Evaluate these limits as x approaches infinity or negative infinity- Question 1 x2 + 3x + 1 lim,m

Q: Find the sum of the following convergent series. (a) tan-(n) – tan-'(n + 1) n=1 (b) 2" + 3" 4" n=1

A: We have to find sum of convergent series. 

Q: Give The 15T four nonzero Ternm oF Me Serbes abour ) He) =

A: Given:fx=excos3x

Q: Give The 15T four nunzero Term ot MeSertes aboufx=625.

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Q: 1. e (3xy-x)dx+e* dy = 0; when x = 0, y = -1 4 Ans. y =-- 1 3

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Q: Solve for the derivative of the function using chain rule. 11. f(x)= ln(sin(8x))

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Q: Showthat dz du

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

Q: 12 dx

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Q: 5. Check if the following is a separable equation. dy * = xy + 1 O variable separable O not variable...

A: The detailed solution is given below Thanks 

Q: Use differentials and the graph of f to approximate the following. (Round your answers to three deci...

A: From the given graph: f(2)=1,f'(2)=0-24-0=-24=-12

Q: 16. Find the area of the shaded region. Leave your answer in terms of pi. 50'

A: The solution is given in the next step.

Q: Find an equation of the tangent(s) to the curve with parametric equations x = 1+ Vt, y = et at the p...

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Q: Determine whether u and v are orthogonal, parallel, or neither. u = -3i + 8j - k v = 3i + j - k O pa...

A: Two vectors u and v are orthogonal if and only if u.v =0 .

Q: 1. Find the general solution of the differential equation: d°y d'y dy , dy - - dx6 dæ3 dx2

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Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 14j as ...

A: ANSWER IS GIVEN BELOW.

Q: What is the derivative of the following? 1. 3x^2 2. -1/2x^2

A: Topic = Derivative 

Q: III. Derive the following HCA 1. The unity rule: = 18 dx du dx 2. The quotient rule: xp dx

A: f(x)=xDerivative formula:f'(x)=limh→0 f(x+h)-f(x)hf'(x)=limh→0 (x+h)-(x)hf'(x)=limh→0 hhf'(x)=1ddxf(...

Q: The coefficient of z2 in the expression (a +z)5 is 640. What is the value of a?

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Q: The region bounded by the curve ×=y2, the y-axis, and the line y=2 is revolved about the x-axis. Fin...

A: We have to find volume. 

Q: S ds V3s? + 1

A: Given query is to find the integral.

Q: Determine any planes that are parallel or identical. (Select all that apply.) O P,: -60x + 90y + 60z...

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Q: 6. (6x°-4x² +1)*

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Q: dy -2 sin x where y (5 = JT dx

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Q: 2. Integrating factor by inspection: Solve the equation: (y – xy²) dx + (x + x?y²) dy = 0 O = In y –...

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Q: Determine whether the planes are parallel, orthogonal, or neither. 3x - 15y – 3z = 7 4x 20y – 4z = -...

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Q: 3. A jar sauce. How many cups of spaghetti sauce do 4 jars contain?

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Q: Find the angle 0 between the vectors in radians and in degrees. (Round your answer for part (a) to t...

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Q: Let g (x) = tan 1x + tan (1/x). Show that g (x) = k, a constant, for any x in the domain. Find the v...

A: Given problem:- Let g(x) = tan-1x + tan-1(1/x). Show that g(x)=k, a constant, for any x in the domai...

Q: Find the coordinates of a point P on the line and a vector v parallel to the x - 7 y + 9 = z + 4 Р(x...

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Q: Give The Taylor series abour fa) = ex mring Series-> for the followingevaluaro ns, and Firor Five te...

A: Put x=-5 and x=1/2

Q: 1 3. f(x) = (-x4-3)2

A: Solve for the derivative

Q: - partial fraction 1 dx x(x² +1}

A: Let's find. 

Q: (b) For the matrix 1 -2 A = 3 -2 -1 \12 3 -5. (i) (ii) (ii) Determine the characteristic equation an...

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Q: If y= Vx (x-1), find dy (Use rules, not a XP de finition

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Q: The functions f and g are continuous and differentiable with f'(x) = g(x). Selected values of the fu...

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Q: 2. What is the slope of the normal line to the curve 4x2 - 9y2 = 1 at point (3,2) ? a. 3 b. - 8. С. ...

A: Normal at any point on the curve is a straight line that intersects the curve at that point and is p...

Q: 10. f(x) = cos (2x)e*²-1

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Q: Find the derivative of the function. f(x) = 7x2 In(9x)

A: To find derivative of given function.

Q: 2 2 V 4 +x-

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Q: U.S. Cell Phone Subscribers The number of cell phone subscribers in the United States between the ye...

A: Given a function relating the number of phone  subscribers from year 2000 to 2010

Q: 6. (Sections 8.8 and 8.9) Determine whether the following piecewise-defined function is a probabilit...

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Q: The Furmetion fla)=t kininen as Taylor series abaut x =0 4s derwamine ite series elow end nerite our...

A: a) fx=8e2xb) gx=9x5e-1 x

Q: Find the area of the triangle with vertices P(1,5, –4), Q(0,0,0) and R(2, 4, 1). NOTE: Enter the exa...

A: We know that the expression for the area of the triangle △PQR is: A=12PQ→×PR→ The given vertices of ...

Q: Solve the seperable differential equation for. dy 1+ x ;x > 0 xy5 dx Use the following initial condi...

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Q: Find the exact value of the cos 75° using a half-angle formula. cos 75° = 2+V3 :: 2-V3 :: 2-V3 VV3-2...

A: Let's find. 

Q: (cos x+xcost)dt + (sin t-t sin x)dx = 0 Ans. t cos x+x sint = c

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Q: Suppose that f(x, y) 3, and D = {(x, y) | æ² + y² < 16}. Then the double integral of f(r, y) over D ...

A: Solved below

Q: 3x dx

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Q: Find the gradient of the function at the given point. g(x, y) = 18xe/x, (3, 0) Vg(3, 0) =

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Q: Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer alge...

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Q: 2. Find the general solution of the differential equation: dy dy -5 + 6y = e* dx? dx

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