Use series to evaluate the limit. X-In(1 +x) lim

Q: Given: z = a' + æy", r = uv² + w®, y = u + ve" az Find when u = 2, v = – 3, w = 0 dv

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Q: Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a…

A: The volume of the hemisphere is: V=23πr3dV=2πr2dr

Q: ; Test the following series whether it is convergent or divergent (show all your works) n2 +7 a) 2…

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Q: S cos³ 3x dx

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Q: r(t) = (tan(5t))i+t cos(t)j – Vtk

A: Given: rt=tan-15ti+tcostj-tk

Q: 3. Use chain rule to find given w = Vx2 +2y2 + z² and a cos (st), y = -2s In t ane 2 = 3s?Vt. 3s2Vt.

A: Follow the procedure given below.

Q: Q2) Find the integral of: L*„6 tan*x dx 4

A: LetI=∫-π4π46tan4xdxTake the constant…

Q: In +4 7n+4 Let 2 5" and an 5" n=1 an+1 a) Find lim an n + 00 7n+4 is n =1 5" b) Determine whether 2…

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Q: Find div F and curl F if F(x, y, 2) = 17y*z*i – 3a*2®j – 3ry®k. div F= curl F=

A: Divergence of F: ∇·F=i→∂∂x+j→∂∂y+k→∂∂z.i→17y4z4-j→3x3z6-k→3xy6 ∇·F=∂∂x17y4z4+∂∂y-3x3z6+∂∂z-3xy6…

Q: Describe the graph of the equation. r= -3 i+tj+(t2-1) k O Itis a parabola in the x = 3 plane, vertex…

A: This is a problem related to parametric equation plotter. Based on the x, y and z value in terms of…

Q: Find V· (V × F), if F(x, y, z) = e®²i+ 4xe®j – 5eV²k. V.(V × F) =

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Q: -24 e 5n costx dy Ln(sinx) dx

A: To solve the following problem

Q: 2. S(e" + e-3)² dt

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Q: Consider the exact first order diff. equ: |M(x,y) = 2.xy- 3.x? N(x, y) = x² - 2y (I): (2xy - 3x )dx…

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Q: Use the formula k(t) ||r(t) × r"(t)|| to find «(t). %3D r(t) = t²i + t°j K(t)

A: We have to find the value of k(t).

Q: COSX sin x dx 4. S 1-ఆశి అరికి న

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Q: 9. Let A be the coefficient matrix for the system of linear equations: 2x + 9y – 5z = 1, — 6х — 2у +…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Find the equation of the tangent line in the given place. complete solution 1.) Tangent to the…

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Q: Suppose that f(z, y) = z*y°. The directional derivative of f(1, y) in the directional ( – 1, – 2)…

A: We can solve this as follows:

Q: Find a power series representation for the function. (Give your power series representation centered…

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Q: Find curl (8z i + 9x j + 8y k). curl(8z i+ 9x j + 8y k) = ( i )i + ( i j + ( )k

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Q: Use the Rules of Differentiation to differentiate the following functions: a. f(x) = 2x³+ 6x d. h(x)…

A: Given data

Q: Find curl (7z i + 8xj+2y k). curi (7z i+ &x j+ 2y k) = (1 i+( j +( )k

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Q: Determine the signs (positive, negative, or zero) of y = f(x) (shown in the graph) and f'æ) and…

A: Consider the graph

Q: Evaluate the line integral, where C is the given space curve. y dx + z dy + x dz, C: x = t, y = t, z…

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Q: dt 1-cos t+sin t

A: First we shall simplify the expression then integrate

Q: Describe the graph of the equation. r = 2 cos t i- 10 sin t j + k O An ellipse in the plane x = 1,…

A: Parametric plot÷

Q: o) rind all veluees of x for which fue Canveryes. for there helues of x, wnite tul fum of tue senes…

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Q: satisfies thé équation:y + 13y - Show that y=e Sin 3x

A: Topic = Derivative

Q: Find r'(t). r(t) = (tan (6t))i+t cos(t)j – Vik I| NOTE: Enter your answer in terms of i, j, and k.…

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Q: Find the limit of the following sequence or determine that the sequence diverges. 15 Select the…

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Q: Show that the function f defined by (x, y) = (1, – 1) f(x, y) = 1² + y (x, y) # (1, –1) I + Y is not…

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Q: 15 dy dt 2-

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Q: For what values of a and b is the line-5x +y b tangent to the curve y = ax when x = 37 a = b D %3D…

A: -5x +y  =b    and curve is y = ax3 at x =3 here for tangent the slope of curve and line is same…

Q: Find V. (V × F), if F(x, y, z) = 3e²*i+9xe*j – 4ev*k V· (V × F) =|

A: Use the curl and divergence for the F.

Q: Find [r(t) · u(t)] and [r(t) × u(t)] in two different ways. dt dt r(t) = ti + 8t2j + t³k, _u(t) =…

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Q: Let g(x) = | f(t) dt, where f is the function whose graph is shown below. What is the value of g'…

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Q: Solve 6+ 3+ ニ 2-t-26 3-7++10 +

A: Please refer to the image below

Q: Find the series radius and interval of convergence for what values of x does the series converge x"…

A: We need to find radius and interval of convergence.

Q: dx 9- x 15.

A: Topic = Integration As per guidelines , At  a time only one question can be answered out of…

Q: Evaluate the limit using L'Hospital's rule 4* – 97 lim

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Q: Problem 5 Part 1: Consider a cost function where C(x) in Philippine peso is the total cost of an…

A: Let's find.

Q: Determine the vector field of F. F(x, y) = 9i – 3j %3D

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Q: Describe the graph of the equation. r = 14 sin 17t i – 14 cos 17t j O It is a circle of radius 14 in…

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Q: Evaluate the definite integral. O e10 e10 - 1 i+ k 10 10 - 1) j+ k 1- e10 - 1 10 e10 i - e j+ 1 k 2…

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Q: S tan -1x dx

A: Solution is done in step 2

Q: Evaluate the definite integral. e16t i + e¬tj +t k )dt O el6 – 1 (e-- - 1) + i+ (e-1 – 1) j + , k 16…

A: To solve the given integral.

Q: The graphs of f(x) and g(x) are shown. For what values of x does f(x) = g(x)? x = -2, x = 0, x = 3…

A: We have to choose correct option

Q: Sy³/y² + 9dy

A: ∫ y3y2+9dyLet u=y2+9=∫u2-9u2du=∫ u4-9u2du=∫ u4du-∫ 9u2du=u55-3u3Substitute back…