A. Solve the following problems using the concepts of Parametric Equations. Show complete solutions. d?y 2. Find the second derivative, dx2 a. x = t2 + 1 and y = t3 t2 b. x = 2 %3D + 2 and y = sin(t + 1)

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) x3…

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Q: Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is…

A: This question is related to infinite series, we will solve it using given information.

Q: dx S x(1+(lnx))²) 2.

A: This question is related to indefinite integration, we will solve it using given information.

Q: Find a formula for the nth term of the sequence (choose one of 2) The sequence 2,6,10,14,18, ..

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 1. Identify the type of conic section whose equation is given, then find the vertices and foci.…

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Q: dæ4 evaluated at x = -1 dx evaluated at x = –1 dx? evaluated at x = -1 dx3 dªx4 evaluated at x = -1…

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Q: dF Find given F(x) = (3s - 4) ds. %3D dx dF dx %3D

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Q: r1(t) = 3ti + 3tj + t°k, r2(t) = t'k d [ri(t) r2(t)] = dt

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Q: 9x² = 164 -8y² + 36x + 64y

A: The given equation is: 9x2-8y2+36x+64y=164...(1)

Q: 240 2 s7 17(s-1)8

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Q: m²-m Find S (m1) dm

A: Given; I=∫m3-m-1mdm   As we know that; The Sum rule; ∫fx±gxdx=∫fxdx±∫gxdx The Power rule;…

Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). 13 ||r(t)| r(t) = t'i+ t'j K(t) :

A: Using given formula,

Q: ||r(t) × r"(t)|| ||r"(t)||³ Use the formula k(t) = to find k(t). r(t) = eti+ej

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Q: Find the arc length L of the graph of r(t). r(t) = 2 cos(t)i +2 sin(t)j+tk, 0<t< 2m L =

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Q: Q9. Find the equation of the tangent plane to f(x, y) = x In(y) + x²y+3 at the point (x, y) = (2,…

A: Consider the equation of the form          F(x,y,z) =0 then the equation of the tangent plane to the…

Q: 10 Consider the function f(z). 6. Let F(r) be the antiderivative of f(z) with F(1) 0. Then F(z)

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Q: Evaluate the integral 24 11) dx, by making the appropriate substitution: u = Ja* (2* – 11)*“dz =

A: ∫ un du =un+1n+1+C

Q: 6n Q4. Determine whether the infinite sequence converges or diverges. /Зп? + 7 n=1 If it converges,…

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Q: Consider the angle shown below that has a radian measure of 0. A circle with a radius of 2.7 cm is…

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Q: na the coordinates of a point P on th line and a vector parallel to the lihe. x - 2 - y + 5 = z + 4…

A: Given query is to find the coordinates of the point p and vector v.

Q: (rece - tan 0) de 2. J]

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Q: Q2) Convert the polar function r tan20 to cartesian. %3D

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Q: the integral dx Va? – x? e may use x- educe the integral to a sine and dx= a cose de substitutions…

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Q: g(b) Use the Substitution Formula, JKax) •gʻ(x) dx = [ | f(u) du where g(x) = u, to evaluate the…

A: The given integral,a) ∫-334rr2+22drb) ∫034rr2+22dr

Q: 12 12 f(x) dx = 16 and 9. If f(x) dx = 5, find the following. %3D f(x) dx

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Q: Given: P(-1, -1, 2) what is o in cylindrical coordinate system?

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Q: Let u = (1,2,3) and v = (2a,2a,a^2) Which of the following values of a ensures thatu and v are…

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Q: 2. Find the area bounded by a curve x = y - 2y? - 3y and the x- axis 3. Find the area bounded by a…

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Q: The concentration of a drug in a patient's bloodstream, measured in mg/L, t minutes after being…

A: We need to find average concentration.

Q: The series 1 k ln k k=2 converges. Choose an option: ()Real ()False

A: Integral Test : Suppose that f(x) is a continuous , positive and decreasing function on the interval…

Q: Find the area in the first quadrant bounded by y=4x-x² and the x-axis

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Q: ||r(t) × r"(t)|| Use the formula k(t) to find «(t). r(t) = e*i+etj K(t) =

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Q: (d) 10*+3 = 62r

A: Given,  10x+3=62x

Q: Find Duf at P. f(x, y, z) = 6x°y°z*; P(1, – 2, 1); u = i %3D Duf = i

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Q: JoFe is going to Fusion Plex to watch one movie. His choices of genre are "action", "horror" or…

A: topic - combination and permutations

Q: Calculate the first five derivatives of f(x) = – sin(x). Then determine f(8) and f(9). (Use symbolic…

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Q: he acceleration function (in m/s²) and the initial velocity v(0) are given for a particle moving…

A: Given query is to find the velocity function and the distance traveled.

Q: Q1/0fin t the Tulorssevies at- for F(): Sinメ Iat ○ F(対 ak y=1 f(x) =

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Q: Q10. For the function f(x, y) = x³e³y_find the maximum value of its directional derivative at the…

A: Here, f(x,y)=x3e3y⇒∇f=∂f∂x,∂f∂y=3x2e3y,3x3e3y⇒∇f(1,0)=3(1)e0,3(1)e0=(3,3)

Q: Differentiate the function. g(u) = 7u + V 5u

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Q: Find T(t) and N(t) at the given point. r(t) = (t² – 8)i + tj; t= 8

A: Given,            rt=t2-8i+tj ; t=8To find : Tt and Nt at the given point.We know that,…

Q: Evaluate the limit, using L'HÔpital's Rule if necessary. sin 3x 1. lim x→0 tan 8x In x5 2. lim x7 –…

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Q: Find the supply function x = f(p) that satisfies the initial conditions. dx 10 x = 140 when p = $5…

A: Here, dxdp=10p-5⇒dx=10p-5dp⇒∫dx=10∫1p-5dp+C...(1)

Q: ||r'(t) × r"(t)|| Use the formula k(t) = to find k(t). ||r(t)||* r(t) = ei+ e*j K(t). ||

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Q: Evaluate the integral and interpret it as the area of a region. 6x + 7 - x dx 55, 55 - 32 9 9 Sketch…

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Q: 72n+1 E(-1)" 22n+1 (2n + 1)! n=0

A: Explanation of the answer is as follows

Q: Find the slope of the tangent line to the graph of y = √x − 1 at the point (5,2).

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Q: Integrals

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Q: Determine the value of c for which lim (1 + 2,5n = ell n-00 сп

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Q: nd the linearization of f(x)= {Vx at c = 64. Use the linearization to approximate 64.05.

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