2 3x-x² lim х>-2 \x-х-6. х2 —х-6

Q: Use the Ratio Test to determine the radius of convergence of Σ n=1 Vn - 11" x" Then determine…

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Q: The graph of the derivative f' of a function f is shown. y = f'(x) 2 4 6 (a) On what intervals is f…

A: Let's find.

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A: see below the answer and calculation

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A: we know two vectors <a, b, c> and <x, y, z> are parallel if (a/x) =(b/y) =(c/z) .

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of PQ.…

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Q: 4, X^ 3^ dx

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y², (12,…

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Q: dy Find by implicit differentiation for the following equation dx 3D8X+6y+7 dy dx

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Q: Question 3: Find A-!, using “super-augmneted ma- [3 1 1 -17 A = 5 2 1 1 -1

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Q: F(x, y, z) = (2xe*) i+ (2y + 3y?22)j+ (x²e* + 2y³z) k is conservative. Find a functionf such that F…

A: To find the function f  And then evaluate the line integral along the given curve.

Q: Evaluate the integral by interpreting it in terms of areas. (10 – 5x) dx

A: Explained below

Q: A/ 10 Evaluate 4/1+ cos 10x dx. A/ 10 4/1+ cos 10x dx =

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Q: Find the interval of convergence of the series. (3x)" 2" n=1 (Use symbolic notation and fractions…

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Q: The rate A (in tons per year) at which a pollutant is being dumped near a city is given by the…

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Q: Use the graphs to evaluate the expressions below. fx) 5- 8(x) 5- 4- 4 3 -1 2 4 5 6 -1 2 3 4 5…

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Q: 15 The population of a district is 600 000 at the beginning of 2015. The population P(n) of the…

A: We need to find A,r and % increase.

Q: Calculate the Taylor polynomials T2(x) and T3(x) centered at x = a for f(x) = 12 sin (x), a =…

A: f(x)=12 sin(x)fπ2=12f'(x)=12 cos(x)f'π2=0f''(x)=-12 sin(x)f''π2=-12f'''π2=0Taylor polynomial…

Q: Suppose that L is a location function of an object, given as L(t) = We will compute the 3t + 7…

A: We can solve this as follows:

Q: Find the angle 0 between the vectors in radians and in degrees. u = 4i + 2j + k v = 2i – 4j (a)…

A: u=4i+2j+kv=2i-4j

Q: Find the equation of the tangent line at the given value of x on the curve. y° +xy² -61=x+3y°; x:…

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Q: For what Valuer of the Constant(k that the function fayt=x"+kxy+y will have a- Saddte Point b-local…

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Q: what are 7 and 8 in standard hyperbola equation? 7) The foci are (-8, 2) and (2, 2). Vertex at (1,…

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Q: Find the derivative of the function y = xta{z) y =

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Q: Find the derivative of the function y = In(5e – 9xe "). y = ||

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Q: th Use the ri"-term test to find wether the fottowing Sexies exe divergent or not- n+2

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Q: Problem 6 Given the series 5.+,25x + 125x + 625 x + a) For which values of x does the series…

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

Q: In this figure, p || g. Find the value of x. (9x + 12)° (x-2)° >4

A: Topic = Geometry

Q: A1 3 y = 2x A1 + A2 = A3 1 y = x²

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Q: 1. 3 Consider the parametric surface 7(u, v) = (2uv, u? - v, u² +v²), where u +v < 2. Evaluate the…

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Q: How 3 Find the absalute maxine and minima for the funCtion (4x-x) Cosy an the rectangular plate…

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Q: dy by implicit differentiation. dx E. Find 1 ー+ー=2 х у 1 x² +y? = xy 2. 1.

A: the process of finding the derivative of a dependent variable in an implicit function by…

Q: 4 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -2 -4 -5 -64 The graph above is a transformation of the function x…

A: Topic:- function

Q: Maximize the function f(x, y) = 3xy– 4x² – 3x – 5y + 12 subject to the constraint 3x + 4y = 5 Find…

A: To find the maximum of the given function wuth the given  constraint .

Q: Use an appropriate substitution and then a trigonometric substitution to evaluate the integral. dx…

A: Given query is to find the integral.

Q: The linear approximation at x=0 to sin(6x) is A+Bx where A is:    and where B is:

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Q: Graphing calculator allowed. The position function of a particle in rectilinear motion is given by…

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Q: Consider the function f(x) x - 2x2 - 4x + 1 on the interval [-1, 3]. Find f'(x). F'(x) = 3x – 4x – 4…

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Q: a b b -b ) Give the determinant of the matrix A = d e -e Lg h -h]

A: Given query is to find the determinant of the matrix.

Q: Find the equation of the tangent line at the given point on the following curve. 3 3 In (x+y)=x y" +…

A: The given equation is  ln(x+y)=x3y3+ln(x2+2)-8, (1,2).

Q: A simple biochemical reaction with three molecules has solutions that oscillate toward a steady…

A: A simple biochemical reaction with three molecules has solutions that oscillate toward a steady…

Q: exercise

A: f(x) = cx4 If x is doubled

Q: a) l . Find the length of the curve 20 y= x, 0sx<3 V5 Length= b)! !: Find the area of the surface…

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Q: A region bounded by f(x) = 3- x, y = 1, and x = 0 is shown below. Find the volume of the solid…

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Q: Use linear approximation, i.e. the tangent line, to approximate 1/1.001as follows: Let f(x)=1/x and…

A: Given problem:- Use linear approximation, i.e. the tangent line, to approximate 1/1.001as follows:…

Q: Find the polynomial function f with real coefficients that has the given degree, zeros, and solution…

A: This question is based on roots of a function.

Q: Verify that the function f(x) = x² – 8x + 5 satisfies the three hypotheses of Rolle's Theorem on the…

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Q: Find the derivative of the function y = 4x sin '(x) + 4/1 – x². y'

A: Here we have to find the derivative of the given function.