18. Find the limit. lim X-8 lim X→8 6 X-8 X-8 (Simplify your answer.)

Q: Find an equation for the tangent plane and parametric equations for the normal line to the surface…

A:

Q: Explain how the range of the function f1x2 = x2compares to the range of g1x2 = f1x2 + k.

A: Given: f(x)=x2 To explain: How the range of f(x) compares to the range of g(x)=f(x)+k.

Q: State in interval notation where the graph is differentiable. A) (-∞, -1) U (-1,3) U (3,00) B)(− ∞,…

A:

Q: 7) Find the horizontal asymptote, if any, of the given function. 2x³-3x-9 f(x) 9x³-5x +3 A)y=5 8) If…

A: Here we have to use the concept of limits

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

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A: Given for the years 1992–2007, The rate can be approximated by the model r(x)=−0.115x2+1.183x+5.623…

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A:

Q: Use algebra to rewrite the expression BEFORE you differentiate. 8x¹7 - 2x¹4 14 x11 A) 32x³ - 2x D)…

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Q: what is the answer to the problem

A: We want to use implicit differentiation to find partial derivatives.

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: Find an equation of the tangent line to the graph of the function f defined by the following…

A:

Q: How many different four-letter passwords can be formed from the letters A, B, C, D, E, F, and G if…

A: The letters A, B, C, D, E, F, and G.

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A: The parametric equations are x = t+3                         .........1y = t2+2t…

Q: A tank has the shape of an inverted circular cone with height 10 m and base radius 6 m. It is filled…

A:

Q: Find the x-intercept(s) of the following function. f(x)=x² - 4x +3 Give your answer as ordered pairs…

A:

Q: Use the Fundamental Counting Principle to solve:You are taking a multiple-choice test that has five…

A: Given data:- n = number of questions = 5 Number of choices for each question = 3 We have to find a…

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: For what value of p does the sum of roots of the equation 6x² - 3px + 5 = 0 equal the product of…

A:

Q: Determine the slope and y-intercept of the graph of 3x - 5y = 30.

A: The given equation: 3x - 5y = 30 To determine: The slope and the y-intercept of the given equation.

Q: Integrate [8³e³ 13 ft³e est dt t³ est dt. =

A: The solution to find the integral  of given integration is as follow.

Q: 32. Sketch the following vectors, and find their components and lengths: (a) 4i +3j - 2k (b) i+j+k…

A:

Q: Find the directional derivative of f at the point P in the direction of a. P(4,0); f(x, y) = 4x³y³;…

A:

Q: PZ π/2 4 2 1 79 -3 -4 The graph of the function f(x) = tan x is given above for the interval a € [0,…

A: Given query is to find indicated limits and vertical asymptotes.

Q: Find the following using the table below. 1 2 3 4 3 X f(x) 4 12 f'(x) 4 1 2 3 g(x) 4 132 g'(x) 4 1 2…

A: We have to find  h'(3) if h(x)= f(x).g(x)  h'(3) if h(x)=f(x)/g(x)  h'(3) if h(x)= f(g(x))

Q: 2y X in the direction of (1, 2). Then, Suppose f(x, y) (b) ▼ ƒ(6, π) = sin 2y (a) ▼ ƒ (x, y) = cos(…

A:

Q: Evaluate lim 1 1 x 2 X-2 X-2 direct substitution. 1 1 X 2 O lim X-2 X-2 1 1 X 2 O lim X-2 X-2 O lim…

A: The objective of the question is evaluate the limit and choose the correct option.

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.

Q: If f(x) = sin x, find ƒ'(x) 5 5 sin(x) cos(x) Find f'(2)

A:

Q: graph each function.f1x2 = 1 x

A: Given, fx=1x

Q: Use the formula for nCr to evaluate the expression 10C6.

A: The expression is given by, C610 n=10r=6

Q: Use a Riemann sum with 4 rectangles of equal width to approximate the area between y = x³ +8 and the…

A: Let's find area by using right hand Riemann sum.

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: Let F(x) = f(x7) and G(x) = (ƒ(x))¹ . You also know that a = 7, ƒ(a) = 2, ƒ'(a) = 15, ƒ'(a¹) Then…

A:

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: • f is not continuous when x = 4 but limx→4 f(x) exists. f has a non-removable discontinuity when x…

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Q: In 2004, an art collector paid $172,536,000 for a particular painting. The same painting sold for…

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

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

Q: Find Vz. = = sin(4y² - 6xy) NOTE: Give your answer in unit vector notation; that is, in terms of i…

A: Given; z=Sin(4y2-6xy)

Q: Area of a Rectangle A rectangle has one vertex in quadrant Ion the graph of y = 10 - x2 , another at…

A: A vertex of rectangle lies on the following: y=10-x2 Since the area of rectangle is maximized when…

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: Use the formula for nCr to evaluate the expression 11C4.

A: Given data:- Here, n=11, r=4 Use formula:- Crn=n!r!(n-r)!

Q: C) Evaluate m√m - 1 dm D) Evaluate 32 dy

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

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Q: Problems: 1.(x³ + xy² − y)dx + (y³ + x²y + x)dy = 0 2. (ex siny + ey)dx - (xe-y-e* cosy)dy = 0

A:

Q: Find the area of the shaded region. f(x) = x² - 4x³ + 12x². g(x) = - 3x +90 The area is (Type an…

A:

Q: me of a Cube The volume V of a cube with sides of length x in. is changing with respect to time. At…

A: Volume of cube is side cube

Q: Find a unit vector in the direction in which f(x, y, z) + == Z y² increases most rapidly at P(1, 2,…

A: Given f(x,y.z)=xz+zy2,point (1,2,-2) The objective is to find the unit vector and rate of change of…

Q: State whether the equation is ordinary or partial, linear or non-linear, and give its order and…

A: See this solution in below.

Q: Find the equation of the plane through the point (3, -3,0) that is tangent to the surface xy² + 3ye²…

A:

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.