Evaluate the following sums. 9 (2) Σ 3 k=1 500 (b) Σ 9 k = 1 264 (c) Σ k = 2 20

Q: Given f(x, y) = 3e¹2 sin(4y) then Vf(0, 1) - [

A: To find the gradient of the function

Q: 1. a) Solve the following differential equations: ydx x i) -1 (tan-¹x) dy = ydx x² +1 (In x)dy, b)…

A:

Q: Write out the first five terms of the sequence with, [(1 - 7)", determine whether the sequence…

A: To write out the first five terms of the sequence with 1-7n+7nn=1∞, to determine whether the…

Q: places. Find the direction in which the maximum rate of change occurs for the function f(x, y) the…

A: we will find the required

Q: If f(x) = 8 sin ¹(2³), then f'(x) = Question Help: Video Message instructor

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Suppose that we use the bisection algorithm to approximate r = √20 which the greatest zero of the…

A:

Q: A company wants to use data thas collected to predict customer satisfaction (as a percentage) based…

A: Please see the below answer.

Q: Centerville is located at (9, 0) in the xy-plane, Springfield is at (0, 4), and Shelbyville is at…

A: Let's say Centerville is point A (9, 0) Springfield is B (0, 4) And Shelbyville is C (0, -4) And the…

Q: 7. Find values of a and b that make the function below both continuous and differentiable at x =/…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the length of the curve Arc length: = y=e", 0 ≤ x ≤ 1.

A:

Q: Let f(x, y) = x² + 2y¹ + 40xy. List the critical points: The critical point at the origin is a…

A:

Q: Let 5xyz = e². дz Use partial derivatives to calculate - and ?х дz ду and enter your answers as…

A:

Q: The marginal cost of the xth box of light bulbs is 10 + C(x) = [In(x + 1)] (x + 1)² 7 and the fixed…

A:

Q: Describe the motion of a particle with position (x, y) as t varies in the given interval. (For each…

A:

Q: Let A = O 2√6 00 O-2 02 Note that the quadratic formula = O -1 2 3 -2√6 Find the sum of all…

A:

Q: Express the given equations in polar equations. x² + y² = 7 4xy = 3 (a) (b)

A:

Q: Use geometry and implicit differentiation to find the unknown rate. 21. A circle is shrinking,…

A:

Q: Let z(x, y) = Calculate дz მs дz Ət дz მs & 8x2 - 4y2 where X = 9s + 3t a y= ?х ду дх д' ' д дz Ət…

A: To find the partial derivatives

Q: Consider the following parametric curve. Find dy dx dx dy dx Find the value of dy dx x = sin(9t) +…

A: NOTE: Refresh your page if you can't see any equations. . substitute the given value of t

Q: Let f(x) = 2 sin(x). a.) |f'(x)| ≤| b.) By the Mean Value Theorem, f(a) − f(b)| ≤ la - bl for all a…

A:

Q: A local club is arranging a charter flight to Hawaii. The cost of the trip is $577 each for 81…

A: Given query is to find the maximum revenue.

Q: You and your friend are shopping at the the nearby Target store. You spent 78 dollars on 3 pounds of…

A:

Q: Find the limit of the sequence an = (−1)n-1n 3n² + 1 If the limit does not exist, type "Diverges" or…

A:

Q: Concept check: Evaluate the following integrals: 1. dx (6-x²)z OIL

A:

Q: Consider the function y = e. Find y'.

A: Given query is to find the derivative.

Q: Given a starting principal of $30000, and a nominal interest rate of 2.0% compounded monthly,…

A: Given query is to find the amount accumulated.

Q: A box with a square base and open top must have a volume of 78732 cm³. We wish to find the…

A: let  length of base = x  height = y volume V = 78732

Q: What is the independent variable in the given differential equation? ду at² O x Oy and t Ot x and t…

A: Given partial differential equation is ∂2y∂t2-4∂2y∂x2=0 We need to choose from correct option about…

Q: The position of an object in circular motion is modeled by the given parametric equations, where t…

A: We have given  x=2sin(π6t) y=2cosπ6t Comparing this with x=asinwt y=acoswt We  get,  w=π6 rad/sec…

Q: Given an interest rate of 5.5% compounded daily (ie: compounded on each calendar day), determine the…

A:

Q: (a) Show that if a varies, then the polar equation raseco (π/2<0</2) describes a family of lines…

A: Let's solve polar equation describes a family of lines perpendicular or parallel to the polar axis.

Q: Use the Integral Test to determine whether the infinite series is convergent. ∞ 7n (n2 +…

A: The given series ∑n=1∞7nn2+135 We have to find the convergent of the series using integral test.

Q: Find the two values of k for which y(x) = ekx is a solution of the differential equation y'' - 8y' +…

A: d dx(ex)=exy(x)=ekx

Q: Use the root test to determine if the following series converges or diverges. 16 Σ n=1 (6+(1/n))²n…

A:

Q: The graph shows the cubic function f (x) and the polynomial g(x). -10-9-8-7-6-5-4 3-2 f(x) 10 9 87 6…

A:

Q: coordinates are giv (a) (7,2π/3) (b) (2,17π/6) (17π/6

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Concept check: evaluate the integrals using the appropriate method: 1. | xe3xdx

A:

Q: reference and terminal point of 13pi/4

A: reference angle - angle between terminal arm and x axis let θ = 13π4

Q: For the sequence an = — 1)" 20 n²

A:

Q: Find the value of each expression without using a calculator. 1.) a. sin 180° b. cos 180° 2.) a.…

A:

Q: Evaluate the sum k(4k+5). 9 9 Σk(4k+5) = k=1 (Simplify your answer.)

A:

Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 600…

A: we need to find out the dimensions that will minimize the cost.

Q: Find the derivative of the function y = y' = || 9x² - 8 x² - 7

A:

Q: At the beginning of the day, Cher had 124 mules in her store. She sold 112 mules during the day.…

A:

Q: Question Differentiate the series represented by the function f below term-by-term to find the power…

A:

Q: 1. Determine what type of conic the equation 9x² - 4y² + 54x + 16y + 29 = 0, represents, find all…

A:

Q: Use the table below to find X f'(x) g'(x) 1 2 1 [1.3f(x)] |x = 5 = 253 1 [1.3f(x)] dx 3 4 1 2 لی اند…

A:

Q: In order to find the area of an ellipse, we may make use of the idea of transformations and our…

A: The region R is bounded by the ellipse:(x-4)216+(y-2)21=1

Q: Find the mass of the ball of radius 2 centered at the origin with a density f(p,q,0) = 7e¯p³. The…

A:

Q: Using the transformation u = -x +y and v=x+y, set up the double integral needed to evaluate the…

A: