(a) lim (x6 + x²) X→-8 (b) lim (x6 +x7) x →∞ = (c) lim lim (x6 x7) = X→∞

Q: If f'(x) = x²(x + 2)²(x − 1)² , how many critical numbers does f have?

A:

Q: Let f(x)=3x^3−18x^2+27x−1 How many critical points does this function have?   How many inflection…

A:

Q: How many inflection points does  Which points are inflection points? (List the labels of the points…

A: To find inflection points of the given graph

Q: Compute the following limit x lim x0 e 1

A:

Q: me: 3. What does the lim h 0 f(x+h)-f(x) h Date: 2 =- - 4 indicate about the graph of the function…

A:

Q: Which of the following conditions form the HYPOTHESIS for the basic form of L'Hopital's Rule? Let f…

A: Use the concept of L’Hopital’s rule when determining a limit.

Q: Evaluate cshc -1(2) (You may enter an exact answer involving ln or rounded to four decimal places.)

A:

Q: Mr. Brust is running down his street. His position is given by the function p(t), where t is…

A: Mr. Brust is running down his street. His position is given by the function pt,  where t is measured…

Q: f(t) f(t) = 0,73t³ — 2.² +0,6-and-g(t) = 0,17² - 0,5t + 1.1--1

A: see below the graph

Q: Let F = (x^3 − 2yz, tan^−1(y^2 + z), −z + 1). a) Find div F b) Determine if F is conservative

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: When you are evaluating the integral Which substitution can you use Which factor you have to ave…

A: Please see the below answer.

Q: A candy box is to be made out of a piece of cardboard that measures 8 by 12 inches. Squares of equal…

A: Solution: Let the side of the square = x Given : Length of cardboard = 12 inches Breadth of…

Q: 14. Find all the critical points of the function f(x, y) = sin(x + y) and determine if they are…

A:

Q: d. y=191og74t e. g(x)=sin ¹(7-x) f. y = ln 1+x² xex

A: Derivative

Q: √3 S 0 x√1+x² dx.

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

Q: Which of the following planes are parallel to the plane x-3y - 4= = 1? (i) 3x-9y- 12 - 1 (ii) -x +…

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Q: 11) The velocity of a particle moving along the x-axis is given by v(t)=-² + 2t + 4 for 0 st s 5.…

A: Given, the velocity of a particle moving along the x axis as, v(t)=-t2+2t+4  for  0≤t≤5 to find the…

Q: Simplify the ratio of factorials. (n + 1)! (n − 1)! X

A: We have given to find ratio of factorials Let, y=n+1!n-1! y=n+1nn-1!n-1! y=n+1n y=n2+n

Q: Suppose a product's revenue function is given by R(q)--7q² +500g, where R(q) is in dollars and q is…

A: Marginal revenue is the rate of change of the revenue function. Marginal revenue is denoted by…

Q: Solve the following IVP, for the parameter b choose among the following 2, 5, 7, 9 y-b √₁ y': , y(0)…

A:

Q: Use the chain rule to find and, where First the pieces: дz dr dr მs ду მა || 11 11 9- = 94 And…

A: z=x2+xy+y2x=4s+4ty=8s+7t∂ ∂x(xn)=nxn-1∂ ∂x(constant)=0

Q: Find D53 te (₁² +²²²) 20-²). Note: Read "D" f(x)" as "the nth derivative of f(x)"

A:

Q: 2 [ (31² - 4t + 7) dt Find the answer of the given integration

A:

Q: Consider the region between f(x) = x - 2 and the x-axis on [2,5]. For each line of rotation given in…

A: 38. The given data is: fx=x-2,  2,5 Around the line x=2

Q: Write (but do NOT evaluate) the iterated integral that gives the volume of the solid bounded above…

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Q: Find a formula for f(n)(x) if ƒ(x) = e7x. f(n)(x) = 0

A:

Q: Solve the given differential equation. 9ydx − 9xdy + x°dx = 8dx The solution is (Type an equation.)

