lim (t i - 6 j +1° k). -5 (t i – 6 j + r² k) = i i+

Q: What is the angle between the vectors u = and v = ? 213° O 188° O 111° 120°

A: Solution:

Q: Establish the identity. 3 csc0 4 cos 0 = 7 cot 0 sec 0 sin 0 Write the left side of the identity in…

A:

Q: Find the area of the region bounded by the given equations. Clearly state the integral(s) used to…

A:

Q: Find the dimensions of a rectangle with a maximum perimeter that can be inscribed in the ellipse 4x…

A: Given ellipse 4x2+9y2=36                ->Equation(1)Let (x,y) be the upper right corner of the…

Q: What is the equation of the tangent plane normal to x2 + y2 + z = 9 at the point (1, 2, 4)? O 2x -…

A: Given; f(x,y,z)=x^2+y^2+z-9  Point (1,2,4)

Q: Find the area of the following region bounded by the graph of f(x) = (x - 5) and the x-axis between…

A:

Q: Evaluate sin 5x) lim, 0 (sin 5z ) 3x O 1 O 3/5 O 5/3

A: Topic:- limit calculus

Q: 4 - xy - 2xy = x' + 3 Find a solution to differential equations by one of the seven ways to solve…

A:

Q: Question

A:

Q: A. Matching Type. Match the functions in Column A with their corresponding derivatives in Column B.…

A:

Q: Verify Green's Theorem by evaluating both integrals Lr dx + x* dy = / dA ду x² dy ax for the given…

A: In this question we verify Green's Theorem                 i.e, verify integral  ∫C y2 dx +x2 dy =…

Q: Sketch the region R and evaluate the iterated integral F(x, y) dA. (1 - 2x + 8y) dy dx 2.0- 2.0 1.5…

A: A detailed solution is given below

Q: Find the coordinates of a point P on the line and a vector v parallel to the line x = 3 - 5t, y = -1…

A: This is a problem related to vector. Based on the general concept and formula we will answer the…

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0<ts 1. (y – x) dx +…

A: Just I have used the given parametric representation of the curve C to change the given line…

Q: _13. If y = sin(4x – 5), then what is y'? а. у'3 сos (4x -5) b. у'- 4cos (4x — 5) c. y' = -cos (4x -…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: If f(x) = u(x)t(x)w(x), then f'(x)= a) u'(x)t'(x)w'(x) b) u'(x) + t'(x) + w'(x) c) u(x)t'(x)w'(x) +…

A: Solution ) f (x) = u(x) t(x) w(x) To differentiate use product rule  [ Formula d/dx ( f (x) . g(x) )…

Q: A tank is being filled with a liquid. Z (1), given below, is the amount of liquid in liters in the…

A:

Q: y²- 4y + 2x = 0, x = 2 and x-axis

A:

Q: xe 1. lim, »o X→0 1-e*

A:

Q: The outside diameter of a thin spherical shell is 12 feet. If the shell is 0.3 inch thick, use…

A:

Q: d Calculate ri(t) r2(t)] and rı(t) x r2(t)] first by differentiating dt the product directly and…

A:

Q: Evaluate the triple iterated integral. xyz dx dy dz Jo

A: To evaluate the triple integral.

Q: Determine whether the improper integral diverges or converges. In x dx O converges O diverges…

A: Use integral test for checking the convergence of series

Q: Use Hooke's Law to determine the work done by the variable force in the spring problem. A force of 5…

A:

Q: A cylindrical container with circular base is to hold 64 in3 . Find its dimensions so that the…

A:

Q: Find V · (V × F) if F(x, y, z) = 10 sin xi + 7 cos(9x – 10y)j + 3zk. V·(V × F)

A:

Q: d Calculate ri(t) · r2(t)] and rı(t) × r2(t)] first by differentiating d dt the product directly and…

A: Given

Q: Determine whether the improper integral diverges or converges. 0. -4x xe dx converges O diverges…

A:

Q: 5. S (3x-x²)dx x2

A: This is a problem related to integration. Based on the general formula and concept we will answer…

Q: Consider the function f (x, y)=-2x'+3x'y+2 y°-9y+5

A:

Q: Activity 1.5.3. A company manufactures rope, and the total cost of producing r feet of rope is C(r)…

A: A company manufactures rope, and the total cost of producing r feet of rope is Cr dollars.To…

Q: 5 4 3 1 T1/2 3T/2 -1 -2 -3 -4 -5 The graph of the function f(x) given above for the interval a E [0,…

A:

Q: Зх+1 a) y =- 1 b) g(x)= Vx -

A:

Q: What is the area bounded by the graphs of y = 8x and y = 16x 16? %3D O A = S*,- 1)dy O A = S*,(-1)dæ…

A: Topic:- application of integration

Q: d²y of the following equation then simplify whenever possible. 3) Find and dx dx- x = 3em y = 4e-m

A:

Q: 2x f(x) 1< x < 3 to + 5 lim n → 00 i = 1

A:

Q: Inn 1 1 1 1 + 25 1 1 a) Σ-(-1)" (- b) 1+ 4 1 + 64 n-Inn. 9. 16 36 49

A:

Q: Find the general solution to the ollowing differential equations: (A) y = 2yx(y'+3)+13x %3D

A:

Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 550…

A: We have to find the minimum cost.

Q: let f be the function given by f(x)=kx/(x^2+1), where k is a constant.  For what values of k, if…

A:

Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Here, the amount of the clay is fixed. dVdt=0...(1) Now, the volume of the cylinder is given by:…

Q: Determine the interval (s) on which the vector-valued function r(t) = ti + Vt + 1j + (t2 + 1)k is…

A:

Q: 12 dx х3 — Зх2

A:

Q: Evaluate the improper iterated integral. 9. x2 dy dx 1 + y?

A:

Q: 3/xyy' = 5

A: We have to solve the differential equation  3xyy' = 5.

Q: Determine whether the improper integral diverges or converges. In x converges O diverges Evaluate…

A: Here we have to determine whether the given improper integral diverges or converges.

Q: Set up an integral for the area of the shaded region. Evaluate the integral to find the area of the…

A:

Q: Find the domain of r(t) and the value of r(to). Edit NOTE: Round your annwer to two decimal places…

A:

Q: Determine whether each of the following functions is (a) continuous (b) differentiable 5. f(x) = 2x²…

A: Find your answer below

Q: (6) (a) For each of the following differential equatons: • Determine the order of the differential…

A: Since the student has posted multiple questions and does not mention any specific question, so we…