Given the vector-valued functions е u(t)= e ti+e-4 + 4tk v(t) = −ti + 4t²j + 4k d find (ū(t) · v(t)) when t = 2. dt d dt (ū· v) (2) =

Q: Determine the quadratic function of the form f(x)= a(x-h)² + k whose graph is given on the right.…

A:

Q: In a time of t seconds, a particle moves a distance of s meters from its starting point, where s =…

A:

Q: Question 3 Suppose f(a,b)→ R is continuous at every point in the open interval (a, b), and that f(x)…

A: Given that :Function  is continuous at every point in the open interval  for all To prove : for all…

Q: Solve the LP problem, If no optimal solution exists, indicate whether the feasible region is empty…

A: To solve the following LP problem..Maximize  subject to

Q: A lamina with constant density o(x, y) = 4 occupies the region under the curve y = sin(лx/5) from x…

A: As we knowThe given curve  from  to

Q: im ²/1 In (4+¹) is Af'(4) where f(x) = ln x (B) (4) where f(x) = (In x)/x (C) f'(0) where f(x) = ln…

A: To find:-

Q: Please assist with the steps below  Find the derivative of the function by using the rules of…

A: Given, F(x)=rules of derivatives are

Q: 45-60. Areas of regions Find the area of the following regions. 45. The region outside the circle r…

A:

Q: find the derivative by using the product and or quotient rule  g(w)=e^w(w^3-1)

A: Given that function  to find the derivative of the given function

Q: Find u v, uu, ||u||2, (u v)v, and u. (2v). u = , V = (a) u. V 27 (b) 306 (c) 306 (d) (e) u u ||u||²…

A:

Q: Find an equation in rectangular coordinates for the spherical equation p = 9 csc (p)

A:

Q: 2. The base of a solid S is an elliptic region with boundary curve 9x² + 4y² = 36. Cross-sections…

A:

Q: Evaluate the definite integral. [₁²₁ (x^² + ²3 ) (x² + +7 + 2x)-² dx

A: Solution-

Q: 45. The region outside the circle r = 1/2 and inside the circle r = cos 0

A:

Q: 4. Determine the distance between the point (1, 0, 1) and the plane [x, y, z] = [1, 2, 3] + s[2, 1,…

A: GivenEquation of plane

Q: P(t) = 0.01484t2 + 0.446t + 15    (0 ≤ t ≤ 22) where t is measured in years, gives the percentage of…

A: We have given,   P(t) = 0.01484t2 + 0.446t + 15    (0 ≤ t ≤ 22)

Q: cos 2 arctan X - 1 √x+1 /x+1/

A:

Q: =r walking through the fifth gate, your computer informs you that more than half of the gates have…

A:

Q: 1. Let R be the region bounded by y = x² and y = 6x - 8. Find the volume of the solid S generated…

A:

Q: 18. If three planes intersect in a point then the triple scalar product of their normal 19. In…

A: Statements are given.18. If three planes intersect in a point then the triple scalar product of…

Q: The graph of the function g is shown. Sketch the graph of the function (x) = same coordinate axes.…

A: Firstly compress the graph of g(x) by a factor 2 to get g(2x) then divide its amplitude by 2 to…

Q: Find the component form and magnitude of the vector v with the given initial and terminal points.…

A:

Q: Please assist with the steps for the problem below    A women's clothing chain store, found that t…

A: S(t) = 5,000(1+e^0.3t)Rate of change can be found using derivative.

Q: Find the volume of the solid obtained by rotating the region bounded by y = 2x², x = 2, x = 5, and y…

A:

Q: The figure below shows the graph of a function f with domain 0≤x≤ 4. Which of the following…

A: we have given graph to find the limits

Q: Use the given graphs of the function f (left, in blue) and g (right, in red) to find the following…

A:

Q: Write a polynomial function, in factored form, with real coefficient whose zeros and multiplicities…

A:

Q: Determine, with justification, whether the following series converges: 4 9. Σn=1 √n

A: To determine with justification, whether the following series converges.

Q: Why is it that (k+1)^4 became (k+1)^3

A: Solution-

Q: 6. Consider the parametric curve x(t) = 1 + cost+cos 2t, y(t) = sint + sin 2t = sin t(1+2 cos t)…

A: Given that                Then            At  , we need to find the value of .

Q: 26. Find a vector perpendicular to both a = [1, 2, 3] and 5 = [3, 2, -1].

A:

Q: Find the derivative of the function. 3 f(x)=√x - ³√x

A:

Q: 0 The initial substitution of x = a yields the form. Simplify the function algebraically, or use a…

A:

Q: Find d²v dt² v=3t² +7t+9 d²v dt² कर U- -

A:

Q: Use implicit differentiation to find an equation of the tangent line to the graph of the equation at…

A:

Q: Consider the following function. Function f(x) = 8x4 - 6x³ - 101x2 - 21x + 36 (a) Verify the given…

A: and factors(x+3) , (x-4)

Q: Find an equation of the plane consisting of all points that are equidistant from (2, -3, 4) and (-4,…

A:

Q: The demand for a certain fraternity's plastic brownie dishes is q(p) = 361,201 − (p + 1)2 where q…

A: Given that q(p)=361201-(p+1)^2

Q: Solve for x. log x - log(x + 5) = -1

A:

Q: S K₁² Evaluate 1 (x − 1)² dx

A: Evaluate ∫1∞1(x−1)2dx

Q: Find the integral using an appropriate trigonometric substitution. 1 x²√√x²+25 dx

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the derivative of the function. 1 f(x) = 3/5x² - 6

A: Given, derivtives formulas

Q: Sketch a graph of a function g that satisfies all of the following a. limh(x) = h(-2) = 1 X-3 b.…

A:

Q: Use for question #1-8 NJ -2 -3 5

A:

Q: Find the area of the shaded region. + -6 -5 -4 -3 -2 square units 8+ y y = x³ · y = x + 6 4 X

A: Consider the graph

Q: If ƒ(x) = 2x² − 4x + 6, find ƒ'(−2). −12x - 2 incomplete. X syntax Use this to find the equation of…

A: Rule of derivative.

Q: f(x, y) = 3y cos(x), 0≤x≤ 2π local maximum value(s) local minimum value(s) saddle point(s)

A:

Q: Each derivative represents the first line of a "first principles" definition for some function f(x).…

A:

Q: Evaluate the limit sin 3x 8x lim x→0

A: given limit

Q: y = cos (πx/2) and y = 1 - x²

A: