13. Determine whether ∞ Σ(-1)* k1/2 k=1 converges absolutely, converges conditionally, or diverges.

Q: Which of the following vectors is in the same direction as the vector a = 5i - 4j + 3k? Select one:…

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Q: Test the series below for convergence using the Ratio Test. n+ 3 3n+3 n=1 The limit of the ratio…

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Q: If z=x+iy where x and y are real, find the real and imaginary parts of:- 1 x² - y² (x² + y²)² X x² +…

A: The number is 1z2 where z=x+iy

Q: Let à = i-5j - 2k. Find |āl.

A: Using the formula if  a→= x i^ +yj^ +zk^then a→=x2+y2+z2

Q: dy Solve the differential equation = dx = -5x√y. √y = -5x² + Cor y = 0 √y = -5x² + Cor y = 0 2 √y =…

A: Here is the solution:

Q: If a xi = 0 and a x j = 0, then Select one: O a is equal to i + j a cannot be determined O a is…

A: Find out the correct option.

Q: Solve the given differential equation by separation of variables. e-y + e-5x - y exy dy dx

A: To find the solution of D.E.

Q: Find all the values of x such that the given series would converge. 5" (x")(n+1) (n+8) 72=1 The…

A: solution is given below

Q: Find the general solution of the given differential equation. 3 +24y = 8 dy dx y(x) = Give the…

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Q: Question 12 a) 3] Find the value(s) of y such that the vectors U₁ = and U₂ = are parallel. b) Find…

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Q: (m) X + x + 1 dx Oseparable exact Olinear in x Olinear in y homogeneous Bernoulli in x Bernoulli in…

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Q: y' = x - 4xy

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Q: The reverse order of 2 2 1 Jo Jy x 1 sinx cos dxdy is sinx cos dydx False True O

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Q: The graph off-1 is given below. Graph the tangent line to f-1 at the point P(1, 1) for f(x) = -x³ +…

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Q: Lim x tends to pi/4- (LHL) √(1-√sin2x)/(pi - 4x)

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Q: Simplify:- 16--// 5 2

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Q: dx dt Please give an exact answer. If z² = x³ + y², = dt 1, dy dt Provide your answer below: = -1,…

A: The objective of the question is evaluate the derivative of the given function at given point.

Q: Here are some patterns made from sticks. 8 8 Pattern 1 Pattern 2 a) Complete this table. Pattern…

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Q: Given the geometric sequence: 24, Find an explicit formula for an, where the first term is a₁ = 24.…

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Q: fins the voulme of the solid with cross-sectinal area A(x).   A(x) = x+2. -1 <x<3

A: fins the voulme of the solid with cross-sectinal area A(x).   A(x) = x+2. -1 &lt;x&lt;3

Q: X Evaluate the integral [sincos dx. X sin cosdx= 5 C

A: The objective of the question is evaluate the indefinite integral.

Q: 28. Using the method of "First Principles" and showing all steps, determine the -3 2x-1 properly…

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Q: Given f''(x) = - 25 sin(5x) and f'(0) = 2 and f(0) = -6. Find f() =

A: In this question, we want to compute the value of f at the given point.

Q: Use the Modified Euler method to approximate the solutions to each of the following initial-value…

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Q: O a = 5i - 4j + 3k and b = 15i 12j + 9k. -

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Q: (b) (c) dy dx separable 7 y-x exact linear in x linear in y homogeneous Bernoulli in x Bernoulli in…

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Q: ODE. Find the general solution of the following. Show complete solution v/x 3. (x + ye )dx-xe dy = 0…

A: Identify the differential equation and solve it

Q: Using Determination of Integrating Factors, solv y' = 2xy - x

A: Given differential equation y'=2xy -x

Q: L sin2t cos3t

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Q: The angle between the two vectors is not equal to Select one: O True O False u= and v= 0= π

A: Here we use the concept of dot product of the vectors.

Q: 8 Given g(x) = -2x³ + x, answer the following: Part: 0/3 Part 1 of 3 (a) Find g(-x). 8 (-x) =

A: We can solve the question as below.

Q: Problem 1. Solve these integrals using substitution (a) [ x(x r(x - 2)5dx, (b) [te²³² test dt.

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Q: 00 To test the series Σ as is the case with all series of this type.) According to the P-test: the…

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Q: The directional derivative of f(x, y) = xey + cosxy at P,(2,0) in the direction of the vector 3i -…

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Q: The Cartesian equation equivalent of polar equation r = 4tane sece is y True False O

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Q: F(x)=5cos(3x) on [-pi, pi] What intervals is f increasing and decreasing?

A: F(x)=5cos(3x) on [-pi, pi] What intervals is f increasing and decreasing?

Q: 6. Mr.Eltohamy is the quarterback of the MPM2D1 touch football team. During the game, he passed the…

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Q: H.W: find dz and dz as functions of u and v if: ди Əv z = 4e* ln y, x = ln(u cos v), y = u sin v

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Q: Let a be a real number. Evaluate the following integral: So f +ydady

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Q: Of all rectangles with a perimeter of 28​,which one has the maximum​ area? (Give the​ dimensions.)

A: We can find the dimensions as below.

Q: 4. Let the universal set U, and the subsets of U are A = {x|x is a letter of your first name}, B =…

A: Disclamier: Since you have posted a question with multiple sub-parts, we will solve first three sub…

Q: Q4\Use Cramer's Rule to find the values of x, y, and z from the following equations: 2x + 3y - Z = z…

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Q: 2. A function f:D →→ R is said to be a periodic function if there exists a positive real number p…

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Q: If the volume of the parallelepiped determined by the vectors A = i + ak, B = 8i - 5j + ak and C =…

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Q: Refer to the figure below. (a) Find the angle opposite the longest side. (b) Find the area of the…

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Q: If a x i = 0 and a x j = 0, then Select one: O O a is equal to k a is any vector perpendicular to i…

A: We know that if two vector are collinear then their cross product is zero, Therefore 'a x i =0 '…

Q: By using a cosine function find a formula representation of the graph in the given figure. Use ()…

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Q: For a given cylindrical tank, the radius is 7 m and the height is 15 m. The tank is filled to a…

A: Use workdone formula for finding the work

Q: The orthogonal trajectories of the family of curves r = c(cosec 0 + cot ) are given by: (a) ke-cos e…

A: See this solution in below

Q: Matrix has only one row call Row Matrix. multiply a matrix (A) by another matrix (B) if the number…

A: We check the given statements are True or False.