Estimate f(x) dx using four subintervals…

A: We have to estimate the given integral.

Q: 9 – 4.x² -dx Evaluate: 9 – 4.x² – 2 sin () +C A f (x) = - B /9 – 4.x² + 2x sin- () +C f (x) = f (x)…

A: ∫9-4x2x2dx

Q: The speed of a runner increased steadily during the first three seconds of a race. Her speed at…

A: Here we will find the smaller and larger distance values,

Q: dz 2ydy In if we let y=z + 4, then the new integral becomes Vz+4 -2 у-2

A: Follow the procedure given below.