Find a formula for the nth partial sum of the series and use it to find the series' sum. 9. +... +(- 1)" -1 5n-1 9- 1. 25 125 1 9 1- (-5) 45 (-5)" 15 O A. S= OB. 1+ 91- 91- (-5)h-1 (-5)-1 15 45 O C. Sn= O D. S,= 1 4. 1+5 1 1+

Q: 5 Problem # 1: Differentiate y : /2х+3 Solution: Answer: Problem # 2: Differentiate f(x) = (3x – 2)…

A:

Q: Find the general solution of the given system. 10 -5 X' = 8 -12 X(t)

A:

Q: Problem 2. Which gives the inverse transforms of the given s-domain function? s2-s3+3/s3(s+5)(s-2)

A:

Q: Evaluate the line integral L(r – y*)dx + (1+ y² + =*)dy, where Cis the circle of radius 2 centered…

A: We have to evaluate the value of the integral

Q: Find the cofactor of the element a13- -2 -1 0 5 4 2 3 5 O A. 3 О В. 19 ОС. -3 O D. 14 3.

A: Given a square matrix, the cofactor of aij is denoted by Aij=(−1) ^(i+j)M where Mij s the minor of…

Q: 1. Which of the following is a function а. у%3D х2 — 5ху b. х2 — 5х + 4%3D у с. у? 3D х2 d. y? = 3x…

A:

Q: The evaluation of So So x y e**dxdy is 0.5 e 0.25 e - 0.5 O e - 0.25

A: Double integral

Q: sinx So Sa* y dy dx fi dx dy 3. 4-

A:

Q: Find an equation of the plane through (-2, 8, – 5) that is perpendicular to the planes 2x – y + z =…

A:

Q: 1. Given: r(r+8)(r – 2) (r+2)³ 8(7r-4) (x+2)4 f(r)= with f'(x) = and f"(x) = %3D %3D (r+2)² ' a.…

A: Given that the function is fx=x3-4x2x+22 its first derivative and second derivative is…

Q: Convert xy = 7 to an equation in polar coordinates in terms of r and 0. %3D (Express numbers in…

A: Using poler coordinate

Q: Find the gradient of the function at the given point. g(x, y) = 11xe/x, (4,0) Vg(4, 0) =

A:

Q: Find an equation of a plane containing the three points (-5, -4, -3). (-10, -3, -1), (-10, -2, 1) in…

A:

Q: Find the point where the function f(x,y, z) = x + 2y + 3z subject to the I takes on its minimum…

A: The given function is f(x,y,z)=x+2y+3z.

Q: -15 n answer does not exist, enter DNE.)

A:

Q: 2. f(x) = x² - 5x + 6 A. x = 1 B. x = -3

A: This is a problem related to limit and continuity parts of the calculus. Based on the general…

Q: (2x - 5y + 3)dx - (2x+4y - 6)dy = 0

A:

Q: 5. y = 4x – x², x = 0 , y = 4 , revolved at y axis -

A:

Q: Does the following series converge or diverge? 4. 4h n= 1 O The series converges. O The series…

A:

Q: 3. Determine whether the following series are odd or even functions. i. f(x) = x² ii. f(x) = x³ iii.…

A: We have to determine whether the given functions are even or odd.

Q: Which method/s can be used to find the volume of solid of revolution of the following? (Choose from:…

A: Note: we have to solve only 1 question so here 1,2 are related so I solve 2 question. Also breif…

Q: Which method/s can be used to find the volume of solid of revolution of the following? (Choose from:…

A:

Q: 3" Use the Ratio Test to determine whether the series is convergent or divergent. En=1 (2n)!

A:

Q: how long will it take for 16200 to double if it is invested at 5.5% compounded quarterly

A:

Q: A 1+ 2 + 3 + 4+ + 127 Σ > B, where .. n=1

A: First trace the rth  term then use the summation notation.

Q: (y?ty)dx - (x² x ) dy = o

A:

Q: 11. Let b be a real number with b > 1. Determine whether > 1 converges or diverges. As part 1+ bk…

A:

Q: Salve the differential equation with appropriate method. Finalize answer equated to ky^n. dy/dx + y=…

A: Let's find.

Q: Calculate -3 + li. Give your answer in a + bi form. In polar form, use the angle 0 < 0 < 27. a = b =

A: This question is based on conversion of rectangular form to exponential to polar form of complex…

Q: ORegion hamded. by. S=-xrd 33-X=4

A:

Q: (-1)" Given: In(1+ x) = > if |a| < 1. n + 1 n=0 3. Use the third degree Maclaurin polynomial of f to…

A: We can solve this as follows:

Q: Use the given graph of f to state the value of each quantity, if it exists. (If an answer does not…

A:

Q: In an insect colony, there are 290 insects after 6 days. If there were initially 80 insects, how…

A:

Q: A projectile is shot from a cannon. The fixed parameters are the acceleration of gravity, g = 9.8…

A: It is given that a projectile is shot from a cannon, the muzzle velocity is v0=500 m/sec at which…

Q: 1. Using Lagrange multipliers, find three positive numbers whose sum is 18 and such that the sum of…

A: The Lagrange multipliers method is a strategy for finding local maxima or minima of a function using…

Q: y' + y = sin x.

A:

Q: 109 109 Suppose that > a; = -13 and > bị = 16. Comp i=1 i=1 the sum. 109 2 (8a; + 24b;)

A: ∑i=1109(8ai+24bi)=∑i=1109 8ai+∑i=1109 24bi=8∑i=1109 ai+24 ∑i=1109 bi

Q: Find the directional derivative of the function at P in the direction of v. h(x, у, 2) %3D хуz, Р(5,…

A:

Q: Does the following series converge or diverge? 1 Σ 2+7n In n n= 1 The series diverges. The series…

A:

Q: Barbara boards a Ferris wheel with a 50-foot radius. The center of the Ferris wheel is 60 feet above…

A: Given information:…

Q: Find the vector equation for the line of intersection of the planes 2x – 2y – 5z = 5 and 2a + 2z = 1

A: Given  equation of planes 2x-2y-5z=5 2x+2z=1

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: Let's find.

Q: Use Lagrange multipliers to find the maximum and minimum values of subject to the given constraint.…

A:

Q: For each of the following functions, determine whether the function is: • Injective (one-to-one). •…

A: We have to check whether the function is Injective, Surjective or Bijective.

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

A: To use Lagrange multipliers to find the indicated exrema, assuming that x and y are…

Q: Evaluate the indefinite wntegral 3tinigas 3. xIn X

A:

Q: You have $7000 to invest for seven years. Which investment will provide the greater return:  5%…

A:

Q: 5. Given the function as f(x,y)=\x² +y² then find the a) Rate of change of f at point P(1, ) in the…

A: This is a problem related to derivative of the function. Based on the general formula we will solve…

Q: Integrate x sqrt of (x+4) dx using algebraic substitution

A:

Q: Question 6 Differentiate: arcsin () + arccos (2) = 1 + arccos () = 1 %3D O y/x O (E) None of these O…

A: Derivative dydx of sin-1xy+cos-1yx=1