dy Find for the following function. dx y = 9 cos x sin x %3D dx II

Q: An investment loses 3.1% of its value every week. Find the half-life in this situation. The half-lif...

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Q: S secºxdx ха

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Q: Solve y" – 2y' + y = 0; y(1) = y'(1) = 0

A: To solve the given differential equation.

Q: Let F and G be vector-valued functions such that F(t) = (cos(nt), e²t-1, t² – 1), Ġ(1) = (1, 1, – 1)...

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Q: 4) Find dy given: y (1-x)(1+ x )(1+ x³ )(1+x*) dx d'y given: y= (5x -3X7x+x) 5) Find dx

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Q: (b) Oppositely directed to 6i – 4j + 2k. 6 i v = V56 2 k + V56 V56 (c) Same direction as the vector ...

A: Given problem:- Find unit vectors that satisfy the stated conditions. (b) Oppositely directed to 6i-...

Q: Find an equation for the plane through points P(1, -1,2), Q(2,1,3) and R(-1,2,–1).

A: This question can be solved by applying the formula of equation of plane passing through three non c...

Q: Evaluate the integral. dx J x4+7 Inx) A In 14+7 In x| +C B In 14+7 In x| +C © O In +C |7+4 In x| D I...

A: On solving this we will get:- option (D) is correct

Q: Find the tangent line approximation T to the graph of f at the given point. Then complete the table....

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Q: 11) Use implicit differentiation to find the slope of the tangent line to the curve at the specified...

A: We will find the slope of the tangent line of the given curve at the specified point.

Q: +oo (x – 1)" Consider the power series >- log n n=2 (a) Show that the resulting series when x = 0 is...

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Q: 1.f(0) = (금x* + 3)" %3D

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Q: 14. What is height of the isosceles triangle with the greatest area that can be inscribed in a circl...

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Q: 3x dx 1+r4

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Q: 1. f sin³ 4xcos³4xdz

A: To evaluate the given integral.

Q: Find the solution of the initial value problem Please fill in a question quickly within a quarter of...

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Q: 4. What is the volume of the prism? 4.6 in 5.1 in 2.1 in 13.6 in 2.8 in

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Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers a...

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Q: af fe and if f(r, y) = 2 + 2y+3,is? 1. Find the partial derivatives

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Q: Find the solution of the initial value problem Please fill in a question quickly within a quarter of...

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Q: Consider the following planes. -6x + y + z = 6 12x – 2y + 6z = 36 (a) Find the angle between the two...

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Q: 1. lim 3 2. lim 57 3. lim log r

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Q: x+5 9 – (x – 3)²

A: Given: I=∫x+59-x-32dx    ....(1)   We know the trigonometric identities; (1). sin2x+cos2x=1 (2). cos...

Q: 4. S sec*(8)dx

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Q: Find the indicated vector. Let u = (-8, 6), v = (8, s). Find 7 u + 9 v. O (-128, –30) O (-14 144) O ...

A: Given query is to find indicated vectors.

Q: xtan dx - y cos xdy = 0 a) Show that this equation is exact if not find identify the integration fac...

A: Let's find. 

Q: Find the area bounded by y = 2 -x squared and y = x A 9/2 7/2 5/2 3/2

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Q: A computer loses 35% of of its value each year. If the computer cost $600 new, calculate its value a...

A: A computer loses 35% of of its value each year. If the computer cost $600 new, calculate its value a...

Q: 2) Show that y = A cos x + Bsin x, where A and B are constants, is a general solution of the differe...

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Q: Exercises: Sketch the region bounded by the given curves, then find its area. 1. y = x², y = 2x

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

Q: x sec(em) tan(enx) dx= sec x2 tan x2 dx A) True B) False

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Q: Evaluate the indefinite integral as an infinite series. ex- 1 dx 2x Σ + C n = 1

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Q: Consider the parallelepiped with adjacent edges u = 4i + 5j + k v = i+j+9k w = i+ 2j + 6k Find the v...

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Q: 1. |x² In x dx; u = In x, dv = x² dx 2. 0 cos 0 de; u= 0, dv = cos 0 d0 %3D

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Q: Given the curve ax? = y³, find the shortest possible distance between the curve and the point (0,8a)...

A: I am attaching image so that you understand each and every step.

Q: If y = csc² x+ 2 , then ſ y dx = cot x + 2x + c True O False

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Q: cos-1(2 x2)

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Q: D. Coefficients linear in two variables 6. (3x – y + 2) dx + (9x – 3y + 1)dy = 0

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Q: (Зл — 1)" 5n /n +1 n=1

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Q: 2n +1 Σ n n tan-1 n n=1

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Q: wnd the point of intersection of the line through (1, -3, 1) and (3, -10, 5), and the plane given by...

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Q: 2 lim (x + 1) - (х* + ) x → 0

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Q: The distance x, in feet, between successive cars on a certain stretch of highway has the following p...

A: We have to find the probability [ P(0 <= x < inf) ]

Q: Determine whether the planes are parallel, orthogonal, or neither. 9x – 8y + z = 6 x + 2y + 7z = 1 O...

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Q: Identify the vertices and foci of the hyperbola with equation x2 = 1 92 402 The vertices are The foc...

A: We will find the vertices and foci. 

Q: Use Root Test to determine whether the series E(-1)"en² sin²n (2) n=1 absolutely converges, conditio...

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Q: Valuate% I-S(t sinzo} de

A: To evaluate the given integral.I=∫0π12sin 2θ2 dθ    

Q: Question 4 Find all the local maxima, local minima, and saddle points of the function. f(x, v) = 36x...

A: Let us consider a function f(x,y) . To get the critical point of f(x,y) we put ∂f∂x=∂f∂y=0 Let (a,b)...

Q: Find a formula for the nth term of the sequence. - 2, 1, 6, 13, 22, ... Determine the sequence's for...

A: We have to find the sequence's formula in terms of n. 

Q: Find the vector component of v = 2i – j+ 3k along b = 4i + 4j + 7k and the vector component of v ort...

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