Macmillan Learning Find a parametrization of the tangent line to r(t) = (ln(t))i +t-¹2j+ 11tk at the point t = 1. (Use symbolic notation and fractions where needed. Give your answer in the form (x(t), y(t), z(t)).) L(t) =

Q: Rewrite the equation with the variables separated. hh' = 6t²dt 0 h = 6t²dt dhe = tdt 6h ○ hdh =…

A: given

Q: Questions #8 to #12 pertain to the accompanying Venn diagram. 10. What is the value of n(A)? a) 12…

A:

Q: Solve the following differential equation with initial value a) dy = 6x² 2y+cos y y (0) = 0

A:

Q: y= dy xy dxx + 1 with y(0) = 6

A:

Q: Find the directions in which the function increases and decreases most rapidly at Po. Then find the…

A:

Q: dy 7. a) Prove that, fo-y4 = 4√/2n e2x b) Prove that, √∞ (e³x+1)² dx: = 2π 9√3

A:

Q: Use the properties of logarithms to evaluate the following expression log3(405) - log3(5) 3 81 A 12

A: We need to solve log problem..

Q: Let r(t) = (14, 15) g(t) = sin(3t) Evaluate the derivative using the Chain Rule. (Use symbolic…

A:

Q: For the following lines: L₁: x =− 3 + 3t, y =− 1 + 4t and L²: *3º = ³-2. a) Determine the point of…

A:

Q: What is the equation of the curve that passes through the point (1, 2) and has a slope of at any…

A:

Q: 4. (6) Evaluate the following limits if possible 1) lim x + 1 X-1 X²-1

A: Note:Since you have asked multiple questions we will solve the first question for you. If you want…

Q: Find the area between the curves: f(x)=x+3 and g(x)=x^2-x

A:

Q: 3) lim x-1 f (x), where f(x) = |x-1| + 1₁ x 71 X X-2, XLI

A:

Q: 2. Differentiate a) each of the following functions. Leave in unsimplified form. b) f(x) =…

A: 2)a) y=x6+5 sqrt(x)b) f(x)=3sinx - cos4xDifferenciate the given functions.

Q: Evaluate the double integral J₂62 6xy dA, where D is the triangular region with vertices (0, 0), (1,…

A:

Q: Given the function f and the point Q, find all points P on the graph of f such that the line tangent…

A: The equation of the line passing through the point (a,b) and slope m is given byy - b = m ( x - a)

Q: 8. Find y'if y = x³ +sin (x)

A:

Q: The revenue and cost functions, both in dollars, for the production and sale of x TVs are given as…

A: The revenue and cost functions, in dollars for the production and sale of x TVs are given as  and…

Q: 6. Determine the point of intersection between the graphs f(x)=2(3)²x-1 and g(x)=3(2)³x

A:

Q: 1. Simplify first, then evaluate. Do not use calculator. a) logg 6-logg 3 +logs 2 b) log, 3√3

A:

Q: 13. If H = {1, 2, 3, 4, 5, 7, 9, 11) and J = {1, 2, 3, 4, 6, 8, 10), then n(HUJ)= a) 4 b) 11 c) 15…

A: Note:Since you have posted multiple questions we will solve the first question for you. If you want…

Q: Let r(t) = (t², 1-t, 4t). Calculate the derivative of r(t) · a(t) at t = 5 assuming that a(5) =…

A:

Q: Which of the following describes the first order differential equation? dy dx = = 3y2 + sin(8x) y +…

A:

Q: A contour map for a function f is shown. Estimate the value of f(1,12) 30- 20 10- 70 140 2 210 3 280…

A:

Q: 3a) Consider the differential equation: y³ (2x+1) sin(x²+x) 2-y³ey (y > 1) Without solving the…

A:

Q: Evaluate the double integral 11₁₂²² x² dA, where D = {(x, y) : 1 ≤ x ≤e,0 ≤ y ≤ lnx}.

A:

Q: Evaluate the triple integral U= 2x - y 2 +2 ·√² ſ² ſ²*³² ƒ(x, y, z)dxdydz where ƒ(2, y, z) = 2 + 2 3…

A: We have to evaluate the integral.

Q: Parametrize the intersection of the surfaces x² + y² = z², 5y = z² using t = z as parameter. (Use…

A: To parametrize the Intersection of given surface .

Q: :. Calculate the total amount of interest earned from this investment during the 4-year period.

A: The amount invested, P=$13000Interest rate, i=5%Compounded frequency, m=2 (semi-annually)

Q: ' + y' - 6y = 3x - e2r y' е

A:

Q: If dy = x cos x² and y = -3 when x = 0, when x = π, y = -3.215 2 1.647 6

A:

Q: 5. Let f(x) = [2-kx k+x with the value of f(1) to be determined. (a) Compute lim f(x) in terms of k.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: (3) Let F(x) = — and g(x)=3x-5 F(x)g (x) 1) Find lim x +2 2) Find f(g(x)) and the natrual domain 3)…

A:

Q: B Using the graph above, evaluate the following limit. lim f(x) 42- O PROF (A)1 (B) 2 (C) 3 (D) The…

A:

Q: Let f(x, y) x + 4y 2¹+4 I Evaluate f(0, 1)

A:

Q: Using the sum and difference of cosines formula, find the exact value of cos Enclose numerators and…

A:

Q: Write the following expression 2ln(8) + 5ln(z) as a single logarithm. O O In (825) Om (87) O…

A:

Q: Let V ∼ exp(7). Write an integral for E[√5 + cos 6V − 2V 2].

A:

Q: 2. Find the limits. Show your side work. 2 x-2 (x - 2)² (a) lim (b) lim tan x I→π/2- (c) lim tan x…

A:

Q: Find the solution of the differential equation r"(t) = (e¹21-12, t² - 1, 1) with the initial…

A:

Q: Q4. As lava from a volcano cools, it flows more slowly. The distance the leading edge of the lava…

A: Consider the given function.

Q: What is the maximum value of for 0≤x≤ 10? 2e - 1

A:

Q: Let D be the triangle in the xy plane with vertices at (-2, 1), (1, 0), and (3, 4). Describe the…

A:

Q: 2:2 y² The point (4, k) lies on the ellipse + = 1. 32 18 Which of the following could be a value for…

A:

Q: Find the derivative of the function at Po in the direction of A f(x,y) = - 4xy-4y², Po(-5,4), A=…

A: Given :- The function To Find :- The derivative of the function at P0  in the direction of A.

Q: True or false: limx→+0+ f(x) = -2₁f f(x)= 2-X², XLO 2x-2, x10

A:

Q: Find all the second-order partial derivatives of the function f(x,y) = 3x + 1y+2: 2²f 11 ах'…

A:

Q: Sue's grade in her math class is related to the number of hours she studies. The rate of change of…

A: here we have to find the score of the sue if she studied 20 hours.

Q: Solve the differential equation with the given initial condition. dy sin x dx y+2' y = with y(0) = 3

A:

Q: For the following lines: L₁: x =− 3 + 3t, y =− 1 + 4t and L₂: 2 a) Determine the point of…

A: