Step 1 To evaluate the sum Si, the following property of summation can be used to find the sum. Σ Σ I= 1 24 Using the above property, s- Submit Skip (you cannot come back)

Q: Find the Maclaurin series for the given function f(x) = e-6x

A: The maclaurin series is: f(x)=e-6x     ,    f(0)=1f'(x)=-6e-6x     ,    f'(0)=-6(1)=-6f''(x)=36e-6x…

Q: Find the volume of the solid that results when the region bounded by y = Vā ,y = 0 and æ = 4 is…

A: Volume

Q: Determine whether the diff eq. is exact. If it is, find the general solution.

A:

Q: A physical education teacher found that 62% of the students exceeded the minimum standards. Which…

A:

Q: Consider the graph and determine the open intervals on which the function is increasing and on which…

A: Here to of the function is at point (1,5), On left side function is increasing ,and at right side…

Q: 12. Solve the second-Order differential equation:- y = e* (use method of variation of parameters)

A:

Q: Determine "k" so that the vectors 3a- 4b and 5a+ 2k b are collinear. Justify your response.

A: Topic = Vector

Q: Use the integral test to determine whether the series converges. Σ 4n - 1 n=1 converges diverges

A:

Q: Use the Root Test to determine whether the series convergent or divergent. 00 n2 + 6 Σ 2. 5n + 2 n =…

A: Given: Here, an=n2+65n2+2n.

Q: • Find the volume of a solid generated by rotating: Complete and chronological solution: 1. Region…

A: Solution is given below:

Q: Prove i = [- 2,5, 1], = [2,1, – 1] and w = [-6,0, – 12] are orthogonal. %3D %3D %3D

A: SEE ATTACHMENTS

Q: Consider the function f(x) = 9x° + 9x® – 6xª – 5. - 5. - Enter an antiderivative of f(x). Do not…

A:

Q: 3/2 <(のーメ)CK dx 2. 2.

A:

Q: 12. Solve the second-Order differential equation: -y = e* (use method of variation of parameters) dr

A:

Q: An object weighing 1000 pounds sinks in water starting from rest. Two forces act on it, a buoyant…

A:

Q: 10 Evaluate the summation i. i=1 55 10 1

A:

Q: A particle is moving with acceleration = 6t + 12. its position at time t = 0 is a(t) s(0) = 5 and…

A: First use the integration to find the velocity then again integrate to get the position function.

Q: A firm estimates that it will sell N advertising, where dollars. Use the derivative to find the…

A:

Q: A stone is thrown straight up from the edge of a roof, 950 feet above the ground, at a speed of 12…

A:

Q: Determine how many acres are in 6.7312 x 10" square kilometers. What is your calculated answer most…

A: Given query is to convert square kilometres to acres.

Q: Let u = cos(r + y), x = 2st +t and y = t – 2s. Use the chain rule theorem to compute du for du and…

A:

Q: 3x + 1 Consider the function f(x) Compute each of the following. Simplify your answer and use x - 3…

A:

Q: 3. Anabelle would like to invite 9 friends to go on a trip but has room for only 5 of them. In how…

A: We can solve this as follows:

Q: 7x-4y-3z = 21 -4x+7y-z = 0 -3x-y+5z = 0 x, y, z?

A: Given

Q: 5. u = 2i, v = -3j

A:

Q: Find Σ +i . Ο 30 Ο 31 Ο 32

A:

Q: Let f(x) = 4x^2 – 7x. Use the ɛ/d-definition of the derivative to prove that f(2) = 9.

A:

Q: Region bounded by y = x* +2, y = x+4 rotated about the x-aKis 2.

A:

Q: Consider the series E (-1)"(3x+6)" . Find the series radius and interval of convergence, n=0

A:

Q: AShift

A:

Q: At how many point(s) does the helix with vector equation r(t) : (cos t, sin t, t) intersect the…

A:

Q: it is always that when the series equal to zero it converges and when it is nonzero it diverges ?

A: For a series to be convergent we must have limn→∞an=0. But the converse is not true.  For example:…

Q: 1. Find the slope of the line tangent to the graph of the function defined by f(x) = 4 + 2x - x2 at…

A: As you mentioned only 1 solved

Q: Sketch the following points in space three, A (4,5,3); B (1,7,4) and C (2,4,6). Prove that point A,…

A:

Q: Find (3+2) - 2i . 406 754 386

A:

Q: 5. Evaluate the expression without using a calculator. Sh (a) sin (쓰) (b) cot(-210°) (c) csc(cos-1…

A:

Q: The following is the graph of a function f(x). -5 -4 -3 -2 -1 2 4 5 -2 -3 -4 -5 Clear All Draw: a.…

A: Given problem:-

Q: 9. (Trigonometric Substitution) Let x = 2 sin(0) for 0 < 0 < . Write v4 – x2 as a trigonometric…

A:

Q: Solve the following differential equation y"+2y' +y=x-1 Select one: O a. YG.S= Ce¯+c,e¯2x+x-3 O b.…

A:

Q: The normal line to the curve y = -2x2 at a point in the fourth quadrant passes through the point…

A:

Q: Use a graph to determine whether the given function is continuous on its domain. H Sx + 2 if x < 0…

A: Given query is to find function is continuous not.

Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

A:

Q: 23. Find the angle between the vectors i = [-9,1, 3] and i = [0,2, – 5]. %3D

A:

Q: Determinant of n x n Matrices. Solve for the determinant of the following matrices using (a)…

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

Q: 1. Consider the function f(x) =-2(3x– 3)* + 1. a) State transformations. b) Use TWO of the following…

A:

Q: —x2 — 4х + 18 (Зх+ 4) (x? + 9)"*

A:

Q: (1) Which is the correct formula for finding the derivative of the product of two functions? O (fg)'…

A:

Q: Find an equation of the circle that satisfies the given conditions. Center (-1, 6); passes through…

A:

Q: 8. S 3tan 3z r sec? 32 da

A: As per the guidelines I can solve only first question

Q: 11. Rules of Definite Integrals: I f(x)dx = 6, and "f(x)dx = 4 , find the following: a) c)

A: