Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.) 6+5+ 25 125 + +... 6 36

Q: 1. Find fr (1, 1) and fr (1, 1) where f(x, y) = 6√/2x4 + y³ − 2x+5xy.

A:

Q: Given √,³ 0-12 f(x)dx = 8 and g(x)dx=-4, what is -4 4 12 √,³ (g(x) − f(x)]dx?

A:

Q: Write out the first five terms of the sequence with, [(1)"] determine whether the sequence…

A:

Q: Use only the properties of summation to evaluate the sum. Use the summation capabilities of a…

A: ∑i=116​(5i−4)= 616 (verified by wolfram alpha graphing utility) Explanation:To evaluate the sum…

Q: Let ā = (1, 5) and 6 = (3,0). Find —ã – b. - - V Λ

A: Answer: <-4,-5>Explanation:For any query with the solution please ask in the comment box.

Q: R is the region bounded above by the graph of f(x) = 2x and below by the x-axis over the interval…

A: Region is bounded by f(x)=2x23 and below by the x-axis over the interval[0,3].Rotating the region…

Q: c) 18x-19 2x²-5x-3 dx

A: To evaluate the following integral.

Q: Oil is leaking from a tank. For 0 < t < 24, the number of gallons G in the tank at time t is given…

A: given function

Q: 12(a) sketch the Cardioid Ө r=1+ cos 0 b) Find the area of the region inside the cardioid r=1+ cos…

A: Given cardioid equation is

Q: se z = x² sin y, x = 1s² + 1t², y = -6st. the chain rule to find oz and as function: as Əz d the…

A:

Q: Demand According to economic theory, the demand x for a quantity in a free market decreases as the…

A: Given:the number x of DVD players people are willing to buy per week from a retail chain at a price…

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time interval…

A: Given that the a particle with position  as t varies,

Q: Let ā = (-1, -2, 2) and 6 = (0, 4, −4). Find the angle between the vector (in radians)

A: To find the angle between two vectors a→ and b, we can use the…

Q: Can you solve y = ln(2x-3)  in a simple fashion?

A: The solution is x = (ey + 3)/2.Explanation:We solve y = ln(2x - 3) for x  by eliminating the…

Q: Given that f(x) Lπx) dx = 6 and [F(x) (a) L₁ F(X 0 f(x) dx f(x) dx = 9, evaluate the following.

A:

Q: Use Green's Theorem to evaluate the line integral of F = (x5,2x) around the boundary of the…

A:

Q: 5 K 7 10

A:

Q: Example 1: z=x³y_x=2t and y=t² Find dz dt

A: since you have posted multiple questions in this question which are not interlinked so i have solved…

Q: 4) A company wishes to manufacture a box with volume 36 ft, has an open top, and is twice as long as…

A: Question No. (4): A company wishes to manufacture  a box with volume 36 ft3, has an open top, and is…

Q: (d) Horizontal asymptotes. (e) Intervals where f is increasing and decreasing. (f) Local minima and…

A: Given: To Find: To determine the following: (d) Horizontal asymptotes(e) Intervals where f is…

Q: A model of tumour growth under chemotherapy from time t = 0 to t = t₁ > 0 is dC C = -C log - dt Стах…

A:

Q: Verify the identity. Show that cos (p+q) cos (p-q) = cotp cotg - 1 cotp cotg+1

A: Need to verify the identity.

Q: Let a (5, 1, 1) and b = (- 5, 1, 2). Find a × b. x V A

A:

Q: Consider the indefinite integral 7x37x264x + 80 dx x²+16x2 Then the integrand has partial fractions…

A:

Q: Let f(x) = x|x|. (a) Sketch the graph of the function. 2 y У 4 2 2 y 4 2 y X y X J -4 -2 -2 2 -4 -2…

A: a)4th graph is correct answer b) Differentiable for all real x  c) f′(x)=2xExplanation:

Q: x+2 3 F) 2x-2

A: given equation

Q: 1. Explain how you can solve the equation graphically, then provide the solution. Algebraic…

A:

Q: Find f'(x). f(x)=4xex

A: The objective of the question is to find the derivative of the function f(x) = 4x * e^x. In…

Q: Find the curve's unit tangent vector. r(t) ti+ k. Osts3 The curve's unit tangent vector is (++ (k.…

A: The given vector valued curve equation is The unit tangent vector given by

Q: if f(x) = 2+2x - 4x sqaured find f prime of 5

A: The objective of this question is to find the derivative of the function f(x) = 2 + 2x - 4x^2 at the…

Q: Find f'(x) and find the values(s) of x where f'(x) = 0. f(x)=(2x-27)(x²+60)

A: given function

Q: X * 0 1 2 3 4 n Process Write a function representing the values in the table. 9.72 8.748 7.8732

A:

Q: Let f'(x)=2x²+3x²-12x+4. Determine the concavity of f(x) on the interval 1 <x<2.

A: We need to determine concavitey of f(x).

Q: P=2^(43112609)-1 Suppose you have traveled to a faraway place where the base of the number system is…

A:

Q: The differentiable functions f and g are defined for all real numbers x. Values of f, f', g, and g'…

A:

Q: Given the graph of f(x) at the left, determine the following: a. f(6) = b. lim f(x) = C. x-2 lim…

A: The answers are as follows: a.  f(6)=4. b.  limx→2​f(x) does not exist. c.  limx→6​f(x)=2. d.…

Q: Find four intervals on which f is one-to-one, making each interval as large as possible. Four…

A: Given graph of function f(x) to find the intervals on which f is one to one

Q: what technique should be used to evaluate these integrals a. Sx (cosx 2) dx b. Sx cos(x) dx √√√x…

A:

Q: If z = tan (金) and x = u² + v² and y = u² – v², find the - following partial derivatives using the…

A: Formula for the total partial derivative is given as follows

Q: Use the formula for the sum of the first n integers to evaluate the sum given below. 3+ 6+ 9 + 12 +…

A:

Q: Evaluate the indefinite integral. sec²(√x)dx

A:

Q: Let ā = (−4, −5, −3) and 6 = (-5, −4, 4) Find a × 6. V >

A:

Q: #1: By Taylor's theorem, we can find a Taylor polynomial P3(1) of degree 3 for the function g(t) =…

A: hello i have attached written solution below please rate helpfullExplanation:hope it helps

Q: The total sales of S (in thousands of DVD's) of a certain movie are given by the following formula…

A:

Q: Find dy dx if y = √Inx +1. 1 dy dx 2 x √In(x)

A:

Q: Use the given information to find the exact function value. Simplify your answer as much as possible…

A: Given that the expression

Q: Let f(t) be the temperature at time t where you live and suppose that at time t = 2 you feel…

A: Given that,f(t) be the temperature at time t where you live and at t=2 you feel uncomfortable.

Q: I am needing assitance with the problem in the attached image, 2.8.

A: Limit at x tending to -5 exist and equal to 5 . At x = -5 f(x) is not continuous.Explanation:Step 1:…

Q: Its the same options for all of them

A: The objective of the question is to identify whether the given statements are correct or due to Type…

Q: Let a =. Find a unit vector in the direction of a

A: