∞ (b) Σne-ni n=3 Does each of the following series converge or diverge? Why? Show all your work and MUST include the name of the convergence test you are using. (Your best three answers will be counted toward your grade. The 4th will be for extra credit) Recall: Here is a list of convergence test we have learned so far: I: Test of Divergence (or Divergence Test) II Integral Test III Direct/Limit Comparison Test IV Alternating Series Test(AST) V Well-known series V(a) Geometric Series V(b) p-Series

Q: 1. profit function for the sale of S21 is as follows: л(q) = −2q² + 350q - 150 The selling price per…

A: a. Total Cost function:The total cost function represents the total cost incurred by the firm in…

Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent: Σ n²…

A: Step 1:if series is cgt then lim an=0 Step 2:arctann range is -pi/2 to pi/2 so series is less or…

Q: Question 2. Solve all clean handwriting

A: Question 2.1 Consider the sequence: 1/2; 4; 1/4; 7; 1/8; 10; ...2.1.1 If the pattern continues in…

Q: An automobile company is ready to introduce a new line of cars through a national sales campaign.…

A: Step 1:Step 2:Step 3Graph of corresponding s(t) using desmos Step 4: After rounding, 7.52 months.

Q: Consider the integral functional I(u = [ £{√1 √1+ [u'(x)]² dx Solve the minimization problem…

A: Step 1: Set up the Euler-Lagrange equation. The Lagrangian function is: L(x,u,u′)=1+[u′(x)]2​ The…

Q: Find the vector equation that represents the curve of intersection of the cylinder x² + y² 4 and the…

A:

Q: y= 5x + te x -5x

A: y=e5x+e−5xxdydx=ddxe5x+e−5xxQuotient Ruleddx[f(x)g(x)]=g(x)f′(x)−f(x)g′(x)[g(x)]2

Q: Consider the following graph on the interval -180° 13

A: As you have already able to figure it out amplitude and period , lets find out the equation, The…

Q: Please solve the following calclus 3 problem: show all work by hand and follow all the steps.

A:

Q: Find the lowest value of y = 8 +x 6 in the interval ≤ x ≤4. 2

A:

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = In(x² +…

A: Step 1:Step 2: Step 3:Step 4:Comparing the values:ln⁡(11/4)≈1.0116ln⁡(3)≈1.0986ln⁡(23)≈3.1355So, the…

Q: The equation x³ + y5 + 7y = 9 implicitly defines y as a single function of x at and near the point…

A: Now, we use the linearization formula: y≈f(a)+f′(a)(x−a) Where:a = 1f(a)=1f'(a)=−1/4x=1.18Plugging…

Q: As machines get older, the cost of maintaining them tends to increase. Suppose for a particular…

A:

Q: Consider the equation below. r = 11 4 + 2 cos(0) (a) Find the eccentricity. e = (b) Identify the…

A:

Q: Consider the following. u = (2,-1), v = (4, 1) (a) Find u . v. U⚫v= (b) Find the angle between u and…

A: Step 1: Given vectors are;u= <2,−1> and <4,1>∴u=2i^−j^​ and v=4i^+j^​ Step 2:…

Q: series calculus 2

A:

Q: Q3 please

A: Step 1:

Q: Is this correct?

A: (a)Integrating the given velocity…

Q: Use the shortcut rules to mentally calculate the derivative of the given function. 1 f(x) = X + + 1…

A: We are tasked to find the derivative of the function "mentally".  Let's look at the first term.…

Q: For the vectors p = [1,-2,3], q=[2,1,3], and r=[1,1,0], determine if the following is true: (p x q)…

A: Step 1: Not true  Step 2: Step 3: Step 4:

Q: Use four rectangles to approximate the area of the planar region under the graph of f(x) =…

A: Step 1: Find the length of the subintervals The formula is△x=nb−a​ We have a = 2, b = 9, and n =…

Q: The total daily cost (in dollars) of producing x park benches is given by C(x) = 1000+15x+0.1x² B.…

A:

Q: 10. Sally reasoned that if she drove 30 km/hr in one direction over a 180 km distance, and then…

A: Approach to solving the question: Detailed explanation: Examples: Key references:

Q: 9. Describe in words and a simple sketch the solid given by the following inequalities (a) 0p≤2, 0…

A: The objective of the question is to describe and sketch the solid defined by the given inequalities…

Q: 2. The following table shows the estimated populations and annual growth rates for four countries in…

A: Answer 2)To find the expected population of each country in 2025, we will use the formula for…

Q: 3.) Find the indefinite integral: √ 3π² + 3x √1- 3 + dx x²

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the intervals on which the graph of f is concave upward, the intervals on which the graph of f…

A: The objective of this question is to find the intervals of concavity and the inflection points of…

Q: Obtain the derivative dy/dx. dy dx y = 13 State the rules that you use. (Select all that apply.)…

A: Step 1:To find the derivative dxdy​ of y=13, we'll use the constant multiple rule. The constant…

Q: Find the points on the given curve where the tangent line is horizontal or vertical. (Order your…

A:

Q: + O 5) Find the volume of the solid under the surface f(x, y) = 1-xy and over the region bound by…

A: The objective of this question is to find the volume of the solid under the surface defined by the…

Q: Find the largest value of the function f(x) = x³ — 4x² – 10x + 5 - - on the domain -6≤ x ≤ 6.

A:

Q: Use the shortcut rules to mentally calculate the derivative of the given function. f(x) = 2x4 +9x³ –…

A: The objective of this question is to find the derivative of the function f(x) = 2x^4 + 9x^3 - 1…

Q: Evaluate the indefinite integral ∫sec^7x * tan^3xdx

A: SOLUTION

Q: Here, l1 and l2 indicate the lengths of the thick lines in meters (m). If these lengths are fixed…

A:

Q: 4. Find the work done when a constant force of 100 N is applied to move an object from x = 2 to x =…

A:

Q: Solutions to question 3 please

A: Step 1:(a) f(x)=apx+q .........(1)  We know that the derivative of ax is axln(a).   Step 2:So,…

Q: Solve (t² + 4) da = (x² + 16), using separation of variables, given the inital condition x(0) = 4. x…

A: To solve the following initial value problem by using separation of variables.

Q: Use the graph of g in the figure to do the following. a. Find the values of x in (-2,4) at which g…

A: Thank you

Q: Q1 please

A: Step 1:As you ask question 1, I solved it but if you need other parts you can ask.

Q: 8. Suzanne told her friend Johnny that he needed to know for the calculus test that the derivative…

A:

Q: Use the product rule and/or the quotient rule to compute the derivatives of the following functions.…

A: Step 1:      Step 2: Step 3: Step 4:

Q: Find the average rate of change for the following function. f(x)=5x³-3x²+2 between x = -2 and x = 3…

A: The formula for the average rate of change is: Average rate of change=b−af(b)−f(a)​ Where: a is the…

Q: Find the maximum and minimum values of the function g(0)=30-7 sin(e) on the interval 0, T 7 2…

A:

Q: lim (-3x+16) x→7 >>> Question Details Done 4. Approximate the limit using a table or graph. Make…

A: Given:Function: f(x)=−3x+16limx→7​(−3x+16)Step 1: Substitute the value into the function. When…

Q: Make a graph on the third eye of the universe, (Sorry, little glitch, question is in the photo.)

A:

Q: Find the exact location of all the relative and absolute extrema of the function. Your instructor…

A:

Q: Find the average rate of change for the given function. f(x)=√5x+1; between x = 0 and x = 7 The…

A:

Q: Find the derivative of the function. 3 In 2x y= 4+5x dy | dx ||

A: Step 1:

Q: (4) Let C denote the following disconnected surface: C = {(x, y, z) = R³ | x² + y² = 1Ux² + y² = 4,…

A: Step 1:(a) To sketch the given surface C, we have a cylinder with radius 2 (inner cylinder) and…

Q: Consider the series n=1 (2x)n n2

A: The objective of the question is to determine the values of x for which the Ratio Test is…