Consider the ellipsoid x² + y² + 4z² = 41. The implicit form of the tangent plane to this ellipsoid at (−1, 2, −3) is x − 2y + 12z = −41 The parametric form of the line through this point that is perpendicular to that tangent plane is L(t) = (-12t, 2 + 4t,-3-24t)

Q: Filling a Conical Tank Water is poured into a containerin the shape of a right circular cone with…

A: Volume of the cone=13πr2hGiven:-Radius of the base of cone=4 feetheight of the cone=16 feet.and…

Q: Graph each of the functions in the same viewing rectangle. Describe how the graphs illustrate the…

A: Concept used: Graphing A graph of a function is a line that represents the function on a coordinate…

Q: Find an equation of the tangent line to the curve y=4^x at the point (1,4)  Tangent line: y=

A:

Q: graph each equation.   y = 2x

A: Given data:- The given equation is, y=2x

Q: DIRECTIONS. Indicate the degree and determine the solution of the following equations. 2.  (3x² -…

A: degree is one .

Q: 6 5 4 3 2 I 1 it y = f(x) X

A:

Q: Find the present value of $6000 payable at the end of 3 years, if money may be invested at 8% with…

A:

Q: Find all the critical numbers of f(x) = 2x4-4x³+3x²+2, then determine the local minimum and maximum…

A:

Q: Graph the function and observe where it is discontinuous. f(x, y) = e¹/(x - y) f is discontinuous at…

A: The given function is fx,y=e1x-y The graph of the function is as follows.

Q: Given lim f(x) = -5 and lim g(x) = -12, evaluate lim [5f(x)-2g(x)]. X→ 11 X-11 X→ 11 O lim…

A: Given that: limx→11f(x)=-5, limx→11g(x)=-12

Q: dx xinx 6. S

A: Given integral ∫dxx ln x Formula ∫1xdx= ln x + C

Q: 7. Use the integral test to determine the convergence of the following series: ∞ n=2 n ln n น

A:

Q: 11 Find the derivative of f(x) = -15sinx + +3√√x-5. X

A: Given function:- fx=-15sinx+11x4+3x7-5

Q: Consider the surface xyz = 16. A. Find the unit normal vector to the surface at the point (2, 2, 4)…

A: Given,              xyz=16⇒xyz-16=0

Q: Effect of Price on Demand for Tires Suppose the quantity demanded weekly of the Super Titan radial…

A:

Q: 4. Linear Equations b. 2y(y² - x)dy = dx

A: We can solve this as follows:

Q: Find the average rate of change of f1x2 = 8x2 - x:(a) From 1 to 2 (b) From 0 to 1 (c) From 2 to 4

A: Given: Given expression: f(x) = 8x2-x Formula Used: The Average rate of change ARC = f(b)-f(a)b-a

Q: ach of the following questions, find the error(s). Then, write out the correct response Given…

A: Given query is to find the composite function.

Q: Find the derivative of the function. f(x) = arcsin (et) f'(x) = Find the domains of the function and…

A: To find out the derivative of the function.

Q: 3. m 1 773 7/2 The graph of the function f(x) = cotxe is given above for the interval x = [0, 2π]…

A: The graph of the function fx is To evaluate: The values of limx→π-fx,  limx→0+fx

Q: Find the exact length of the curve. x = 5 + 12t², y = 6 + 8t³, 0≤ t ≤ 3 12117-1)

A:

Q: FIND F'(x) for F(x) = -7 w/out USING the √5x³-20x quotient TULE

A: Given query is to find the derivative of the function.

Q: Use the formula for nPr to evaluate the expression 8P0.

A: Given: The given expression is:  8P0 Formula Used: Prn = n!(n-r)!

Q: Find a parametrization of the parabola x = y². Don't forget an interval for the parameter. (Hint:…

A: Please see the below picture for detailed solution.

Q: Use the formula for nCr to evaluate the expression 12C5.

A: Given: the given expression n: 12C5. Formula Used: Crn = n!r!(n-r)!

Q: The function s(t) describes the motion of a particle along a line. s(t) = t3 − 7t2 + 6t   (a) Find…

A:

Q: For the piecewise linear function f(x) graphed below, find the following. (If an answer does not…

A: Given: To find: limx→2- fx , limx→2+ fx, limx→2 fx

Q: In the triangle shown above, if increases at a constant rate of 3 radians per minute, at what rate…

A: According to given problem dθ/dt = 3 radians/minute                                           ---…

Q: Evaluate f(x) ƒ(1) = f(x + 7) = f(x) + f(7) f(x + h) = = = x + 2 at the indicated values.

A:

Q: Graph the functions in Exercises .37. y = sqrt(x + 4)         38. y = sqrt(9 - x)

A: Given data:- 37. y=sqrt(x + 4) 38. y=sqrt(9-x)

Q: Find the exact length of the curve. X = t 2 + t y = In (2 + t), 0≤t≤1

A: Given: x=t2+t, y=ln(2+t) We know that exact length of the curve is given by  s=∫t1t2dxdt2+dydt2dt

Q: You are dealt one card from a standard 52-card deck. Find the probability of being dealt a heart.

A: Given: Total number of cards = 52 Formula used: Probability = Number of favourableNumber of outcome

Q: Use the chain rule to find the derivative of f(x) = 4√/10x¹⁰ + 6x6 Type your answer without…

A:

Q: Suppose Use this to compute the following limit. Limit= Number What Theorem did you use to arrive at…

A: Snadwich TheoremSqueeze Theorem:  If g(x)≤f(x)≤h(x)  for all x in an interval containing a point…

Q: (a) Find the distance from P1 = 1 - 2, - 32 to P2 = 13, - 52.(b) What is the midpoint of the line…

A: Given, P1=-2, -3 and P2=3, -5

Q: PZ π/2 54 3 2 1 -2 -3 -4 -5 Find lim f(x) = The graph of the function f(x) = tanx is given above for…

A:

Q: DIRECTIONS. Indicate the degree and determine the solution of the following equations. Homogeneous…

A:

Q: Use a software program or graphing utility to solve the system of linear equations. (If there is no…

A:

Q: The function s(t) describes the motion of a particle along a line. s(t) = t3 − 10t2 + 32t − 230…

A:

Q: DIRECTIONS. Indicate the degree and determine the solution of the following equations. Homogeneous…

A: Let's solve differential equations by using homogeneous Function.

Q: Evaluate the following integral, showing all calculus and algebra work. 2x² √2x²+x=1d + x - 1 -dx

A:

Q: A chemical substance has a decay rate of 6.5% per day. The rate of change of an amount N of the…

A:

Q: A tube is being stretched while maintaining its cylindrical shape. The height is increasing at the…

A: NOTE: Refresh your page if you can't see any equations. .   (height is increasing at a rate of 2…

Q: 3. Consider the initial value problem y′ +y=1-², y(0) = 30› where yo denotes some real constant. (a)…

A: To find the solution of given differential equation.

Q: A consumer purchased a computer after a 20​% price reduction. If x represents the​ computer's…

A: A consumer purchased a computer after a 20​% price reduction. If x represents the​ computer's…

Q: Enter your answer as an ordered pair. Provide your answer below: f(x) = 7x² - 12x - 8

A: The given function is  f(x)=x2-12x-8

Q: (Question-Solution-Final Answer-Conclusion format) E. Generate solution of the first-order…

A: The solution of given exact differential equation is as follow.

Q: In this exercise you will conclude that a limit does not exist by computing the limiting using two…

A:

Q: Geometry A wire of length x is bent into the shape of asquare.(a) Express the perimeter p of the…

A: Given: A wire of length x is bent into the shape of a square. (a) To express the perimeter p of the…

Q: You want to make an 80° angle by marking an arc on the perimeter of a 12-in.-diameter disk and…

A: Given data:- The given angle is, θ=80° The given diameter is, d=12 in So, the radius is, r=6 in.