A: 9ydx-9xdy+x2dx=8dxwe know  d dx(yx)=xdy-ydxx2∫xndx=xn+1n+1+c

Q: Find the triple integral of the function f(x,y,z) = x2cos(y+z) over the cube 3<x<4,0<y<pi,0<z<pi.

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Q: a. X 1 e te. e2x 0.5x So dx

A: To Find  : ∫01ex+e0.5xe2xdx

Q: Find the minimum and maximum values of the function y=-3x² + 2x - 4 on the interval [-1,4] by…

A: Given that function is y=-3x2+2x-4 on the interval -1,4. It is required to find the maximum and…

Q: Find the points on the curve  y = 2x3 + 3x2 − 12x + 4  where the tangent line is horizontal. (x,…

A: Given query is to find the tangent line is  horizontal.

Q: e graph of y = f(x) is shown. Assume f'(x) is continuous. 8 7 6 5- 4 3 2 -7 -6 -5 -3 -2 -1 nd xf(x)…

A: Given query is to find indicated limit.

Q: Use the following function along with its first and second derivatives to do the following: A. Find…

A:

Q: Let f: R² → R be defined by f(x, y) = 3x¹ + 7y³ +7 and set z = f(x, y). Find an equation for the…

A: To find the equation of the contour line of f at level z=9, we need to solve the equation f(x,y)=9.…

Q: Translate the given matrix equation into a system of linear equations. (Enter your answers as a…

A: Given :- 2-12-43413-800xyz=9-10

Q: Find the interval(s) where f(x)=x²-3x³-6x² - 2x +4 is concave up.

A: Given function:- fx=x4-3x3-6x2-2x+4

Q: f+lc 2. A conical oil tank with vertex down has a radius of 24 feet at the top and is 36 feet high.…

A: Given: The radius of the oil tank =24 feet.Height of the oil tank=18 feet3.

Q: 14. Given f(x) = ax+b b-ax a. What is the root of f(x)? X b. What is the equation of the function's…

A: Given function:- fx=ax+bb-ax

Q: The domain of the function is f(x,y)=cos ¹(x² + y²-3) O a. {(x,y)|x>0 and y>0} O b. {(x,y)|y>0} Oc.…

A: The Domain of Cos-1(x) function is [-1,1].

Q: Use the Riemann sum midpoint rule to calculate the distance John run in 5 seconds

A: We need to use Reimann sum.

Q: Use the chain rule to find and , where First the pieces: 器 Әх Əs ду Əs || dt - || || And putting it…

A:

Q: We recall that a point P on a curve y = g(x) is called an inflection point if g continuous there and…

A: The given function is: gx=160+8x3+x4  Find the inflection point.

Q: e volume of the frustum of a right circular cone with height h = 71, lower base rac

A:

Q: Let f(x, y) = 2x2-3y² -x+y+1, find the maximum and minimum values of f(x, y) over the triangle with…

A: The given function is:f(x,y)=2x2-3y2-x+y+1

Q: te f(x) = x 2-12 X-4

A:

Q: ke for this investment to reach a value of $11,800.00?

A: Given query is to find the investment to grow 11800.00

Q: Consider the graph of Ax + By = C where A, B, and C are positive constants and A B. If the value of…

A: Solution: Given data, Ax + By = C where A, B, C are positive constants Ax+ By = C → (i)   X-…

Q: At what point on the curve  y = 8 + 2ex − 4x  is the tangent line parallel to the line  4x − y =…

A:

Q: Draw a graph of f(x) = additional point on the graph. 1 1 -5 -4 -3 -2 -1 4 3 2 H -1 -2 -3 -4 -2x -…

A: We can draw the given function by using the vertical and horizontal asymptote and two points on the…

Q: Evaluate the limit lim 11e-3 using L'Hôpital's rule. After applying L'Hôpital's rule, the limit…

A: