For the vector-valued function r(t) = (cos 2t, sin -(cos 2t, sin-4) 3 (4) what is the magnitude of r'

Q: A kite 40 m above the ground moves horizontally at the rate of 3 m/s. At what rate is the angle…

A:

Q: Find all values x = a where the function is discontinuous. 6. f(x) = -3/(6x - 8)(8 - 2x)

A: A function is said to be discontinuous at a point where it is not defined.

Q: Find the general solution of the given second-order differential equation. + 36y = 0 y(x) = y"

A:

Q: | Let ƒ(x) = 8x sin¯¹(x). Find f'(x). ƒ'(x) = Find f'(0.4). f'(0.4) = 0

A:

Q: ρπχ-1 x-0 tan (2x) b) lim

A:

Q: Evaluate the following limit or explain why it does not exist. 1 X lim (x + cos x)* x-0 Select the…

A:

Q: Consider the equation below. 2 1 + sin(0) (a) Find the eccentricity. e= r= li

A:

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A:

Q: Use a graphing utility to graph the curve represented by the parametric equations. Indicate the…

A:

Q: Consider the following function and its graph. f(x) = 2(x + 1)3(x + 7) (x − 3)2(x + 2)2 The x…

A:

Q: Suppose that over a certain region of space the electrical potential V is given by the following…

A:

Q: Use the formula k(t) k(t) = = ||r' (t) x r"(t)|| ||r'(t)||³ 10t: r(t) = e¹⁰ti + e¯tj е to find к(t).

A:

Q: 2 Evaluate f x² sin x dx. Show all work.

A: we have to integrate x2sinxdx

Q: Use differentials to approximate the quantity. √8.7

A:

Q: Find the average value of the function over the given interval. 43. y = x^2 - 4x + 1; [0, 2]

A:

Q: The table shows the percent of workers that stayed in their chosen field. The data are modeled by…

A: Given: The data are modeled by the following quadratic function, where  corresponds to 1990 and  is…

Q: The following graph is of f'(x), the DERIVATIVE of the function f(x). You will use this graph to…

A:

Q: Factor f(x) into linear factors given that k is a zero of f(x). f(x) = 2x³ + 5x²-97x + 180; k=4…

A:

Q: y = 8x², x = 1, y = 0,

A: We know that the formula of disk method about the x-axis is V=int_a^b pi [(f(x))^2-(g(x))^2] DX

Q: Find the derivative of the following function. 1 -2 y ==—= (2x-5)² + (₁ - 12/31 - ²2 4- 14 3x3

A: solving the problem by power rule of derivatives

Q: O O O 4π- 4 4π+4 4+ 3π Find the area between y = 1 and y = 2cosx + 5 for 0 ≤ x ≤ T

A:

Q: e indicated function y₁(x) is a solution of the given differential equation. Use reduction of order…

A:

Q: Solve the given differential equation by undetermined coefficients. y"" - 3y" + 3y - y = x - 5ex

A:

Q: a wire 4 ft long cut into two pieces. One piece forms a circle with a radius r and the other forms a…

A:

Q: Find the absolute extreme values of the function on the interval. 24. f(x) = e^x - x, -5 ≤ x ≤ 2

A:

Q: Find an equation for the conic that satisfies the given conditions. parabola, vertex (0, 0), focus…

A: Given:We are required to find:

Q: sin 8-1 Ө lim- 8-00

A:

Q: Find the area of the region cut from the plane 9x + 2y + 6z = 3 by the cylinder whose walls are x =…

A:

Q: Use the chain rule to find the indicated partial derivatives. z = x² + x²y₁ x = s + 2t - u, y = stu²…

A:

Q: please provide in clear format or clear handwritten

A: Given curve Now we have to find the area under the given curve from  by  using left sum with…

Q: Find the limit. NOTE: Enter the answer using round brackets. t² +5 1 lim +∞ 5t² +6'5t =

A:

Q: Solve the given differential equation by undetermined coefficients. y"" - 3y" + 3y - y = x - 5e*…

A:

Q: Find the area of the region that lies inside both curves. r = 2 + cos(0), r = 2 - cos(0)

A:

Q: Determine the area under the standard normal curve that lies to the right of (a) Z= 1.21, (b)…

A: To find the area to the right of .(a) (b) (c) (d) .

Q: Solve the given differential equation by undetermined coefficients. y" - 6y' + 9y = 9x + 7 y(x) =

A:

Q: 4. Use implicit differentiation to find the equation of the tangent line to z²+zy + y² = 3 at the…

A: The slope of the tangent line to the given curve is equal to the derivative of the given function at…

Q: Use the intermediate value theorem to show that the polynomial function has a real zero between the…

A: Using intermediate value theorem, we can show that f(x) has a real root in given interval.

Q: Find the exact value of each of the following under the given conditions. 5 tan α = a. sin (α + B) 8…

A:

Q: 2 Approximate the area under the curve y = x² + 2 from x = 1 to x = 4 using a left sum with 6…

A:

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Given

Q: For the given equation, list the intercepts and test for symmetry. y=x³-512 What are the…

A: The given equation is,

Q: Express f(x) in the form f(x)=(x-k)q (x) + r for the given value of k. f(x)=x³ +5x² + 9x+6, k = - 2

A:

Q: ion (see figure). A Utility company plans to lay electrical cable underwater from the island to the…

A:

Q: If 7 1/2 yards of varnished cambric (insulation) cost $22, what is its cost per yard

A:

Q: 8 2. Consider the power series: Σ(3x - 1)^. n=0 ● Identify the center of the power series. Determine…

A:

Q: Use the formula K(t) k(t) : = = ||r'(t) x r"(t)|| 3 ||r' (t)||³ 10t: r(t) = e¹⁰ti + e¯tj to find…

A:

Q: 10. You have 800 ft of fencing to make a pen for hogs. If you have a river on one side of your…

A: Here we are given that ; We have 800 ft of fencing to make a pen for hogs. Also, there is a river on…

Q: Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. lim 1+- X→∞…

A:

Q: Find an antiderivative of the given function. 31. 18x^2 + 16x + 7 32. 2/5x^7/5

A:

Q: Find the intervals on which f is increasing and the intervals on which it is decreasing. f(x) = -2…

A: