r(t) = (8tet - 6)i + (sin(3t) − 2)j + (4 ln(t + 1) + 5)k. dr (a) Compute (0) and -(0). Show your process. dt (b) Use your answer from part (a) to find the equation equation for the line tangent to the curve at t = 0. (c) Explain how dr (0) and the tangent line are related geometrically. dt

Q: The inputs are € The outputs are y E Is the relation a function of a? O Yes O No (Enter your answer…

A: Given: The graph of the relation is shown below:

Q: Problem 2: a. Find the differential equation by eliminating the arbitrary constants of the family of…

A: Use diffential concept

Q: 1. Verify if the given general solution is a solution of the indicated differential equation. 1.…

A:

Q: 18. A juggler tosses a ball into the air. The ball leaves the juggler's hand with an initial feet…

A:

Q: (m+n)a=ma + na conveys which property of scalars? O O O O distributive property none of the above…

A:

Q: +2x =

A: Here is the solution:

Q: Eliminate the constants in the following: 1. 2.²²2 + 1/² = 1 a b

A:

Q: Find the following limit. lim (-x² +9x-1) X-6

A:

Q: please find the derivative of (x5 - 2)/sin (3x) + 5

A:

Q: 110 S dx 5e2x-3

A:

Q: Consider three arbitrary vectors u, v, w E R³. Using the definitions of the cross and dot products,…

A: We need to prove  u.(v x w) = w.(u x v) = v.(w x u)

Q: Evaluate the multiple integral 2x [ [² r dz dy dr Do not include spaces.

A:

Q: Set up, but do not evaluate, an integral that calculates the length of the curve y = 2/x+4 from x =…

A:

Q: Determine whether the given differential equation is linear or nonlinear, and give its order.…

A: In this question, we need to check whether the given differential equation is linear or non-linear…

Q: Use logarithmic y = differentiation to find dy/dx. (x + 1)(x - 10) (x - 1)(x + 10) X>10

A:

Q: Given r(t) = 5t8i - 9 sin (t)j + e³tk and s(t) = −4ti +8tj+4tk, find [2t² r(t) + 2t¹s(t)]. dt Sorry,…

A:

Q: 6 Find the antiderivative of r' (t) = (est, e-7t, - - 2) Provide your answer below: r(t) = ()i +…

A: We can solve this as follows:

Q: A=70(1.06)t what is the rate in percentage

A:

Q: Find the equation of the normal plane to the curve R (t) (t, t², t³) at the point (1, 1, 1). =

A:

Q: Identify whether the limits of the following does exist or not. If yes, find the limit and if not,…

A:

Q: Determine if the graphs below display even symmetry, odd symmetry, or neither. -4-3-2 5 --4- 3 2-…

A:

Q: Evaluate the multiple integral Г.Г. I'24 -1 -4 1 24x²yz³dr dy dz Do not include spaces.

A:

Q: 1. For the given functions, state the range and find (f-¹)(a) using th ate formula for the…

A:

Q: Given the function f(x) = 3x + 2x² a. Simplify f(-x) f(-x) = b. Determine whether the function is…

A:

Q: In Exercises 17 -28, determine whether the sequence con- verges or diverges. If convergent, give the…

A:

Q: Problem 3: Determine the two-variable function F(x, y) if Fy (x, y) = y sin(πxy) — x given that x^2…

A:

Q: 1. 2. Find the following limits, if they exist. (If a limit does not exist, enter DNE.) 3. 4. f(x) =…

A: Here we have to find the limit of the function.

Q: Determine the two-variable function F(x,y) if Fy(x,y)=ysin(pi x y)+x given that

A:

Q: 9. Evaluate the indefinite integral without using the calculator. State main of the result and show…

A: Solution is given below.. fro quetion 9 a,b

Q: Eliminate the arbitrary constant Y = cx+c²+1

A:

Q: 2. y' = 2y4+x4

A:

Q: Question Find parametric equations of the line tangent to the curve r(t) = (√t — 5, ln (t + 3),…

A:

Q: 2. y = 4-5x 4+5x

A:

Q: Problem 2: a. Find the differential equation by eliminating the arbitrary constants of the family of…

A:

Q: .) y = 4x ³-2x+1 .) 9 8 = X 3.) √√x+2 X 2x+1 X+ 2 = 4

A: We have to find the whether the given is a rational function , a rational equation ,a rational…

Q: 2. Consider the plane determined by the three points (3,−1, 2), (8, 2, 4) and (−1, −2, —3). (a) Find…

A: Given: Three Points P=(3,-1,2),Q=(8,2,4) and R=(-1,-2,-3) PQ = <5, 3, 2> PR = <-4, -1,…

Q: Problem 1: Using differentials, approximate the change, in terms of 7, in the total surface area of…

A: Use diffential concept

Q: Which of the following is the differential equation of the family of circles with center on the line…

A:

Q: Find the length of the curve R(t) = (2t, cos 2t, sin 2t), 0 ≤ t ≤ π

A:

Q: After a Logarithmic expression (involving 3 or more Logs) has been simplified, the result is 3…

A: Given 3log48

Q: -5 -4 -3 -2 -1 -6- -5- 4 -3 2 1, O y = f(x) -y = g(x) 1 2 345 X

A:

Q: Eliminate the constant: 3x 3x y=c₁₂e³+€₁₂€ ³ Oy"-4y+3y=0 Oy"-6y¹+9y=x Oy"+ 6y' +9y=0 Oy"-6y'+9y=0

A: Given: From the above, we see that the root of the characteristic equation will be 3, 3. So, the…

Q: oblems involving the solution of a DE subject to the conditions on the function or its derivatives…

A: Topic: differential equations

Q: A function is a ratio of quadratic functions and has a vertical asymptote x = 5 and just one…

A:

Q: Find the tangential and normal components of the acceleration R(t) = (2sint, t, 2cost)

A:

Q: View Policies Current Attempt in Progress Solve for t using natural logarithms. 4 = 1.97¹ Round your…

A: Solving for t

Q: ind the constants A and B such that y(x) = Ae¯ to the IVP y" + 5y + 6y y (0) = 1 y' (0) = 16. = + Be…

A: Topic:- application of derivatives

Q: ²

A: Given that

Q: Determine the value of k such that y=4x²-3e2x is a solution to x (1− x) y''+ (2x² - 1) y'+k(2x - 1)…

A:

Q: Find dy by implicit differentiation. dx √xy = x²y + 29 dy dx X

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…