Find the unit tangent vector to the curve at t r(t) = t°i + 3t?j, t= 2 T(2) =

Q: n-1 1. b) Determine whether the series is convergent or divergent. If it's convergent, 4" n=1 find…

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Q: 10 Find div F and curl F if F(x, y, z) = xz°i+ 5y"x²j+ 4z?yk. div F= curl F=

A: Solution:

Q: Evaluate the given integral by changing to polar coordinates.     sin(x2 + y2) dA   R, where R is…

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Q: I need help with this question (Not honor class) (Not grading)

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Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: 4 3…

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Q: y = sin3x

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Q: Find the volume of the solid generated by revolving about the y- axis the region bounded by the…

A: Given problem:- Find the volume of the solid generated by revolving about the y- axis the region…

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A: Given , A tank originally contains 100 gal of fresh water. Then water containing (1/2) lb of salt…

Q: 2 _9 ii)lim- t-3 t2+4

A: Given query is to find the limit of the expression.

Q: A model for the length of daylight (in hours) in Philadelphia on the tth day of a particular year is…

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Q: Inx 6. lim,

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Q: For the given position vectors r(t), compute the (tangent) velocity vector r'(t) for the given value…

A: Find derivative of position vector then we get velocity vector then put the given value

Q: Find the curvature and the radius of curvature at the stated point. r(t) 2 cos(t)i+ 3 sin(t)j+ 10tk;…

A: Solving

Q: 8. Relationship Between Continuity and Differentiability: (a) Justification needed): If lim…

A: To discuss the  relationship between continuity and differentiability.

Q: A spring has a natural length of 22in. A force of 16001b stretches the spring to 32 in. How far…

A: We will use rules of spring stretch to solve it.

Q: Find the directional derivative of f(r,y, z) = e² cos(Tyz) at (0, 1, ) in 2-1 -y-1= I-2 the…

A: To Find: Directional derivative

Q: Represent the plane curve by a vector-valued function

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Q: Evaluate the limit using L'Hospital's rule: Lim0+1 In(x+1) 2xe"

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Q: X+2 At what points is the function y = continuous? 2 X- 9x + 14 ... Describe the set of x-values…

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Q: Find V. (V × F), if F(x, y, z) = 5e"*i+ 6xe®j– 2ek. V · (V × F)

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Q: 31.| CSC I COLI dt

A: We will use substitution method to solve both the integral.

Q: Find the length of the curve r (t) = i + 6t°j + 2t°k, 0 <t < V1 L =

A: We will find the length of curve.

Q: Evaluate the line integral (6x + 8y)dx + (3x – 3y)dy along the curve C: x = 4 cos t, y = 8 sint…

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Q: Use the graph of the function f to decide whether the value of the given quantity exists. (If an…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

Q: f' (x) = 3x* – 5x² + x

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Q: e

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Q: Find div F and curl F if F(x, y, z) = x'i – 3j + yzk. div F= curl F=

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Q: Evaluate the integral: (5si + 9s²j + 10k) ds Answer : i+ j+ k

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Q: Find the particular solution that satisfies the initial conditic (e* + eX), f(0) = 1, f'(0) = 0 2…

A: Here we have to find the particular solution of given differential equation.

Q: Graph the eauation - include local+ Absolut extreme Points if applicable - -include inflection…

A: maxima minima

Q: nd the S (1–) dx A. x– 2 In|x| – +c B. 3x – 2 In|x| –-÷+c C. 2x – In|x| –+c D. x– In|x| - +c

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: r(4) (arcsin(t), arcos(1),0

A: Given: rt=arcsint, arccost, 0   As we know that; ddxarcsinx=11-x2ddxarccosx=-11-x2

Q: An arithmetic sequence is given below. 10, 3, -4, -11, th term d, Write an explicit formula for the…

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Q: 6. Consider the DERIVATIVE f' graphed below. Sketch a possible graph of the original function f on…

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Q: Evaluate the following integral: |sec2 (z) tan (z) dz = 因团 +C Be sure to enter powers of…

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Q: Find the principal unit normal vectóř tô thể curve at the r(t) = /2ti + e'j + e-k, t = 0 %3D

A: Principal unit normal vector

Q: 17-20 Express the limit as a definite integral on the given interval. 17. lim sin x, Ax, t, [0, 7]

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 14th term of the following geomnetric sequence. Find the 1. 2, 4, 8, 0. 昌 唱

A: Use geometric series concept

Q: (a²- x²}3½ dx

A: see below the answer and calculation

Q: 14. Find the curl of the vector field F = x²i – xevj+ 2xyzk

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Q: 4 fy 1 -3 -2 1 -1 -2

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Q: Use the Egyptian's formula to calculate the area of a circle with diameter of 8 units. (roundoff…

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Q: Find the Laplace transform of f(t) ={0, 0 ≤t ≤1         7t −7, t ≥1 .}

A: Given :f(t)=00≤t≤17t-7t≥1

Q: Find an arc length parametrization of r(t) = (e' sin t, e' cos t, le') r1(s) = (|

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Q: Find the unit vector in the direction of (3, -2). Write your answer in component form. Do not…

A: We will find the unit vector.

Q: H.W (5) Solve the following differential equations of (3x -6xy)dx+(-3x' -2y)dy 0

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Q: dx

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Q: al)= gi+ sk vio)= 5), ro) 0

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Q: dx 2.

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Q: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y 0, y= 4+ x°…

A: Here we have to find the volume.