Determine whether the series is convergent or divergent. Σ 122 O convergent O divergent If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.)

Q: 3. In evaluating the integral ſ x²dx (x-1)²(x²+1)' you will decompose x²dx (x-1)²(x²+1) into simpler…

A:

Q: 1. If g (2) = 59 and fg'(x) dx = 25, what is g(5)?

A: Since you have posted a multiple question, we will solve the first question for you. If you want any…

Q: The lengths of the edges of a cube are increasing at a rate of 1 ft/min. At what rate is the surface…

A:

Q: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a…

A: The Maclaurin series for f(x) is given by f(x) = f(0) + f'(0)1!x + f''(0)2!x2 + f'''(0)3!x3 + …

Q: xdy-[y+xy' (1+ In x)]dx=0 is

A:

Q: Find T(t) and N(t) at the given point. r(t) = 6 cos(t)i + 6 sin(t)j; t = T(-₁) = (53) 3. N(₁) = Z =…

A:

Q: 1. A bumblebee was released and started to travel along a straight horizontal line. The directed…

A:

Q: Scos2x (2 2 Cos 2X (2 cos 2X -1) dx

A:

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. If it…

A:

Q: XB-5 \\f(x) #3 g(x) Find the area enclosed between f(x) = 0.6x² + 10 and g(x) = x from x = −5 to x =…

A: The given problem is solved below in detail.

Q: = fx x²zdx- dx − yx² dy + 3 dz along the curve C shown in the figure. - Z 2 2 [x²zdx - yx² dy + 3 dz…

A:

Q: Using trigonometric substitution to evaluate: find x * S dx, √x²+16 x4 O x=4 tang O x=4 sing Ox=4…

A:

Q: Solve the following Bernoulli’s differential equations 2ydx + x (x^2 ln y - 1)  dy = 0

A:

Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

A:

Q: Use the formula k(t) k(t) = ||r' (t) x r"(t)|| ||r' (t)||³ - r(t) = t²i+t³j to find k(t).

A:

Q: [₁ 2x - x² dx

A: To integrate.

Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx.

A: This question can be solved using the concept of mid point rule of definite integrals.

Q: 2.S x² -4 X -dx

A: Note: Asper company guidelines, we are supposed to answer the first question only. Kindly ask the…

Q: Find the differential dy: y = In (sec² (3ª²–2x+5)).

A:

Q: Using n = 2 equal-width subintervals, approximate the area of the region bounded by the graph of,…

A: This is a problem related to reimann sum calculation. Based on the general formula and concepts we…

Q: A 6 inch by 6 inch piece of cardboard has square cut out of its corners so that it can be folded up…

A:

Q: 2ydx+x(x² In y-1)dy=0

A:

Q: Evaluate the iterated integral. 7 2 z z [ [²] ² 1 -1 J-y Y (-72+3 ln (7)) x dx dz dy

A:

Q: Evaluate [sin2xcos2x, dx 1 Acos4x+C 1 ® - cos4x+C B 1 -cos4x + C Cos 1 -cos4x + C

A:

Q: 49³y dx3 - 13 dy+ dx + 6y = 0

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

Q: 1. fx² In x dx = f x² dx f In x dx (In x − 1) + C Is the solution correct? If your answer is yes,…

A: We have to give reason and then solve the integration .

Q: A Ferris wheel at a carnival has a radius of 27 feet. Suppose a passenger is traveling at 9 miles…

A:

Q: Let f(x)=x²-x²-1 and Xo = 1. To the nearest three decimal places, find X5 using Newton's method of…

A:

Q: Suppose that z = x³y², where both x and y are changing with time. At a certain instant when x = 2…

A:

Q: Let f(x) = 5 on [−3, 1]. x+5 Find all numbers c in [-3, 1] for which the derivative is equal to the…

A: We are given a function f(x) = 2/(x+5) on [-3, 1].   We have to find all the c in [-3, 1] such that…

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

A:

Q: 6. Use Green's Theorem to find the counterclockwise circulation and the outward flux for the field F…

A: This is a problem related to vector calculus. based on the general formula of green's theorem we…

Q: x1/2 dx x3/4 + 1 Let x = z8 dx = 8z7dz Is the substitution the most appropriate one? Explain your…

A:

Q: A cylindrical can, open at the top, is to hold 800 cm³ of liquid. Find the height, h, and the…

A:

Q: 17. Evaluate the line integral xezds, where C is the line segment from (0,0,0) to (1, 2, 3).

A:

Q: 14. Which of the following has ex³-¹as an antiderivative? A. x²x¹-1 B. 3x²x³-1 C. 3xe*¹-1 D. xex -1

A:

Q: compute the surface area of example 9.10.2 by rotating f(x) = √x around the x-axis

A: Given

Q: HOW ALL WORK sing Standard Labeling, solve the triangle with ß = 56°, a = 6, and c = 8. Round…

A: Given query is to solve the triangle.

Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where 0 ≤ t ≤ 1. [(x + 3y²) dy

A: We can solve this as follows:

Q: Kuya Bill is selling 'Bill phones'. If the cost for selling a phones is given by 10000 C(x) = 120x +…

A:

Q: 2. dx 1+√√x

A: integration

Q: 21. SHOW YOUR WORK Solve the system of equations in three variables: x - 3y + 2z == 10 2xy + 3z =- 9…

A:

Q: Using trigonometric substitution to evaluate:, find dx * √x + √2-x² dx, O 3 cosø dø O 3sec^2 Ø dø O…

A:

Q: Let f(x) = √√√x – 2. a) Find f(x + h): b) Find f(x + h) - f(x): c) Find_f(x+h)-f(x). h d) Find…

A: We have to solve multiple part

Q: Find Vf if f = 2 2 2 x² + y² + z² V.

A: Given,            f=1x2+y2+z2To find : ∇f

Q: 'ind the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A:

Q: 3. In evaluating the integral S fractions. Let x² dx (x-1)²(x²+1)' you will decompose x² dx…

A:

Q: 5. Consider the surface obtained by rotating the graph of f(x) = 1/2, 221, around the z-axis. This…

A: We will show this using integration ∫1∞1xdx = ln x1∞ = limx→∞ln x = ∞

Q: 3. f(x) = 3+ |2x − 4|, a = 2;

A:

Q: Derive the following funtion. Basic rule should be applied. y=x+ √ x

A: