For the function f(x) = 1 – 1/ (x + 2)2, find the following: f(-x)

Q: Find the particular solution of the differential equation that satisfies the initial condition. (Ent...

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Q: b) E(-1)"+1 Vñ Inn n-1

A: The given series is: ∑n=1∞nln n which is an alternating series with bn=(-1)n+1nln n, n≥1  

Q: 1. y = 2x2-5 at ( 2, 3) %3D

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Q: Find equations of the tangent plane and normal line to the surface z + 19 = xe cos z at the point (1...

A: We have to find tangent plane equation and normal line.

Q: 2. Let f(t) be a continuous function on the interval [0, 27]. Suppose the 1st order Fourier approxim...

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Q: Determine whether the integral is convergent or divergent. The integral from negative infinity to 0,...

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Q: 3. lim f(x) = -2, 4. lim f(x) = +00, X-2- lim, f(x) = 2 and f(2) = 0 lim 1437(x) = -0

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Q: Sec o

A: The solution is given in the next step.

Q: (a) Find the differential dy. y = ex/4 dy = (b) Evaluate dy for the given values of x and dx. x = 0,...

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Q: sinh(2 In(c)) = (A) 를 + (B) c² – (C)를 높 2c 1 2c2 (D) c -! 1 (E) 0

A: Topic = Functions

Q: Find the linear approximation L(x) of the function f(x) = /1 - x at a = 0. L(x) = Use L(x) to approx...

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Q: Suppose that in 1662, a man bought a diamond for $34. Suppose that the man had instead put the $34 i...

A: The continuous compounding formula is P(t)=P(0)ertwhere P(0)= the initial amountr = the rate of inte...

Q: How much money must you invest now at 4.5% interest compounded continuously in order to have $10,000...

A: We know continuous compounding formulaP(t)=P0ert where value at time t P0=principal amount r= annual...

Q: Show that the equation has exactly one real root. 3x + cos(x) = 0

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Q: Determine the speed (in meters per second) of a particle with a trajectory (3 sin (3t), 8 cos (3t)),...

A: We have to find dsdtt0=π4

Q: Find the equation(s) of the tangent line(s) at the point(s) on the graph of the equation y-xy-12=0, ...

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Q: x(x²-x+2) dx is equal to 3

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Q: /3 Without using a calculator: tan¬1 ( 3

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Q: 16 Evaluate x1² (x4 – 2x² + 1)²dx. - 81

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Q: dx xVx2/3-7 XVX

A: An proper and improper integral is an definite integral. ∫1x2+a2dx = 1atan-1xa+C

Q: There is a jump discontinuity at x = 2 and ƒ(2) = 3 %3D

A: There is a jump discontinuity at x=2 and f(2)=3

Q: A restaurant purchased kitchen equipment on January 1, 2017. On January 1, 2019, the value of the eq...

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Q: Find the average velocity over the interval [1,4] Find the average velocity over the interval [1,1 +...

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Q: A parallelogram is formed by the vectors [1, 2] and [3, -4]. Find the area of the parallelogram. O 1...

A: Given query is to find the area of parallelogram.

Q: Show that V is not a subspace of R³: V is the set of all (x, y, z) such that x + y + z = 3

A: We need to prove that V is not a subspace of R3  .Below find the solution in the image.

Q: Based on the graph, fill in the table with the appropriate values lim f(x) f(c) -2 -1/2 1 3 4

A: Given

Q: Evaluate the Integral iF the funthun X = = XSin (xy) ニ over the vecfongulor region R- [0,1][1, 2]

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Q: Show your complete solution.

A: Given that: 1. f(x)=3x2+2x2. f(x)=1x3. f(x)=8x-2

Q: (x'y-xy°)(xdy+ydx) 3. +dy = 2xdx

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Q: 24. f(x, y) = In(x² + y)

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Q: Identify and sketch the following quadric surfaces. Label the vertex/vertices in your sketch. (a)  ...

A: Follow the procedure given below.

Q: graph of f(x) =÷ at the point ( 1,-). %3D

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Q: Find f(x) and g(x) such that h(x) = (f o g)(x). Let g(x) = 2x + 1. 3 h(x) = /2x+1 f(x) =|

A: topic - functions

Q: Find x' for x(t) defined implicitly by x +tx+t° - 4 = 0 and then evaluate x' at the point (-2,-6). x...

A: We have to find the value of x' at point (-2, -6) 

Q: Find the equations of the items described below 1. Any line perpendicular to r(t) =t+ 2. The plane ...

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Q: Use implicit differentiation to find y' and then evaluate y' at (3,0). 9 ey =x? - y? y' = y' (3,0) =...

A: Let's find. 

Q: If f(x)=x, then f'(5) = (A) 0 (B) 5 (C) 1 25 (E) (D) 5

A: Topic:- derivatives   

Q: The graph of f is given. State the numbers at which f is not differentiable. y -4 -2

A: In this question we have to state the number at which f is not differentiable according to the given...

Q: A projectile is shot upward from the top of a 220-foot building with an initial velocity of -22 feet...

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Q: ind by implicit differentiation if y is defined as a function of x by the equation xy' + x? = x + 3y

A: Topic = Differentiation

Q: Using the ratio of successive terms, what can you conclude on the given sequence increasing decreasi...

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Q: 2. lim 2. lim f(x) = 1 and f(0) = -3 1. lim f(x) = -1 and f(1)DNE x-1

A: 1. limx→1f(x)=-1 and f(1) DNE2. limx→0f(x)=1 and f(0)=-3

Q: Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given m...

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Q: 1. Y= 3x -x- 2

A: Find your answer below 

Q: Let f(z) = z – 6z. Calculate the difference quotient (3+h)-{(3) - for h = .1 h = .01 h = -.01 h = -1...

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Q: oint (, y; 2) is tiver by The temperature at a point (x, y, z) is given by T(«, у, 2) — 1500е s me w...

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Q: Evaluate the iterated integrals  ∫1 0  ∫1 0 dxdy

A: Given query is to find the value of the integral.

Q: 2x+9 10. S x2+6x-4

A: Follow the procedure given below. 

Q: Evaluate the integrals C f (z) dz, where C is the unit circle centered at the origin and f (z) is g...

A: As you have asked multiple subparts so I have answered first three subparts as per the guidelines.

Q: (a) Find the point of intersection of the tangent lines to the curve r(e) = (5 sin(at), 6 sin(æt), 4...

A: Given:   r(t) = ⟨ 5 sinπt , 6 sinπt , 4 cosπt ⟩    When t = 0 and t = 0.5