Find an equation of the plane that passes through the point P(2, 5, 1) and has the vector n = (1,4, 3) as a normal. O x+ 4y + 3z = 0 O 2x + 5y + z – 25 = 0 O 2x + 5y + z+ 25 = 0 O x+ 4y + 3z – 25 = 0 O x+ 4y + 3z + 25 = 0

Q: Evaluate the volume of the solid generated by revolving the plan

A:

Q: x³ + x2 – 4 1. Consider the function f(x) 4.x = x +1+ Note that x² – 4 x² – 4 - x²(x² – 12) (x² –…

A: Solution is given below:

Q: A Use the method of Lagrange multipliers in Problems 7-10. I SL.

A:

Q: Find the gradient of the function at the given point. In(x2 – y) – 9, (3, 8) z = Vz(3, 8) =

A: use partial derivative for finding the gradient.

Q: We want to use the Basic Comparison Test (sometimes called the Direct Comparison Test or just the…

A: We have to find if first series converges.

Q: Reindex the series to start at k = 0 y = E, (k+ 1)æ*+3 = E£o

A: The given series is y=∑k=7∞k+1xk+3 we have to re index the series to start at k=0. Rewrite the given…

Q: Find the area of the triangle with vertices P(1, 3, –6), Q(0,0, 0) and R(4, 5, 1). NOTE: Enter the…

A:

Q: Use Lagrange multipliers to find a vector in 3-space whose length is 7/3 and whose components have…

A:

Q: y'sec²xdx – (1– 2y'tanx)dy = 0

A:

Q: 3. Given below is a table of values of a function Write the limit of a function by concluding using…

A: Function table values are given, we have to find the limit using table values.

Q: 20x at P(4,0) in the x + y Find the directional derivative of f(x,y) direction of Q(2, –1). NOTE:…

A: The expression for the directional derivative of the function f in the direction of u is:…

Q: Compute the length of the curve r(t) = (21, In(?), r²) over the interval 1 < t < 7. (Use symbolic…

A:

Q: Find the vector component of v = (4, – 1,7) along b = (6, 6, –7) and the vector component of v…

A:

Q: 2x 2x Find the absolute maximum and absolute minimum of the function f(x) = - 1 over the interval…

A:

Q: The student should answer the question below: Evaluate the given equation: | ydA where T is the…

A:

Q: You manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into…

A: Given that the ice-cream factory makes two flavors creamy vanilla and Continental mocha. It is given…

Q: Find the vector component of v = 2i – j+ 3k along b = 2i + 4j + 4k and the vector component of v…

A:

Q: The reverse order of f, S, sin y² dydx is f, S sin y? dxdy False True

A:

Q: Show that y = e^2t is a solution of y’’’ - 2y’ - 4y = 0 (where ‘ denotes d/dt), and find the general…

A: We need to solve differential equation and show that y = e^2t is a solution.

Q: Use the Mean Value Theorem to show that f(r) = 2x sinh(x – 1) + 2" – x %3D has a critical number…

A: Given: We can see that the function is continuous in [0, 1] and differentiable in (0, 1). So, the…

Q: Two​ neighbors, Wilma and​ Betty, each have a swimming pool. Both​ Wilma's and​ Betty's pools hold…

A:

Q: 4x + 5 S(x) = 9- 3x A. x = 0 B. x = 3

A: To determine whether the given function is continuous and differentiable at the given points or not.

Q: A particle is moving on a straight line has acceleration a=5-3t and it's velocity at time=2. If s(t)…

A: Solution: a = 5-3t v(2)=7 s(2) - s(1)=?

Q: 2. f(x) = x² - 5x + 6 A. x = 1 B. x = -3

A: This is a problem related to limit and continuity parts of the calculus. Based on the general…

Q: 1 8 - Find an equation of the plane containing the Point P (2,1, -1) and having the normal vutor N :…

A:

Q: 2y Find the directional derivative of f(x, y, z) at P(5, 2,-4) in the direction from P to Q(4, 3,…

A: To find the directional derivative of the given function.

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Solution is here

Q: Let g be a function that is defined for all x, x # 2, such that g(3) = 4 and the derivative of g is…

A: Here, g(3)=4 &amp; g'(x)=x2-16x-2, x≠2

Q: If measure of a = x+28 and measure of b = 5x-4, determine the value of x.

A:

Q: Compute the length of the curve r(t) = (41² + 1, 81² - 5,1) over the interval 0 < t < 2. (Use…

A: To find the length of the parametric curve  r(t)=4t2+1,8t2-5,t3 over the interval 0≤t≤2. Here, let…

Q: Jose must choose between two job offers. The first job pays $62,000 for the first year. Each year…

A:

Q: Determine whether the lines Lj and L2 are parallel. L1: x = 3 – 4t, y = 5 + t, z = 8 – t L2: x = 5 –…

A:

Q: Let a ci + j and b = 12i + 16j. Find c so that the angle between a and b is . Round your answers to…

A:

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (5, 2)…

A: Given query is to fins equation of the line.

Q: 16. Determine if 4x – 3xy + yʻ is homogeneous or not. If it is homogeneous, state the degree of the…

A: Given : f(x,y)=4x2-3xy+y2   To Check : f(x,y) is homogenous or not and it's degree, if it is…

Q: = -14 – 5t = -5t y = 21 + 3t = 5t – 43 Given the skew lines l1 : Y = 9 – t and l2 : = 2t – 7 (a)…

A: Since, you have ask a question with multiple sup-parts, as per company guidelines we will solve the…

Q: Maximize f(x, y) = 3xy Зху subject to x + y = 1

A:

Q: Find parametric and symmetric equations for the line satisfying the given conditions. Through the…

A: Given query is to find the parametric and symmetric equation.

Q: = [] Given: h (t) Find h'(t). t² +2

A:

Q: . Prove the following using the epsilon-delta definition of a limit. b. lim x² = 4 X→2

A:

Q: sin40 Prove 8cos 0 – 4cos0, show preliminaries to perform sino

A:

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 6j as…

A:

Q: 2. Use the Mean Value Theorem to show that f(r) = 2x sinh(x – 1) + 2" – x has a critical number…

A:

Q: 2. Evaluate the following limits. x2-4x+4 a. lim x→5 x*-8x³+24x²–36x+16

A:

Q: Find parametric equations of the line through (-3,0, 4) that is parallel to 5i– 8j+k. x(t) y(t) =…

A: Parametric equations of a line passing through the point P(a,b,c) and parallel to the vector v→=…

Q: DIFFERENTIAL EQUATIONS Solve the following application problems. *show the every details of your…

A:

Q: Given that arcsec e) + (x – y²)² = 2. (a) Find dy using implicit differentiation. dx dy using…

A: Given,            arcsecyx+x2-y232=2

Q: Find the limit. Use L'Hospital's Rule where appropriate. If there is a more elementary method,…

A:

Q: The area A of the region S that lies under the graph of the continuous function is the limit of the…

A:

Q: Tutorial Exercise Find the sum. 4(k + 1)²(k – 4) k = 0 Step 1 Recall the definition of summation…

A: