Question 3. The parametrization of a curve C is given by r(t) (a) Find r' (π/6). = (sin(t), cos(t), t²) on the interval [0, π]. (b) Find parametric equations for the tangent line to the curve C at the point where t = π/6.

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A: We have to solve Questions 12.

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A: directional derivatives

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A:

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A: Given :fx=7xgx=x+2hx=1x+5

Q: II. Trigonometric Substitution. Evaluate the following integrals using trigonometric substitution.…

A:

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A: Given, ∫0π4141-cos12xdx

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A:

Q: ƒ (t) = -{ 5,03

A: We know the followingLf(t)=∫0∞e-stf(t)dtLeat=1s-aLtn=n!sn+1Lsinat=as2+a2Lcosbt=ss2+b2

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A: Here we will draw inequality,

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A: Given :f(x)=cosxx1=1.6

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A:

Q: 3. Integral xdx 10x -234

A: We will use substitute method to solve this integral.

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A:

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A: We need to determine Maclaurin series for xarctan(x2).

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A:

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A: The given data is: limh→0f10+h-f10h=-5

Q: 6. Find the radius of convergence and the interval of convergence for E-0¹ (x-2)".

A: 6. The given power series     ∑n=0∞12nx-2n

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A: The given differential equation is;  d2y/dx2-3dy/dx+2y=cos(e-x).

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A: Given :I=∫01dz7z+16

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A:

Q: Find the coordinates of the points of inflection for the function. 14) f(x) = 7e-x²

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Q: Find the sum of the values of f(x) = x³ over the integers 1, 2, 3, ..., 10.

A:

Q: SSF-n de of F-xy 1-2 k outward (normal away from the z-axis) through the cone z-6√ Use a…

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Q: Assume x and y are functions of t. Evaluate dy/dt. 12) x3+y3=9;- dx dt 13) xy + x = 12; dx dt = 4, x…

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Q: -1.5 -4.5 -1.5 Let [ f(x)dx = 5, |_^*^* f(x)dx = 6, [*¹*³ f(x)dx = 5. -6 -6 Find and -3 [²₁ f(x) dx…

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

Q: Evaluate each integral. √x+Yy dz Jx - "X rx + y 0 Jx-y y dz dy Now evaluate J = = y dV, where E =…

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Q: y = 1/2 (e² + e^¹), − 1 ≤ x ≤1

A:

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A:

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A: Given that,

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A:

Q: for (#)(x). 100. Find the restrictions in the domain, if any, for then select all answers that are…

A: It is given that: h(x)=x2-5x-24,j(x)=5x+15

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A: Given :w=x3yz+xy+z+3x=3costy=3sintz=2t

Q: Question 4. Determine if the series Σ n=1 5n+1 7-2 converges or diverges. If the series converges,…

A: We have to find the given series is convergent or divergent  , if the series is convergent give its…

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A: Given :Equation of unir circle : x2+y2=1

Q: 4. Find the area of the region bounded by y=6-2-2² and the z-axis. 125 (a) A= square units 6 (b) A =…

A:

Q: Find the integral of the following indefinite integral equations: Jx dx / (5 + 9x4) Jx dx/v(16-9x4

A:

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A: Given that,uc=c1-ρ1-ρρ≠1ln cρ=1

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A:

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Q: CHECKPOINT 1.24 Integrate the function [²₂x³dx.

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Q: Q2.B. A bag contains 19 tickets numbered from 1 to 19. A ticket is drawn and then another ticket is…

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Q: Solve the following linear programming problem.   ​Maximize: z= 39x+10y subject​ to: 8x+6y ≤48…

A: Given that, Maximize: z= 39x+10y subject​ to: 8x+6y ≤48   13x+y ≤48…

Q: Please determine if the sequence converges or diverges. \left(\frac{n!+6}{n!-2}\right)

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A:

Q: Solve the given differential equation. 16x2y" + 16xy' - y = 0 C₁ cos(In(x)). + C₂sin (In(x)) 4 4…

A: here we have to solve differential equation.

Q: Consider the following equations. 124 O Sketch the region bounded by the graphs of the equations. y…

A: