Let f(x) lim I→ 6+ if x = Calculate the following limits. Enter "DNE" if the limit does not exist. lim →-6- f(x) = lim I→ 6 = f(- 6) (−5 − x)² +2 if x # - 6 2x + 14 6 f(x) = f(x)= = =

Q: The surfaces p= 3 and 5, p = 100° and 130°, and z = 3 and 4.5 identify a closed surface. (a) Find…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Determine the solution of the following differential equation: d²y dx² dy -8-+16y=0 dx where y(0) =…

A:

Q: Suppose that the position of a particle is given by s(t) = 4t³ + 5t +9. (a) Find the velocity at…

A:

Q: What is the max area of a rectangle placed between the x-axis and the function f(x)= -x^4 + 3

A: Answer : Maximum area should be 4.225 unit2 .

Q: Part 1 A rectangular tank with a square bottom has base side lengths of 3 feet and a height of 10…

A: Disclaimer:  “Since you have asked multiple questions, we will solve the first question for you. If…

Q: Two cars are moving towards an intersection. One car is 170 meters north of the intersection and…

A:

Q: What is the max area of a rectangle placed between the x-axis and the function f(x)= -x^4 + 3

A: To determine the maximum area of a rectangle placed between the x‐axis and the function fx=-x4+3.

Q: Find a power series representation for the function. (Give your power series representation centered…

A:

Q: 1. Evaluate the following matrix operation: [5 3 a. A = 1 -4-3-1 L2 b. |B| C. C = 31-33+231 5+20 0 1…

A:

Q: 3.2 Bus A leaves Worcester at 08:00 and travels north along the N1 at 50 km/h. Bus B leaves…

A: Given that The Bus A leaves at 8:00 with speed of 50 km/hand bus B leaves at 10:00 with 70 km/hSo,…

Q: You are driving on a toll highway from King Road to Queen Road (a 50 km drive) in 25 minutes . Two…

A: Suppose, s(t) is the position function after t hours of time in km. Now, s(t) will be continuous and…

Q: Find the area of the shaded region

A: The objective is to find the area of the shaded region.

Q: 2 94

A: according to question function is f(x)=x+4 x=1,2,3,4 f(1)=1+4=5 f(2)=2+4=6 f(3)=3+4=7

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

A: Given f(x)=1xa=1

Q: Find the partial derivatives fx (3,5) fy (3,5) for the function f(x,y)= y^2/x-y

A:

Q: Find the curvature of r(t) = √√7ti + etj + e-k at point P(0, 1, 1).

A:

Q: 0 4 From a square piece of metal of side length 6 m, four squares are removed as shown in the…

A:

Q: Consider y = √x+1. (a) Find its inverse relation. Is this relation a function? Why? If the inverse…

A:

Q: π 7. fz sin¹x cos¹ x dx

A: To evaluate the following integral by using Walli's formula.∫0π2 sin4 x cos4 x dx

Q: Break up 9 m/s 4.5 m/s [S], 7.8 m/s [W] 4.5 m/s [S], 4.5 m/s [W] 3 m/s [S], 6 m/s [W] O4.5 m/s [W],…

A: Please see the below picture for detailed solution.

Q: tan' (2)

A:

Q: (1) Find the derivative of the function f(x) = 2x³ - 12x² +4 and use it to find the critical numbers…

A: Solution is given below:

Q: Let ƒ(x) = x³ + 3x² − 9x + 22. (a) Use the definition of a derivative or the derivative rules to…

A: The given function fx=x3+3x2-9x+22 use the derivative formulas, ddxxn=nxn-1ddxax=addxa=0 where, a be…

Q: Test and k=/ each name K+ k³+1 of all the tests following. you for use. Conver

A:

Q: Solve (y³ + 2y² +9y+18) dx = (5x²y² x²y + 17x²) dy

A: integration using partial fraction

Q: 6. Find the area bounded by the curve ay = x² and the lines y = a and y = 4a.

A:

Q: 3. The graph below represents f(x). a) State the number of stationary points and label them…

A:

Q: What form of the particular solution is appropriate for the differential equationy "'- y'=4? A B C D…

A: To determine the form of the particular solution that is appropriate for the differential equation…

Q: Use cylindrical coordinates to calculate: Sw(x² + y²) dV = [[[_x² + y²³ av W: x² + y² ≤64, 0≤ z ≤ 16

A:

Q: 1. a) Copy the graph. YA 4 2 4-20 2 f(x) AR 2 4 x (g(x) b) Use the superposition principle to…

A:

Q: The graph of g' is given below: W Notice this is the graph of the derivative of g not the graph of g…

A: Observe the given graph and answer the each part.

Q: 8. Give examples of sets of three vectors that are a. Collinear b. Coplanar c. Not coplanar Explain…

A: Solution: a) Collinear : Two or more vectors are called collinear when they are parallel to the same…

Q: Find the differential dy of the given function. (Use "dx" for dx.) y=6√x + 7 x dy

A: To find the differential dy of the given function.y=6x+7x

Q: B.Verify if a given function is a solution to a differential equation. 1 d²y dy 1x². +x=y= ln x dx²…

A:

Q: The graph of g' is given below: W Notice this is the graph of the derivative of g not the graph of g…

A: Given graph of g' is shown below

Q: EX #3: Roller Coaster A hypercoaster is a special circuit roller coaster with a height measuring…

A: A hypercoaster is a special circuit roller coaster  with a height measuring greater than 200 feet.…

Q: Calculate the following definite integral: 2x² + 5x dx

A: Given ∫022x2+5xdx

Q: If f(x) f'(x) = [ 7-x² 3+x² find:

A: Topic = Derivative

Q: Det er mine absolutely it each convergent, Conditionally convergent, you > k=1 the following is or…

A: Given ∑k=1∞coskπk

Q: 2. Suppose a population of insects grows exponentially, there were 130 insects after the third day…

A:

Q: Which if the following is a power series representation of the function f(x) a. Σ(-x - xn+¹) n=0 Ob.…

A: We have to find the power series representation for given function.

Q: What is the interval of convergence of the series + +∞ (x+3)" 2n O a. (-5, -1) O b. [-5, -1] O c.…

A:

Q: 0 A = 2 -3 -1 B = -1 2 -2 −1 3 0 ³.0 - [ C 1 3 4 Use the above matrices to compute the following…

A:

Q: What is correct form of the particular solution associated with the differential equationy'''=8?

A:

Q: Use the geometric series f(x) = f(5x) = 1 1-5x ∞ Which of the following is the power series…

A:

Q: Given r(t) = 9t² i + 18tj and t = 1, find the tangential and normal components of acceleration. ат…

A:

Q: EQUATIONS 5y" - (y')4 = y³ sin x yy" + 2x = tan x )' - - 8² 8f + (9) St² - 8³ M dy³ dy² xt' + (t")3…

A:

Q: Find the radius of convergence, R, of the series. R = 00 I = n = 1 xn n45n Find the interval, I, of…

A:

Q: Two cars are moving towards an intersection. One car is 190 meters north of the intersection and…

A:

Q: Evaluate both integrals of the Divergence Theorem for the following vector field and region. Check…

A: