10.  Use the Integral Test to determine whether the sum converges. ∞     n = 1 n 9 + n2 Evaluate the following integral.   ∞ x 9 + x2 dx   1

Q: radioactive cesium-137 has a wide variety of uses and is commonly used in hospitals for diagnosis…

A: Given query is to find half life.

Q: show tha (cos(r)e")=e" (cosa - sin x).

A: Given query is to find derivative using definition.

Q: Use the Squeeze Theorem to evaluate the limit Enter DNE if the limit does not exist. Limit= lim sin…

A: limx→0 sin x cos1x4

Q: 0.2" lim- 2.3" 0.2" ||

A: Given query is to find indicated limit.

Q: Cartesian coordinates of a point are given. (a) (−6, 6) (i) Find polar coordinates  (r, ?)  of the…

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

Q: x² dx 2 √x² + 16

A: NOTE: Refresh your page if you can't see any equations. . ....................(1) substitute  take…

Q: X= 4+ 2+X

A:

Q: If a cup of coffee has temperature 96°C in a room where the ambient air temperature is 19°C, then,…

A: Find average temperature of first 20 minutes.

Q: If sets A={10,20,30,40}             B ={30,40,50,60}             C= {50,60,70}             U =…

A:

Q: The concentration C of a chemical in the bloodstream t hours after injection into muscle tissues is…

A:

Q: INSTRUCTIONS: Find for... dy dx x² + xy-y² = 4

A: The given equation is x2+xy-y2=4 We have to find the derivative dydx.

Q: Find the possible points of inflection of f. b. Create a number line to determine the intervals on…

A:

Q: Sand poured upon the ground at a constant rate of 12 cubic feet/min forms a conical pile whose…

A: The given data is: Sand poured upon the ground at a constant rate of 12 cubic feet/min dVdt=12 cubic…

Q: Enclosing the Largest Area The owner of the Rancho Los Feliz has 3300 yd of fencing to enclose a…

A:

Q: The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the…

A: Given query is to find the rate of change of base.

Q: A cylinder shaped can needs to be constructed to hold 450 cubic centimeters of soup. The material…

A: Given A cylinder shaped can needs to be constructed to hold 450 cubic centimeters of soup. The…

Q: (a) lim h→0 (b) lim x-0 e cos² h - 1 h 1 + tan x X √1 - tan x

A:

Q: Find fx(x,y) and fy (x,y). Then, find fx (-1,2) and fy (3,1). f(x,y) = In 1+4x³y²| {x(x,y)= fy(x,y)…

A:

Q: Enter a letter and a number for each formula below so as to define a continuous function. The letter…

A:

Q: Let f(x): = 3.2x + 15.8 if x - 2 if x = 4 4 Determine which one of the following rules for…

A:

Q: Consider the function. y = (2x² + 1)³ (a) Decompose the function in the form y = f(u) and u = g(x).…

A: We have to find given decomposition and derivative of y.

Q: A company's revenue from selling a units of an item is given as R = 1600x − 3x². If sales are…

A: To find the rate of increase of revenue.

Q: A population numbers 10,000 organisms initially and grows by 2.9% each year. Suppose P represents…

A: NOTE: Refresh your page if you can't see any equations. . the initial population is a=10000 and the…

Q: Suppose an investment of $24,000 is invested at an annual rate of 4.7%, compounded continuously.…

A:

Q: 0.5t Find the time 42 59 The concentration of a drug t hours after being injected is given by C'(t)…

A: Given query is to find the time when concentration is maximum.

Q: write the exponential funcetion y=50(1.025)^t in the form of y+a(e)^kt, indicate whether the…

A:

Q: In t​ years, the population of a certain city grows from 400,000 to a size P given by…

A: Topic = Derivative

Q: Find the points on the sphere x2+y2+z2=2 that are closest to and farthest from P0(3,1,-1).

A:

Q: 6) Find the following indefinite integral using the by parts method. N f-10xin (2x) dx = fudv = uv-…

A: Given that ∫-10xln(2x)dx=∫udv=uv-∫vdu We have to solve the integral by by parts formula. The…

Q: 3. A girl is being pulled at the rate of 3 m/s at the instant (t = 0) when her friend released her…

A: Let's find speed of girl after half a minute.

Q: Find the Taylor polynomials p1​, ​..., p5 centered at a=0 for f​(x)=4e^−2x.

A:

Q: ← Convert the following angle in degrees to radians. 345° 345° (Simplify your answer. Type an exact…

A: We need to convert the degree angle into radian.

Q: Question Find the Maclaurin polynomial på (x) for f(x) = 5ª. Provide your answer below:

A:

Q: Find a degree 3 Taylor polynomial approximation of f(x) = (1+x)¹/2 centered at 0.

A:

Q: Use the following information to determine cos(2x) cos(x)=1/5 and tan(x) is positive or  cos(x)=1…

A:

Q: A model for the average price of a pound of white sugar in a certain country from August 1993 to…

A:

Q: A cell culture contains 7 thousand cells, and is growing at a rate of r(t) thousand cells per hour.…

A: Use the formula given and the initial amount cell to find the final amount.

Q: Suppose that X is a binomial random variable with n=300 and p=0.2. Approximate the probability that…

A: Probablity to find the x≤r by binomial distribution is…

Q: For the given cost function C'(x) = 44100 + 800x + x², First, find the average cost function. Use it…

A: Given query is to find average cost function and minimize it.

Q: lim In 5n5 In (5n) 50 O O 8 10

A:

Q: A fence 6 feet tall runs parallel to a tall building at a distance of 3 ft from the building as…

A:

Q: I. Find the intercepts, the critical points and point of inflection for each of the following…

A: we need to find out the intercepts, critical points, point of inflection, etc.

Q: K Find the area between y = 11xex and the x-axis from x = 0 to x = 1. The area is square units. ***

A:

Q: 8 .3 X (1+x)5 - dx

A:

Q: a) Find the linear approximating polynomial for the following function centered at the given point…

A: Solution: a) f(x)=e-x Now it's the first derivative f'(x)=-e-x Now it's the second derivative…

Q: Find the portial fraction decomposition for the rationa expression. 5x+2 (x+2) (2x-1)

A: Given a rational function5x+2(x+2)(2x-1)We need to perform partial fraction decomposition on it.

Q: Find the absolute maximum and absolute minimum values of f on the given interval f(x) = x √4- x2…

A:

Q: Let bn = 8 2n + 7 Then, bn is positive, decreasing as n → ∞, and lim bn n→∞

A: NOTE: Refresh your page if you can't see any equations. . the given sequence is  so it can be…

Q: Consider the Cobb-Douglas Production function: P(L, K) = 28L0.5 -0.5 Find the marginal productivity…

A:

Q: Find the volume of the solid whose base is the semicircle y = √1 - x² where -1 ≤ x ≤ 1, and the…

A: To find:- Volume of solid whose base is the semicircle y=1-x2 where -1≤x≤1and the cross sections…