Derivatives: using (4 step rule). 4. f(x)=sin3xcos3x 5. f(x)= x² cos(x² +1)

Q: Solve the equation: Зx(ху — 2)dx + (х3 + 2у)dy %3D 0. O x³y – 3x² + y? = c O 3xy – 3x? + y² = c

A: Here is the solution

Q: Determine if the series converges or diverges without using the different tests discussed in Lesson…

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Q: Determine if the sequence is increasing, and/or bounded. 3 — п (b) { (a) 1 — Зп - 3n n=1

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Q: Solve the initial value problem +3y , 0>0, y(1) = -5. de

A: To solve: θdydθ+3y = sinθθ2, θ>0, yπ=-5 ⇒dydθ+3yθ = sinθθ3 This is a linear differential equation…

Q: Find the intervals on which f is increasing and decreasing. f(y) = sin y - y cos y on 2' 2

A: Find your answer below

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

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Q: A light shines from the top of a pole 20 m high. A ball is falling 10 meters from the pole, casting…

A: We sketch lines on the given image as below: Let us assume x = The height of the ball = BG.  y =…

Q: In R³, consider the triangle formed by X (2,0, 4), Y (0,5, 0) and Z (-2,0,0). Us- ing vector and…

A: Let's find.

Q: Find the volume of the solid bounded by the graphs of the given equations.   z = xy,    z = 0,…

A: Given problem:- Find the volume of the solid bounded by the graphs of the given equations.   z = xy,…

Q: In R?, using vectors and angle between vectors, verify that the points P (13, –1 Q(-9,3) and R (-3,…

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Q: A. Given: lim f(x)=-9 lim g(x)= 2 2. lim[3h(x)–6] 4. lim[f(x)- g(x)+ h(x}] lim h(x)=4 x→8 x→8 x→8 1.…

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Q: dx 7. S; x³ Vx2-4

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Q: Give the curve r = 3 cos 0 b) Find the points on the given curve r = 3 cos O where the tangent line…

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Q: DERIVATIVE OF TRIGONOMETRIC AND INVERSE TRIGONOMETRIC FUNCTIONS. Find dy/dx, 1. y = sin (x? + 3x +…

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Q: a) Find the fifth term of the sequence 16 31 46 61 15' 21' 27

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 2.) Use the comparison test to determine if the series is convergent or divergent: 2n+3 Σ 3n2 +2 n…

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Q: a) f(x)dx = f(x) b) f(x)dx = y = f(x) Area A = 1 Area B = 2 Area C = 2 | 5f(x)dæ = A c) Area D = 0.6…

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Q: 1.(a) Do there exist integers a, b, c such that gcd(a, b) = 30, gcd(b, c) = 24, gcd(a, c) = 54?…

A: (1) gcda,b=30=2×3×5  ...(1)gcdb, c=24=23×3    ...(2)gcda,c=54=2×33     ...(3)

Q: Homogeneous or Not? State the degree of the function. 4x^2-3xy+y^2

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Q: Find the curve given by x = vt and y =(? – 4), t 2 0 find the slope and concavity at the point (2,…

A: Here, the parametric curve is given by: x=t, y=14t2-4, t≥0

Q: Solve the area of the surface of revolution generated by revolving the arc of the curve, x=y° from…

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Q: If the function / is continuous for all real numbers and if f(x)= ² when x*-2, x+2 then f(-2) = O…

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Q: EVALUATION. Do as indicated. Write TRUE if the statement is true otherwise write FALSE. 1. The given…

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Q: It is determined that the value of a piece of machinery declines exponentially. A machine that was…

A: A machine that was purchased 5 years ago for $66000 is worth $36000 today.

Q: The sum of the geometric series 1 3-1+ 3 1 + 9. 1 +- 81 - 27 is: none 13 914 OO O

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

Q: y y=x + 1 x = 4 y= 0

A: Area , A = ∫∫R dy dx

Q: Evaluate the integral. In(x) dx, y > 0

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Q: Find the arc length of the parametric curve. x = e', y = e, z = v2t; 0<t< 5

A: This question can be solved using the concept of length of arc of curve in parametric form.

Q: of the curve defined by x=3t-t anc

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Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, -1). %3D %3D v (0, 6) %3D b =

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Q: Find a and b such that v au + bw, where where u (1, 2) and w - v- (0, 6)

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Q: 4. Use the given graph of a functionf to answer the following questions. y= f(x) a. State all the…

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Q: Question For the function f(x), whose graph is shown below in blue, find lim f(x). The red vertical…

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Q: Find the direction cosines and angles of u and show that cos a + cos ß + cos y = 1. (Round your…

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Q: Use the formula k(t) ||F(t) × r"(t)|| to find k(t). ||r(t)||° r(t) = 11 cos(t)i+11 sin(t)j+6tk K(t)…

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Q: decimal number o.11 11 Eaual ^ true O evror

A: This is a problem related to decimal points conversion into p/q form. Please follow the procedure…

Q: nin m Find the distance between the point and the line given by the set of parametric equations.…

A: This question is based on 3-d line.

Q: 5x2 + x + 16 dx x3 + 4x 9)

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Q: What is the area of the region bounded above by y = 2x and below by y = X on the interval [0, 3]? 8…

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Q: Find the component form of v given its magnitude and the angle it makes with the positive x-axis.…

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Q: Convert the point (x, y) from Rectangular to polar coordinates (r, 0). 3. (–1, v3)

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Q: Find the directional derivative of f at P in the direction of a. f(r, y, 2) = xy + z²; P(0,3,1); a =…

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Q: Lets compute a derivative in reverse! Given the function f(r) = e² + sinhr + + z find a function…

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

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Q: Find the vector v with the given magnitude and the same direction as u. Magnitude Direction ||v|| =…

A: A vector v with given magnitude in the direction of u is given by v.uu.

Q: IM Given that > п+1 = 0.47199 determine the value of n3 n + 1 n=3 n3 n=5

A: This is a problem related to series and sum calculation. Based on the general formula and concept we…

Q: Find the diameter of the circle 4x? + 4y² + 24y – 4x – 35 = 0. B. 6V2 C. 3V6 A. 6V3 D. 3/2 E. None…

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Q: Verify that the two planes are parallel. --x + 6y + 2z = 7 *+ 3y + z = 8 Find the normal vector, n,,…

A: The normal vector to the plane ax+by+cz=d is given by n=a,b,c

Q: The one-to-one functions g and h are defined as follows. g (x) = 3x+13 h= {(-8, -3), (-3, 2), (3,…

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Q: Find the gradient of the function at the given point. 2 = In(x2 – y) - 9, (2,3) Vz(2, 3) = Need…

A: This is a problem related to derivation. Please follow the procedure given below for solution.