Find the component equation for the plane that passes through the points P = (1, 2, −1),Q = (1, −1, −2), and R = (3 − 2, 5).

Q: Evaluate the integral [(6te7¹²) + (6e¯6t) j+ (7) k]dt. 0 ... [[(00²²³) + (60°) + (7) ►]α = 0+0¹0*…

A: We have definite integralWe have to evaluate it

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) - 14y² lim (x,y) → (0,0) x²…

A: We have f(x,y)= (x4-14y2)/(x2+7y2)We have to find limit when (x,y) approaches (0,0)

Q: Sketch the graph of fby hand and use your sketch to find the absolute and local maximum and minimum…

A:

Q: Identify and express the function from the graph given either as a sine or cosine function. 2π -7514…

A:

Q: Consider the function below. x + 1 f(x) = + 1 (a) Find the exact value of the maximum of f. f(x) =…

A:

Q: Find the volume of rotation for the region enclosed by the graphs of y = x³ + 7, y =9-x² and x = 3…

A:

Q: Question 8 a) Two variables, p and q, are connected by the formula p = 120e0.5g + 80 where q > 0. i)…

A:

Q: Integrate G(x,y,z) = z over the parabolic cylinder y=z², 0≤x≤ 4, Oszs√2.

A: Integrate G(x,y,z)=zover the parabolic cylinder y=z2,0≤x≤4,0≤z≤2.

Q: Find the foci of the following hyperbola: (x − ¹)² – (v − 1)² = 1 9

A: (x−1)24−(y−1)29=1

Q: Find the solution of the differential equation that satisfies the given initial condition. dy/dt =…

A:

Q: The second derivative of g is g"(x) = 6x x = 2 is a critical number of g(x).

A:

Q: Brandon is on one side of a river that is 80 m wide and wants to reach a point 200 m downstream on…

A:

Q: Question 4 a) 63 In the expansion of (+kx), the coefficient of the x² term is 256 Find the values of…

A: Since you have asked multiple questions in single request.We will be answering only first question.

Q: Use the integration Factor Method to find the general solution of y +x у=4х2

A: Given

Q: How many shortest lattice paths start at (5,5) and a. end at (13, 13)? b. end at (13, 13) and pass…

A:

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

A:

Q: Question Completion Status: QUESTION 3 Explain whether the given equation defines an exponential…

A: Any equation is said to be an exponential function if it is in the form of ; ;.

Q: Find the Jacobian of the transformation. x = 2v + 2w², y = 4w + 4u², z = 6u + 6v² a(x, y, z) a(u, v,…

A:

Q: What is the average rate of change of the function y = 30 10 20 None of these 5x² over the interval…

A:

Q: Find the derivative of the function. y = [x + (x + sin²(x))³]4

A:

Q: (4)Evaluate the definite integral (a)(1+ si 0 1+ sin x)dx (b) (2t+cost) di (b) f( -x/2 x+ X - dx R/4…

A: Explanation of the answer is as follows

Q: Find the volume of the solid enclosed by the curves y = 2√√√√x.y = x² about the x-axis.

A:

Q: Consider two positive infinite series S = Σn-1 a₂ and T = b and assume that for every value of n, an…

A:

Q: The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time…

A: The radioactive isotope of lead, Pb-209, decays at a rate proportional to the  amount present at…

Q: 4. Use Green's Theorem to write a double integral equal to the given line integral. Then evaluate…

A:

Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations. x =…

A: Using iterated integral, we can find the required area.

Q: 24 If [ ²4 F f(x) dx = 15, then compute the value of the following definite integral. [2²FC f(3x³)x²…

A:

Q: Determine the angle of rotation of the conic section given by: -4x2 + xy +5y2 - 5x= -2 (round your…

A:

Q: The equation 4y2 +12y-9x2-15x + 45 = 0 can be changed into a vertex equation by completing the…

A: 0

Q: When gas expands in a cylinder with radius r, the pressure P at any given time is a function of the…

A: Given that a steam engine pressure and volume equation PV1. 4 = k. And also given that pressure and…

Q: The cost function for a certain commodity is C(q) = 87 +0.179 -0.008q2 + 0.00089³. (a) Find C'(100).…

A:

Q: Find the solution of the differential equation that satisfies the given initial condition. y'(x) =…

A:

Q: Find the location of the center of mass of the 2 dimensional planar lamina whose shape is the…

A: The location of the center of mass of the 2-dimensional planar lamina whose shape is a rectangle…

Q: Calculate the Derivative k(u) == are sec(u) 3u + 2

A:

Q: The number N(t) of supermarkets throughout the country that are using a computerized checkout system…

A:

Q: Use the given transformation to evaluate the given integral, where R is the triangular region with…

A:

Q: Fig. 28 shows the graph of the derivative of a continuous function g(x). y=g'(x) 01 2 0000 List all…

A:

Q: If S is the hemisphere x² + y² + z² = 16 with z> 0 then the surface integal s(x-2y)dS is o

A:

Q: 3x² - 8x + 1 | x² − 4x²+x+6 dx; use А x-2 + B x+1 + с x-3

A:

Q: Find limx³ sin 0+x X by using the Squeeze Theorem. Be sure to show all work.

A:

Q: [8x³ex dx

A: I=∫8x5ex6dx

Q: The average rate of change of y with respect to x over the interval [0, 3] for the function y = 3x +…

A:

Q: The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time…

A:

Q: (d) Give the local maximum and minimum values of f (x). Enter your answers in increasing order of…

A: The given function is..(d) Find the local maximum and minimum values of .

Q: Rewrite the Cartesian equation y = r(0) = Enter theta for 0 if needed. 7x as a polar equation.

A: The cartesian co-ordinate is (x,y) and the polar co-ordinate is .

Q: For how many n = {1, 2, ..., 695} is n a multiple of one a multiple of one or more of 8, 3, or 7?

A: In the range of [1, 695] the number of numbers divisible by an integer k =  represents the floor…

Q: Write the equations in cylindrical coordinates. (a) 8x² + 8y2 - z² = 4 2 8p²- 2 = 4 (b) 9x - y + z =…

A:

Q: Find the limit. lim (t i − 7 j + t² k) 1-9 lim (1 i − 7 j+t² k) = i+ i j+ i k

A:

Q: Consider the function f(x) = 2x² 10x + 5, 0≤x≤ 7 < Find where the absolute maximum and minimum…

A:

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y1…

A: Consider the graph cep