(d) (u v)v (e) u (3v)

Q: Composition. Suppose we want to find the composition of a function with itself. Let g(x

A: We will put value of x =g(x)

Q: J In(x² + 1)dx

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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: Find the following. (0, 1), v = (5, -5) (a) lu|| (b) v|| (c) ||u + v|| (d) (e) ||v|| u+v

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Q: Given that f(1) = r°h(x) h(– 1) = 5 h'(– 1) = 8 %3D Calculate f'( 1).

A: Given that fx=x6hxh−1=5h'−1=8

Q: Area. Suppose the area of a circle is decreasing at a rate of3m2/sec, the rate of change of the…

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Q: ALL WORK Solve the triangle, if possible. If the triangle represents the ambiguous case, solve for…

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Q: Integration by Substitution. The rate of growth of Grass carp, one of the most common type of fish,…

A: The given data is: ∫025x+10x2+4x+4dx

Q: 10. xy' + 2y = 6x²/y

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Q: For the function f(r) = - 2x – 5x, f(r + h)- f(r) evaluate and simplify: h Find the value of the…

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Q: 2. t23* dt

A: The given problem is solved below in detail.

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

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Q: Identify the inside function, u = g(x), and the outside function, y = y = (x2 – 6x + 9)2 u = g(x) y…

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Q: Find the arc length of the parametric curve. x = e', y = et, z = v2t; 0<t < 8 L ||r'(t) × r"(t)||…

A: Given parametric curve x=et  , y=e-t  , z=2 t   ;  0≤t≤8

Q: 4. So -dy Vy+1

A: To evaluate: ∫01yy3+1dy Substitute y3=u2⇒13y-23dy=2u du⇒13u4dy=2udu⇒dy=6u5du. As y→0⇒u→0, y→1⇒u→1…

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: The other type of question in chapter 7 is solving trigonometric equation. We will not be practicing…

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

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Q: S(a – x)°dx

A: We need to integrate given function.

Q: Expand f(z)=1/(z-1)(z-2) in a Laurent Series valid for the given annular domain: 1 < |z| < 2

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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: 14

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Q: A block of mass m = 2.00 kg is attached to a spring of force constant k = 410 N/m as shown in the…

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Q: Find the following. = (3, 5) U = %3D (a) ||u|| (b) ||v|| (c) ||u + v||

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Q: (1 2. 14 Approximate | * -6) dx using 4 rectangles. It is approximatley : (If necessary, round to…

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

A: To solve the following problem

Q: Find the length of arc of the given curve. 5. R= (sin 2t , cos 2t , 2t³/2), 0 sts1.

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Q: If L is a line in 2-space or 3-space that passes through the points A an B, then the distance from a…

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Q: A particle is moving with acceleration a(t) = 36t + 8. its position at time t = 0 is s(0) = 17 and…

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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: CURRENT OBJECTIVE Determine the limit at infinity of a polynomial function Question For the…

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Q: given magnitude and the same direction as u. Magnitude ||v||-5 Direction u- (-4, 6, 4) Submit Answer

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Q: nsider the Integral I when answering the following questions. g(x) dx

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Q: ind an equation of the plane with the given characteristics. The plane passes through the points (4,…

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Q: 3. S w°cosw dw

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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: Given the function: f(x) = 47' - 8z 9x' + 8x2 + 8x - 4

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Q: Find the following. (0, 1), v = (5, -3) U = (a) ||배 (b) ||v|| (c) |u + v||

A: Explanation of the answer is as follows

Q: omposition. Suppose we want to find the composition of a function with itself. Let g(x) = -4(x+3)2…

A: Given, g(x)=-4(x+3)2

Q: 4. Find the area under the following curves over the indicated interval: (c) z = -3t2, y = 2t, for 2…

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Q: Use the formula k(t) ||r'(t) × r"(t)|| to find k(t). ||r(t)| r(t) = 11 cos(t)i+ 11 sin(t)j + 6tk

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Q: Consider the following. u = (6, -1, 0) v = (-2,3,0) Find u x v. Determine if u x v is orthogonal to…

A: Explanation of the answer is as follows

Q: Find the derivative of the function. y = x2 In x2

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Q: You are given a sphere of radius 2. A hole of radius b (b < 2) is drilled through the center of the…

A: Follow the procedure given below.

Q: Let f be a twice differentiable function such that f(1) = 2 and f (3) 7. Which of the following must…

A: We have to choose correct option  Here using Lagrange mean value theorem

Q: ピ+5 1 lim t一+0|5t2 +6'2t (?, ?)

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Q: Find a and b such that v-au bw, nhere u-(1, 2) and w- (1. -1) v - (4, 5)

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Q: 3. Find the length of the curve r = e® for 0ses 2n.

A: Given polar curv er=eθ   ; 0≤θ≤2π

Q: A nursery has determined that the demand in June for potted plants is The cost of growing x plants…

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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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