Find the radius of convergence of the power series. (If you need to use ∞o or -∞o, enter INFINITY or -INFINITY, respectively.) ∞ Σ (-1)^ x^ 8n n = 0 O →

Q: d²y_dy + y = 0 dx d³y_d²y dx³ dx²

A: Auxillary equation ism3-m2-m+1=0m2(m-1)-(m-1)=0(m2-1)(m-1)=0(m+1)(m-1)(m-1)=0m=-1.1.1  are the roots

Q: veen y - II [U, 1].

A: We will find the area .

Q: Find a general solution. Show the steps of derivation. Check your answer by substitution. -1.2 6. y'…

A:

Q: ergence or divergence of the given series or state that the Root Test is in 1 n=1 non x.)

A: Given :

Q: 2. Show that F is a conservative vector field and then use that fact to evaluate SF. dr along the…

A: We need to show F is conservative vector field.

Q: Use the Root Test to determine the convergence or divergence of the given series or state that the…

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

A: Cos(c+d) = Cosc.Cosd - Sinc.Sind  Sin(c+d) = Sinc.Cosd - Cosc.Sind

Q: F (y)= 2 y-3

A: The given function is  F(y)=2/(y-3).

Q: 6. Without graphing the function on your calculator, find the limit. Use L'Hopital's Rule where…

A: Solution of the problem as follows

Q: 4. sinx 1-sin² x dx

A: integration

Q: Differentiate: arcsin (# )+ 0 1 (E) None of these O x/y O y/x 00 + arccos (-) = 1

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Q: Cheyenne, Wyoming, has a latitude of 41° N. At this latitude, the number of hours of daylight D can…

A: Given :  D = 2.914 sin(0.017t 1.321) + 12.134

Q: Evaluate the definite integral. NOTE: Enter the exact answer. 12 5.² 11 |ti + t²j||dt 0 = =

A:

Q: -2x Find the derivative of f(x) = xe O f'(x)=e-2 (e-22) ²- O f'(x)=x²e-2 (²-2) O (E) None of these O…

A: We have to find the derivative of  f(x) = xe-2x.

Q: Match the vector field with its graph. F(x, y) = yi 1 |||||||||| 三 6 靈

A:

Q: Evaluate the triple integral zdV where E is the solid bounded by the cylinder y² + z² = 64 and the…

A: Here, to evaluate: ∫∫∫Ez dV where E is the solid bounded by the cylinder y2+z2=64 and the planes…

Q: 1 find the total differential dz. z=xsin y + x² z = (2x² + 3y)² z=5x-7y

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Q: f(x) = 2x + 3 x 1 1 ; a = 1

A: limx→1+f(x)=limx→1+x2+2                =12+2=3limx→1+f(x)=3

Q: If In a 2, ln b = 3, and ln c = 5, evaluate the following: = (a) In (10-2) = b-4c² (b) In √6-³c-²a-1…

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Q: -10 -10 8 61 0

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Q: Find the exact length of the curve. X x=√y (y - 3), 16 ≤ y ≤ 25

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Q: 6. 2x³ cot x4 dx 7. S x4 sec (x5 - 9) dx 8. Stan ³ x dx

A: We can solve this as follows:

Q: Find dy. Do not simplify your dx answers cashy (x² + + 7) = x curt y² 1. COS -241

A: As per the instruction, we will be answering only the first question. For (1),…

Q: Solve y"+y' + y = 6sin (2x) supo

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Q: r(t) = (t, In(t), √t), to = 1 e the equations for the line to approximate r(to + 0.1). to + 0.1) =

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Q: Find an equation for the conic that satisfies the given conditions. hyperbola, vertices (0, ±2),…

A: follow the procedure given below.

Q: Find all solutions of the equation in the interval [0, 27). 2cos’x– cosx−1=0 Write your answer in…

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Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

A: To find the domain of a vector-valued function  r(t) = a(t) i + b(t) j + c(t) k, we will need to…

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

A: Using greens theorem

Q: Homework 11 Parametric: Problem 3 Suppose a curve is traced by the parametric equations as t runs…

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Q: Find the slope of the tangent line to the polar curve r = sin(70) at 0=. Enter as an integer or…

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Q: Find the limit. lim t→3(t i-4 j + t² k) a z→3(t 1-4 j + P²³ k) = [i i+ Mi + M k

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Q: 10 (1 - 6x)² convergence R Represent the function Co= C1 = C2 = C3 C4 = Find the radius of || as a…

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Q: Ex. (7) Sol:- Solve y" +y'+y=6sin (2x) ➤ For y y"+y' + y = 0 Homogeneous [6sin (2x)=0] m² +m+1=0 1…

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Q: If f(x) = 6 + 6x - 2x², find f'(-3).

A:

Q: Let f(x)=x2+2x-1 and g(x)=2x-4. Find 3f(x)-2g(x)

A: Given fx=x2+2x-1 & gx=2x-4 To find 3f(x)-2g(x):

Q: Find r'(t), r"(t), r'(t) ・r"(t), and r'(t) × r"(t). r(t) = 2t2i - 2tj + 0 18k (a) r'(t) (b) r"(t)…

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Q: How many terms of the series do we need to add in order to find the sum to the indicated accuracy?…

A: The error in the approximation of a given series is always less than the last term that is used for…

Q: 8. Use differential to estimate the value of √ 4.01 four decimal places. 9. Use differentials to…

A: We have to find 8.The value of √4.01-1/√4.01 upto four           decimal places.  9. The value of…

Q: For the given function sketch the graph; determine if f is continuous at xo and determine if f is…

A: Given: Graph:

Q: Evaluate the line integralſ (x+2y) dx + x² dy, where C consists of line segment from (0, 0) to (2,…

A:

Q: Activity 2.2 For the given function sketch the graph; determine if f is continuous at xo and…

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

Q: (D² - 3D + 2)y = 2e-* +8

A:

Q: Find the length and width (in feet) of a rectangle that has the given area and a minimum perimeter.…

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Q: Suppose that f(x) and g(x) are given by the power series f(x) = 3 + 4x + 3x² + 2x³+... and g(x) = 6…

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Q: An irrigation channel is constructed by bending a sheet of metal that is 3 m wide, as shown in the…

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Q: Find the area of the shaded region below. УА x=y² - 4y (-3, 3) Area = = x = 2y-y² FI

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Q: equation and the initial condition. 8. f'(x) = 9x² + 1, f(0) = 7

A: Given problem:- Solve  f'(x) = 9x² + 1, f(0) = 7

Q: 8 765 4 3 2 1 -7-6-5-4-3-2 4 -2- -3 Clear All Draw: 4 -3 -6- 1 2 3 4 5 6 7 8

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Q: = ||r' (t) x r' (t)|| ||r' (t)||³ to find k(t). r(t) = 7 cos(9t)i + 7 sin(9t)j + tk Use the formula…

A: find curvature