Find r'(t), r"(t), r'(t) r"(t), and r'(t) x r"(t). r(t) = 2²1-3tj +2³k (a) r(t) 5,2 3ti - 3tj + k (b) r"(t) 3i + 5tk (c) r(t).r"(t) 9t+ 25,3 (d) r(t) x r"(t) X

Q: Find an equation of the plane that passes through the point (-1, 6, 0) and is perpendicular to the…

A:

Q: A particular commodity has a price-supply equation given by p= 369(1.033)*, where x is the numbers…

A:

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

A:

Q: Suppose f(x) = x³ + 12x² − 27x + 7. Find the absolute extrema of f on each of the following…

A: Suppose  Then we have to find the absolute extrema of f on each of the following intervals. The…

Q: Find parametric equations of the line that contains the point P(-2, 1, -3) and intersects the line…

A:

Q: Given f(x) = -6 - 3x², find f'(x) using the limit definition of the derivative.

A:

Q: d dx J3 (2t³+3) dt = -3

A:

Q: 12. Find the absolute maximum and minimum values of the function f(x, y) = x² − 2xy +2y over the…

A: Given function f(x,y) = x2-2xy+2y

Q: Determine the formula for the nth term of the following sequence: -6, -2, 12, 42, 94, 174,..

A:

Q: Find the location of the absolute extrema of ƒ(x) = = Absolute maximum at x= Absolute minimum at x =…

A:

Q: 14) Find the equation of the line passing through the point (2,3,4) and perpendicular to the plane…

A: Point p ( 2 , 3 ,4 ) Plane 3x + y + 2z = 6

Q: a. L-1 2s s2-5

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Answer each question part, showing your step by step workings to reach the conclusion. a) Simplify…

A: Note:-Since you asked multiple subparts , according to our policy we can solve only first three…

Q: y = x tan x² + x 1

A:

Q: Given that the directional derivative of f at the point (8,−1,8) in the direction of a = 6i-3j-2k is…

A:

Q: Suppose that the polynomial function fis defined as follows. f(x)=(x-11) (x-7)(x+5)²(x+12)³ List…

A:

Q: What is the area under the graph of y = x³ + 3 for the interval [1, 3]? 13 26 32 52 64

A: Given dataEquation of graph,Interval

Q: c. f(t) = 3 cost t π/2

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: d²x dt² d²y dt² (x(t), y(t)) = 4y + et = 4x - et

A:

Q: Tutorial Exercise Find the average value have of the function h on the given interval. h(u) = (14 -…

A:

Q: Solve the initial value problem. 7. dy/dx = 1/x^3 + x,  x > 0;  y(1) = 1

A: To solve the initial value problem.,

Q: Calculate the coefficients of the first four terms of the binomial expansion for the binomial (x +…

A:

Q: The graph below is the function f(x). -5 -4 -3 -2 -1 7 -1 -2 -4 2 3 4 5 Determine which one of the…

A: The graph below is the function .To determine the rule of continuity which is violated firstly at .

Q: Find all intersection points of the following curves. b. Find the area of the entire region that…

A:

Q: Match the vector field with its graph. F(x, y) = xi + 3yj O ## X 14 Ell 5 VI X

A: F(x, y) = xi + 3yjOption C is the wright choice

Q: Find a unit vector in the direction in which f(x, y) = 3x¹y³ increases most rapidly at P(−1, 1), and…

A:

Q: Find the general solution for the following differential equations 1. 2y" + 18y = 6tan 3x

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

Q: QUESTION 20 Find all real numbers that satisfy the equation. √3 sin x = {x1x = 7+2mm} X= (x1x - 72m…

A: Explanation of the answer is as follows

Q: The graph of a derivative f' is shown to the right. Use the information in the graph to determine…

A:

Q: Evaluate. (Be sure to check by differentiating!) [(8+xº) ³x7 dx

A:

Q: Sketch the graph of a function y=f(x) that satisfies the given conditions. No formulas are required-…

A:

Q: Determine whether the improper integral diverges or converges. +3 So (+² + 8)²0 converges O diverges…

A:

Q: The perimeter of a rectangle is fixed to 12 units. The rectangle is rolled into a cylinder by gluing…

A:

Q: The wind-chill index W is the perceived temperature when the actual temperature is T and the wind…

A: The solution is shown in step-2

Q: Find the area under the graph of f over the interval [-2,4]. x²+2 x≤2 3x X>2 f(x) =

A:

Q: Suppose the wholesale price of a certain brand of medium-sized eggs p (in dollars/carton) is related…

A: Suppose the wholesale price of a certain brand of medium-sized eggs  (in dollars/carton) is related…

Q: Consider the function f(x) = 6x² - 4x¹. (a) Find all critical numbers c of f. (b) f is concave up…

A:

Q: Suppose f(x) = = 17 - X (a) The rectangles in the graph on the left illustrate a left endpoint…

A:

Q: Find the derivative of: 5e-8 sin (-2x²)

A:

Q: 11. Find and classify all the critical points of f(x, y) = y³ + 3x²y - 6x² - 6y² + 2 g(x, y) = x³ -…

A:

Q: Evaluate using integration by parts. 1 T 0 7xe5x dx

A:

Q: The graph of g(x) is given below. Use this graph to determine the value of the following limit. -3…

A:

Q: Use the Chain Rule to find the indicated partial derivatives. z = x² + x²y, x = s + 2t - u, əz əz Əz…

A:

Q: Based on the graph below, estimate the average rate of change from x=1 to x=4. -1 3 2 1 -5/3 1 2…

A:

Q: Find the absolute maximum and absolute minimum for the function on the closed interval. g (t) = cost…

A:

Q: Find the line integrals of F = 4yi + 4xj + 3zk from (0,0,0) to (1,1,1) over each of the following…

A: The solution is shown in step-2

Q: Solve the given initial-value problem. (Assume w # y.) d²x w²x = Fo cos(yt), x(0) = 0, x'(0) = 0 dt²…

A: ,

Q: Use the method for solving Bernoulli equations to solve the following differential equation. dy dx…

A:

Q: Use the Law of Sines to solve the triangle. Round your answers to two decimal places. A = 100°, a =…

A:

Q: Problem #10: Problem #10: What is the smallest number of terms of the series Σ (1)" +1 n3n estimate…

A: The solution is shown in step-2