6)    State whether the series converges absolutely, conditionally, or not at all. ∞ n = 1 (−1)n + 1 1 n + 9  The series converges absolutely. The series converges conditionally.     The series diverges. please shoow step bys tep .

Q: Fill in the blank. (Enter your answer in terms of t.) 1 "ਜ + na =

A:

Q: The area under one arch of y=sin(0.5x) is O 0.2 O 0.5 O 0.8 None of them

A: Given: y=sin(0.5x)

Q: Use the properties of the derivative to find[r(t) × u(t)] given the following vector-valued function…

A: As we know that; The Sum/Difference Rule: f±g'=f'±g' The Power Law: ddxxn=nxn-1 And a·f'=a·f', where…

Q: 1. Choose a solution to the differential equation y" - y = x²e² + 5.

A:

Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. r = 4 cos 0 -…

A:

Q: f(x) = 2x^3 − 3x^2 − 18x − 8 Factor f(x) into linear factors. Don’t forget to include the leading…

A: Please see the below picture for detailed solution.

Q: Mark the critical points on the following graph. 20 16- -5 -4 -3 -2 -1 12 18 4 T -8 -12 Clear All…

A: The objective of the question is determine the critical points of the given graph.

Q: appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace 1 { (s² + 1)(s² + 25).

A:

Q: 7 My Drive Computers Shared with me Recent Starred Trash Storage Buy storage 1 Screenshot (16…

A:

Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 16x2 +…

A:

Q: Approximate the area under the curve graphed below from x=2 to x = 6 using a Left Endpoint…

A:

Q: Find the equation for ​(a) the tangent plane and ​(b) the normal line at the point P0(1/2,1,e) on…

A:

Q: Find V. (Fx G), if F(x, y, z) = 4xi+j+13yk and G(x, y, z) = xi + yj – zk. V. (Fx G) =

A:

Q: Answer true or false. If f is not piecewise continuous on [0, co>), then L{f(t)} will not exist. O…

A: For the solution of the problem follow the next step.

Q: Test for convergence or divergence: e me emrin n=1

A: Find the limit as n tends to infinity

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = (et-e-t)² L{f(t)}…

A: Given function f(t)=(et-e-t)2  f(t)=e2t+e-2t-2×et×e-tf(t)=e2t+e-2t-2   Formula L(eat)=1s-aL(c)=cs

Q: Talse. If f is not piecewise continuous on [0, co>), then {f(t)} will not exist. True False

A:

Q: Find the general solution to the linear differential equation: y" - y' - 2y = 0 O y = C₁e²x + С₂е¯x…

A: Given that a linear differential equation y''-y'-2y=0. We need to find the solution of this linear…

Q: Given the function below f(x) = -324x³ + 1053 Find the equation of the tangent line to the graph of…

A:

Q: curl(9z i+ 10x j + 4y k). (9z i+ 10x j+ 4y k) = ( i Textbook and Modia )i + (i )j + (i

A: To find out the curl of the given vector.

Q: (a) ах = Du DE = du, ada voa waye by oz + + + 2x DE 2. (x²= y² + x) x (2x+₁) + (-2xy-9)x (-2y) (2x +…

A: We have to simplify (x2 - y2 + x) × (2x + 1) + (-2xy - y) × (-2y)

Q: Use substitution method and find the indefinite integral Adx

A:

Q: Find an equation of the tangent line to the graph of the function at the given point. y = 8x…

A: Given: y=8x arccos(x-1) and point (1,4π)

Q: Evaluate the following integral. Sx² e 19x dx --- 2 Let u=x. Use the integration by parts formula to…

A:

Q: Find the sum of the following: 1 Σ 5n² +5n n=1 a. b. n=1 3+2-1 4n

A: a) ∑n=1∞15n2+5nb) ∑n=1∞3+2n-14n series converges: The series  ∑n=1∞an converges to k, then the…

Q: Find the value of (2) for a solution (x) to the initial value problem: y" + 4y + 4y = 2x + 6; y(0) =…

A:

Q: The shaded area bounded by y=x^2 and y=x^3 is 0.016 0.083 O 0.055 O 0.16 (1, 1)

A:

Q: Consider the function f(x) = 6 - 7x² on the interval [ — 4, 3]. Find the average or mean slope of…

A:

Q: The formula for the volume of a cone is given below. Find the rate of change of the volume for each…

A:

Q: Find r'(t). NOTE: Enter your answer in terms of i, j, and k. r'(t) r(t) = (tan−¹(5t))i+t cos(t)j —…

A:

Q: 2. Let f(x) = 2x²-3x+1 ,x 0.5 Determine constants A and B such that is continuous for all values of…

A:

Q: Mark the critical points on the following graph. 2²e-², 6,0.3 34 2.7 2.4 2.1 1.8 1.5 1.2 0.9 10.6 Q3…

A:

Q: 1 *{{37² +3=6} S

A:

Q: Given: f(t) sint cost. Evaluate: F(2) Use 2 decimal places. 0.13

A: Given data÷ ft=sintcost We need to find F2=?   Useful trigonometry relation÷ 2sintcost=sin2t…

Q: A 4-pound weight stretches a spring 2 feet. The weight is released from rest 15 inches above the…

A: Given that, A 4-pound weight stretches a spring 2 feet. The weight is released from rest 15 inches…

Q: Evaluate dw/dt at t=9 for the function ​w(x,y)=ey−ln x​;  x=t2​, y=ln t. Options are: 1) 7 2)…

A: Given query is to find indicated derivative.

Q: 5. Use the definition of a Maclaurin Series to express f(2) = as a Power Series. Give the 8th degree…

A:

Q: Solve the given initial value problem. 0x²y² + xy³ = 2 0x²y² + y² = 3 ○ xy² + xy³ = 0 Oxy²y³ = 1…

A:

Q: Evaluate 09 9121IN N OC 2 01 2 1 2 I -1²-2 dydx.

A: Given query is to find the value of the integral.

Q: Solve the given differential equation. All solutions should be found. dy dx e5x+10y ot (1603) NOTE:…

A:

Q: Use integration by parts and find the indefinite integral f(x+2)e dr

A:

Q: Determine whether the series Σ=1 (Limit Comparison Test) 2n²+3n √5+n5 converges or diverges.

A: Given :∑n=1∞2n2+3n5+n5

Q: (x-2y) dx + (2x+y)dy = 0 TEST FOR HOMOGENEITY OF DEGREE N: Let: F(x,y) = M(x,y)DX + N(x,y)dy…

A:

Q: Which of the following is not a unit vector? 2 A. • (-3/35.0,-/) √5' √5 B. (cos 1, sin 1, 0) C. (1,…

A:

Q: Given [*₂h(t)dt = -5 h(t)dt = 22 and evaluate the following integral. ["h(t)dt = | [h(t)}dt h(t)dt =…

A:

Q: Find the curvature and the radius of curvature at the point t = 0. et cos(t), y et sin(t), z = 9et K…

A:

Q: 6. Use an integrating factor to solve the following first order differential equation (x² + 1) + xy…

A:

Q: lar solution uch that y(1) = 0 lar solution )dx when x = 2, y = 3 om separating the variables of the…

A: We have to find the solution of the given differential equation according to the given information

Q: Which of the following functions are solutions of the differential equation y" - xy + y=0? Oy=1-22…

A:

Q: Find the divergence of F(x, y, z)= x î+y³ ₂² 7 +xz³ k. O1+3y²z²+3xz O1+3y²z²+3xz² 01+3y²₂² O 1

A: