Suppose we know that the points P (0, -1, -1), Q(1, 1, 4), and R (2, -4, 0) form a triangle in 3-space. We want the standard form of the plane that contains that triangle. Evaluate PQ and PR. Write down the standard form of the plane that contains that triangle. (???)(x-???)+ (???) (y-???) + (???)(~-???)= 0

Q: 1 94. Prove that the derivative of f(x) = In x is f'(x) %3D by completing these steps.

A: The given function is f(x)=ln x

Q: Which of the following is the formula for finding the distance between two points on the coordinate ...

A: The formula for finding distance between two points (x1,y1) and (x2,y2) is, d=(x2-x1)2+(y2-y1)2 Opti...

Q: Evaluate the following indefinite integral. Use C for constant of integration. * cos(10x) + sin(20x)...

A:

Q: S, (4Vw) dw 4.

A: You have asked only question number 4,4. According to question,Given integral,∫914w dw

Q: y = ex between x= 1 and x= 4 The average rate of change of y between x= 1 and x = 4 is (Round to fou...

A:

Q: Evaluate the integral. 2Vy dy Vy e dy =

A:

Q: In Exercises 19–22, show there is a number c, with 0 ≤ c ≤ 1, such that f(c) = 0.  19. F(x) = x3 +x3...

A: Use intermediate value theorem

Q: Find the DE of the family of plane curves described and sketch some of its members. Straight lines w...

A: We have to determine the diffential equation

Q: Construct a difference table to predict the next term of the sequence. –50, –68, –78, –80, –74, –60,...

A: Arithmetic series 

Q: Find the equation of the tangent line to f at x=a f(x) = + 2 at a = 1 O y = -15x – 22 O y= -15x – 8 ...

A:

Q: Find lim,-2 f(x) 2 -3 -2 -1 2 3 lim→-2 f(x) = 0 %3D lim, -2 f(x) = 2 lim,-2 f(x) = 1 Does Not exist

A:

Q: Solve the differential equation: y dt + t (t + y) dy = 0

A: Given that: y2dt+t(t+y)dy=0

Q: Current Attempt in Progress Determine whether the series converges, and if so find exactly its sum. ...

A:

Q: Of all the points on the graph of z = 10 - x^2 - y^2 that lie above the plane x + 2y + 3z = 0, what ...

A:

Q: 4. Use the product rule twice to prove that if f, g,h are differentiable, then (fgh)' = f'gh + fg'h ...

A:

Q: 4. F(t) = e-tsinh (4t)

A:

Q: the wapiti Indians make woven blankets, rugs, and skirts. each blanket requires 24 hours of spinning...

A:

Q: 10. Let f(x, y) = x²y + y. Find the minimum and maximum values of f subject to the constraint x² + y...

A: Given: fx,y=x2y+y The constraint equation is: gx,y=x2+y2=5   Now apply the Lagrange's multiplier; ∂f...

Q: Which of the following could be the value of n in the equation f(x)=x^n if f is a polynomial functio...

A:

Q: Check the differentiability and continuity of the function below.: 3x 1. f(x) = 2. f(x) = 5- x² at x...

A:

Q: 3. Center: (3, -5) radius: 2

A:

Q: 3. Sketch OP = (3, -4, -2) including the rectangular prism that frames it. Use and label the axes, i...

A:

Q: Differentiate the following function. Use any method and show the step-bystep solution. b. m = (2...

A:

Q: Use the difference a+1 – an to show that the given sequence {an} is strictly increasing or strictly ...

A:

Q: The quadratic approximation for a function f(x) at a=2 is given by q(x) = 16+ 32(x – 2) +24(x – 2)² ...

A: Given that: q(x)=16+32(x-2)+24(x-2)2

Q: | log(22 +1) dr d.x

A: Follow the procedure given below

Q: 1. Find the equations of the normal and osculating planes of the curve x Int, y 2t, z = t2 at the po...

A: Equation of the plane :  r→.n^ =a→.n^ ; where 'r→' is the position vector and 'a→' is the given poin...

Q: Perform the calculation. 45° 17'- 29°48' 45° 17' - 29°48'= (Simplify your answers. Type an integer o...

A:

Q: 3.) y tanʼxdx +ln* ydy = 0 dy_ (y?+4) Inx In (y?+4)Y 5) dx

A: y tan2x  dx + ln4y dy = 0∫-tan2x  dx =∫ ln4yy dy∫(1 - sec2x) dx  = ∫ t4 dt   (where, t = ln y)Hence,...

Q: mín z = 2x1+ 3x2 2x1 +X2 2 2 -X1 - X2 > -4 -X1+ 2x2 > 1 X1, X2 >0 sa (P)

A: Note :- As you write just define the auxiliary problem for given LPP Problem. So i am define only th...

Q: Written Works Find the equation of the tangent line to the following functions at the specified poin...

A:

Q: Evaluate. 25х —31 dx J (x + 5)(x² + 1) %3D

A:

Q: ´sin x-sin x cos x lim x2

A: This can be evaluated as follows:

Q: 6x Evaluate the indefinite integral. x4 + 1 + C

A:

Q: Solve the equation: (x⁵+3y)dx - xdy

A: Given that:  (x⁵+3y)dx - xdy=0

Q: (b) Find the instantaneous rate cf change of C with respect t i when x = 100, (This is called the ma...

A: Given function C(x)=5000+10x+0.05x2 Aim: (a) To find the average rate of change of C with respect of...

Q: O Convert the following integral to polar coordinates. Do not evaluate the integral. 1 V1-x² (x + y)...

A:

Q: V1+ x² dx 2.

A: Follow the procedure given below

Q: A. Direction: Find the Laplace Transform of the following. 5. F(t) 1.5 sin (3t – n/2)

A:

Q: (+++)" В. y C. y = 2x/x² + I

A:

Q: dy _ (y² +4)ln x 5. х. dx In(y + 4)"

A: Find the general solution

Q: coS X =dx sin? x

A:

Q: y)dx + ( 2+ x + ye" )dy =0

A:

Q: Suppose that the total profit in hundreds of dollars from selling x items is given by P(x)=5x-5x+7. ...

A: Average rate of change of f(x) as x changes from a to b is given by, A(x) = [f(b) - f(a)]/(b - a)

Q: -1 [cos'x { v(1-x)}]'dx log.{1*(= 1+( sin (2xv(1-x²)) TT

A:

Q: 20KdL do = 29000습 0.75in(+4) in 72 20dL d8 = o[29000]0.75 (36 + 4) 8=0.0134 inch ans

A:

Q: (3x2-7)* y = (3x2+5)4

A: Given:- y=(3x2-7)4 /(3x2+5)4 To find:- Derivative of given function

Q: If s is a position function, measuring distance (m) travelled in seconds what does the expression   ...

A: limit

Q: 7. Let f(x, y) = In(x)+2 ln(y) – x – 4y. Find the critical point of f and determine if it is a local...

A: Let's find. 

Q: Find all values x= a where the function is discontinuous. For each value of x, give the limit of the...

A: