5. Use geometry to evaluate (V4- x² dx 2 O 2n O 4t

Q: Evaluate the integral. NOTE: Enter the exact answer. c10 1 xe"y dy dx

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Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)…

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Q: Evaluate the line integral / (2x + 7y)dx + (4x – 6y)dy along the curve C: = 6 cos t, y = 12 sin t…

A: Let's find.

Q: A torus is formed by revolving the region bounded by the circle x? + y? = 49 about the line x = 8…

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Q: Find the Maclaurin series for the function. (Use the table of power series for elementary…

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Q: fast

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Q: In exercises 11–30, find all critical numbers by hand. If avail- able, use graphing technology to…

A: 13)f(x)=x34-4x14f'(x)=34 x-14 -414 x-34f'(x)=34 x-14 -x-34 f'(x)=034 x-14 -x-34 =03 x-14 =4x-34 34…

Q: Question Specify which of the following sequences converge en n+V5 an =5- %3D n2 Cn = an and Cn the…

A: If limn→∞an  exists and is finite the then sequence an is converges.

Q: 1- Show that the following subset is a subgroup. H = {o e S, l0(n) = n}cS,

A: We have to show given subset is a subgroup.

Q: 3 The series E converges if n=2 (n+ 1)P (n – 1)ª (a) p+q1 (c) p+q=1 (a) p+q=2 (e) -1<p+q<1

A: Solve the following

Q: Define a function S: Z+ --> Z+ as follows. For each positive integer n, S(n) = the sum of the…

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Q: dy is dy xy dx dx The general solution of y² + x² "

A: Solution is given below:

Q: Problem 5 Find the Maclaurin series for f(x) and its associated radius of convergence. (a) f(x) =…

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Q: Find the arc length in the second quadrant of the curve x23 + y23 2/3 = 9 from x = - 27 to x = – 1.…

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Q: Find the points on the curve where the tangent is horizontal or vertical. You may want to use a…

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Q: Sketch the region of integration. (Select the correct graph.) rIn 6 6 dy dx In y y y 61 6 4 3 2 1 4…

A: Area

Q: Evaluate JJ xy dA , where R is the region in ху ´(1, 3) (5, 3) R (2, 1) (4, 1) A) 56 в) 67 38 D) 90

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Use The Formula К(T) = ||R' (T) × R"(T)|| ||R'(T)|

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Q: Evaluate (2x - y) dx + (x + 8y) dy. C: x-axis from x = 0 to x = 3

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Q: A torus is formed by revolving the region bounded by the circle x² + y² = 9 about the line x = 5…

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Q: Consider the following planes. 5x + 2y - z = 22 x - 4y + 2z = 0 (a) Find the angle between the two…

A: Solution is done in step 2

Q: dy 18. Given y = 5t ( 3 - t), t = In p and p = e*. Find and simplify %3D dx

A: Given: y=5t3-t, t=lnp, p=ex   As we know from the chain rule; dydx=dydt·dtdp·dpdx    .....(1)   The…

Q: Question * Using the Nth term test for divergence 1 2n + 14 n=1 diverges since lim is equal to 1.…

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Q: Consider the following algebraic functions. F(x) = -x2 + 6x + 5 g(x) = x+ 5 Sketch and shade the…

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Q: Find the solution of the following nonlinear ODE through separation of variables given that y(0)=1.…

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Q: Each unit of a product can be made on either machine A or machine B. The nature of the machines…

A: Here, from the given details, C(x,y)=30+x26+260+y39 That should be minimized using…

Q: 40senz are solutions of the differential equation senr It's known that y1(x) 2(z) : 4z2y" + 4ry' +…

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Q: Evaluate the following sums using summation formulas. 10 10 10 Σ b. ) k? а. C. k=1 k=1 k=1 10 а. k=1…

A: We have to evaluate the sum

Q: 1 -dt , find g'(2). V4 +t5 If g(x) =

A: Let's find.

Q: Consider the equation y"+ay'+by=f(x) where a and b are real constants. If the general solution of…

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Q: Find the area of the shaded region. r = Vcos 20 r = 9 cos 0 NOTE: Enter the exact answer. A =

A: We have to find area of shaded Region.

Q: Evaluate the definite integral. 14t i + e*j+t k)dt (el4 – 1) i – (e-1 – 1) j + k 1-(6" -1) + i- (e~-…

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Q: Find the length of the curve of the graph of the indicated function. y = In(sen x), between points…

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Q: 12 9.

A: Use Trigonometric ratios

Q: Use a double integral to find the volume of the indicated solid. 9 z = 9–2 y 2 y=2 4 X=4

A: Consider the solid

Q: Using appropriate substitution xp: V9x2-36x + 37 Is equal to

A: We have to integrate given function

Q: Evaluate the integral by first reversing the order of integration. NOTE: Enter the exact answer. e…

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Q: Suppose the Sunglasses Hut Company has a profit function given by P(q) = – 0.02q + 5q 38 where q is…

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Q: Find the length of the curve, L. y? = 64 (r+ 5)* , 0 0

A: To evaluate the length of the given curve.

Q: Find the values of c guaranteed by the Mean Value Theorem (MVT) for f(x) 1 ax +7 over the interval…

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Q: Find the arc length L of the graph of r(t). 1 .3 r(t) = i+t j+¬V61² k, 2 <153 L =

A: Solve the following

Q: Use a triple integral to find the volume of the given solid. The solid bounded by the parabolic…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize…

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Q: for the following differential equation (assume zero initial conditions), write the state variables…

A: Solution: Given

Q: test the converg ence and divergence 27-1 2. (2h-1):

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Q: r=1+ 3sino

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Q: We know that y dy? arctan (e*+1) so whats the value for dx 1 a) e2a+2 +1 1 Ob) els+1)* +1 Need This…

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Q: If we have that f: R → Ris a continuous function , in which f'(7) = 6 and f(7) = -2 an equation of…

A: We have to find out tangent line

Q: Find the length of the curve of the graph of the indicated function. y = 4x3/2, between points (1,4)…

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Q: Use Green's Theorem to evaluate the line integral. | 2xy dx + (x + y) dy C: boundary of the region…

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