d Calculate [r₁(t) · r₂(t)] and [r₁(t) × r2(t)] first by differentiating the product directly and then by applying the formulas d dr2 dr₁ [r₁(t) r₂(t)] = r₁(t). + r₂(t) and dt dt dt d dr₂ dri [r₁(t) × r₂(t)] = r₁(t) × + x r₂(t). dt dt dt

Q: Find dy/dx: 1. у%3D Jo = San* sec? t dt

A: A detailed solution is given below

Q: Sketch the graph the integrands and use areas to evaluate the integrals. 1. L'lx| dx Sketch the…

A: The graph is shown below, where the shaded region represents the area.

Q: 2. Use the following partial graph of f(x) to answer the next question. f (x)' 10. The value of (f…

A: First we find f(x). Here f(x) is straight line which are passing through the point (4,0) and (0,6).…

Q: 6. The initial population of a town was 12000. After 5 years the population increased to 38000…

A:

Q: 2. Use the graph below of y = f(x) to answer the following question. point 8 4. point 1 point 2 3 2.…

A: To answer the given function using the given graph.

Q: 6. The initial population of a town was 12000. After 5 years the population increased to 38000…

A:

Q: Solve the given differential equation by undetermined coefficients. y'' − 12y' + 36y = 24x + 2…

A:

Q: Select the conic section represented by the equation. 4x 2 + 3 y 2 - 2 = 0 parabola point ellipse…

A:

Q: 1. JC y = f(x) is transformed to g(x) = 3 f (2x – 6) + 9. The domain and the range of each function…

A: Solving

Q: {In (n+10) – In (n+5)}°

A: an =ln(n+10)-ln(n+5)an =lnn+10n+5limn→∞ an =LIf the limit exists and finite, then the sequence is…

Q: Rewrite cos(t+π/3) in terms of sin(t) and cos(t).

A:

Q: Consider the series n+5 Determine whether the series converges, and if it converges, determine its…

A:

Q: Find the x-value maximizing the shaded area on the interval 0 < x < 18. One vertex is on the graph…

A: First  I have found the Area of the shaded region region then find the critical point and then find…

Q: The particular solution of the following equation by using the method of undetermined coefficients 2…

A: A detailed solution is given below.

Q: 1 x + ex 2 g dx

A:

Q: 9-x2 dx x2 Evaluate:

A:

Q: A radar, using the polar coordinate system, detects that two airplanes are currently located at…

A:

Q: The non-homogenous solution of the following equation by using variation of parameter method y" + y…

A: Given

Q: Find an equation for the tangent plane to the surface given by f(x,y)=÷(4x² – 2y²) at the point…

A:

Q: Q2// Solve the following differential equation: e2y dx + 2(xe2y – y)dy = 0

A:

Q: f(x) = -x² + +9 square units

A: Given the query is to the area bounded by the curve.

Q: d а. dx (e* cos.x) cOs x

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: If 0 < 0 < 7, which of the following points DOES NOT coincide with the polar point (-r, 0)? Select…

A:

Q: Given that the vectors X1 = () e- -2t ,X1 = (C)e-6t are solutions of a system x' = AX, do they form…

A:

Q: A radar, using the polar coordinate system, detects that an airplane is currently located at the…

A:

Q: A teacher has prepared 20 mathematic and 30 geometric and 25 physics questions for a test he can…

A: This question can be solved using the concept of combination.

Q: Consider the polar equation defined by r= 5 cos(2 sin 6), where 0<0< 2x. Determine the missing…

A:

Q: Evaluate the integral. (y – 2)(2y + 1) dy Jo |

A: ∫xndx=xn+1n+1+C ∫1dx=x+c

Q: Sketch the graph the integrands and use areas to evaluate the integrals. V16 – x² dx

A:

Q: The graph of a function f is given. Use the graph to estimate the following. y 5 (a) All the local…

A:

Q: determine which statement is true (A) Not a function (B) Function; domain: R (C) Function;…

A: Graph÷

Q: Let C(x)= x2+4x+1 dollars be the cost function, where the x represents the quantity. The estimate…

A: Cost

Q: 19x + 900 The average cost for a company to produce x units of a product is given by the function…

A: To find change in average cost as production goes from 150 to 151 units.

Q: 4. Find the volume of the solid that lies under the paraboloid z = x? + y² and above the region R in…

A: We want to find the volume.

Q: Solve the system. Give your answer as (a, y, z) 3z - y + z = 7 -2x + 2y + 3z = – 18 3z-6y + 6z = 0…

A: Use the method of elimination and find the value of x, y and z.

Q: A-28. 3. |A| = 3, B = 8, and the angle formed by A and B is 45°. Determine A - 2B

A: We have to solve above question

Q: Find an equation of the tangent line to the graph of the function at the given poin y = x²ex - 2xex…

A:

Q: Solve the following set of equations with LUdecomposition: 3x1 – 2x2 + x3 = -10 2x1 + 6х2 — 4хз — 44…

A:

Q: Sketch the graph the integrands and use areas to evaluate the integrals. + dx -2

A:

Q: Begin with the Maclaurin (Taylor) series: cos r = 1 - 2! 4! 6! (a) Evaluate cos 0. (b) List the…

A: According to the guidelines, we are instructed to answer 1 question or 3 sub question,the others can…

Q: Evaluate khefaltowing cartesian integrals by changing them inteequiv alent Palar integrals: dy dx

A:

Q: . Consider the polar curves C1:r= 3 sin20 and C2 :r = 3 cose, and let R be the shaded region as…

A: r=3 sin 2θ and r=3 cos θ R is the shaded region: To Find:a. Find all points of intersection of C1…

Q: Find an equation of the line tangent to the curve r = sin 30 at the point where 0 = klo

A: Polar curve

Q: In order to evaluate Vr2 – 10x + 29 dx, the correct substitution is Ox=-5+2 tan(t) Ox=2+5tan(t) Oa =…

A:

Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

A:

Q: Find the n-th Taylor polynomials for 1 about x = 3 and express it in f(x) = x+ 2 sigma notation.

A: Taylor polynomial of nth degree of f(x) centered at 'a' :          f(x) = f(a)…

Q: Consider the polar curves Cı :r = 3 sin 20 and C2 : r = 3 cos 0, and let R be the shaded region as…

A:

Q: Find fr(r, y) and fy(x, y) given f(r, y) = tan r - cos(r² – y²).

A:

Q: Evaluate y' of the given functions y = /3x + 4)(x + 3)

A: We can find the derivative as below.

Q: 22// use the tests indicated in front of each of the series ollowing to determine if the series…

A: 1. Summation of (k+1)/(k2-1) from k=2 to infinity.  2. Summation of 1/(5k+1) from k=1 to infinity.