5. Find a Taylor series expansion around x = 1 for f(x) = 6. Without solving the exact answer, calculate sin(2) by evaluating up to six terms of Maclaurin series of sin x. Express the answer to 5 significant digits.

Q: solution

A:

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

A:

Q: d Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating d dt dt the product directly…

A:

Q: Sketch the region enclosed by the curves and find its area. у %3 сos 9x, y —D 0, х - x = 18' 9 NOTE:…

A:

Q: Edit Evaluate the line integral -ydx + xdy along the curve C : y = 21x from (21, 21) to (0,0). NOTE:…

A:

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: Evaluate I| xy dA where R is the region in y = x2 A) 13/7 B) 16/3 18 D) 20

A: We have to evaluate the integral.

Q: find the equation for x in y=3x-x^3

A: Solving

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A: We need to evaluate integral using Green's theorem.

Q: Express the area of the given surface as an iterated double integral, and then find the surface…

A: We have to find the surface area.

Q: moving in the xy-plane. Position Vector Point r(t) = 6 cos ti + 6 sin tj (3/2, 3V2) (a) Find the…

A:

Q: Find V· (V × F), if F(x, y, z) = 7e*²i+ 6xe"j –- 6e²k. V·(V × F)

A:

Q: A conical tank with a diameter of 2 m across the top and 3 m high is filled with water. Find the…

A: The given problem is solved below in detail.

Q: Evaluate the double integral over the rectangular region R. y'dA; R = {(x, y): -1sxs1, - 8 <ys 8} |…

A:

Q: Find div F and curl F if F(x, y, z) = 10e"Y i – cos yj+ 8 sin? z k. div F= curl F=

A:

Q: Find the limit. lim (t i - 9 j+ 1? k) lim (t i – 9 j+ k) = i+ j+ k i i i

A:

Q: ||r'(t) × r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). 3 r(t) = t'i + tºj %3| K(t) =

A: Use the given formula and find the required expression.

Q: What is the volume of the largest cone having its circular base circumscribed about a face of a…

A: To determine the volume of the largest cone having its circular base circumscribed about a face of a…

Q: Describe the graph of the equation: r = 5ti – 8j + (1 + 5t)k. [Choose the correct answer.] O The…

A: Given, r= 5ti -8j +(1+5t)k Therefore, The equation is given by, r= &lt;0,-8,1&gt;+t&lt;5,0,5&gt;

Q: Evaluate the definite integral that represents the volume of the solid formed by revolving the…

A: Explanation of the answer is as follows

Q: Evaluate JJ xy dA , where R is the region in ху ´(1, 3) (5, 3) R (2, 1) (4, 1) A) 56 в) 67 38 D) 90

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: The strength E of an electric field at a point (x, y, z) due to an infinitely long charged wire…

A:

Q: Use the Babylonian's formula to calculate the circumference of a circle with diameter of 30 units.

A:

Q: Use a double integral to find the volume under the plane  z=32x+yz=32x+y and over the rectangle…

A:

Q: Edit Find div F and curl F if F(x, y, z) = 13y*z'i – 11x°2°j – 5xy'k. div F= 0 curl F= k (-55 a' 2º…

A:

Q: Find the area of the region(s) enclosed by the curve y = |2x - 6|, the x-axis, and the lines x = 0…

A: Given: y=2x-6x=0 and x=4

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A:

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

A:

Q: Find the directional derivative of the function at P in the direction of v. g(x, y) = V x2 + y2,…

A:

Q: Question 13 2 Evaluate the iterated integral. yz dx dz dy

A: Evaluate the iterated integral .

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 8 1 lim t+o 5t2 + 6't (?,?) - (

A: We have to find limit of given function

Q: Determinant of 2 x 2 Matrices. Solve for the determinant of the following matrices: [7 -3] A = 4 6 B…

A: We know that for a matrix A=abcd=ad-bcA=7-346=7*6-(-3*4)                       =42+12…

Q: sine "/2 Evaluate the iterated integrals r cos e dr de A 1/6 1/2 11/9

A: Explanation of the answer is as follows

Q: Find the centroid of the region. NOTE: Enter the exact answers. (¤, g) = |(?, ?) %3D y = =? 1

A: y=x7

Q: Use the arc length formula to find the length of the curve y = 3x – 5, -2sxs 3. Check your answer by…

A:

Q: r = V cos 20 r = 5 cos 0

A:

Q: Verify Green's Theorem by evaluating both integrals ам | y2 dx + x2 dy dA ду for the given path. C:…

A: Solution is given below:

Q: 27х3-8а3 y3= y= 3x-2a Зх-2а

A: Y'=?

Q: Consider the following planes. 3x + 4y – z - 56 x - 8y + 2z = 0 (a) Find the angle between the two…

A: Find the angle between the two planes..

Q: Find the approximate area under the curve of f (x) =x+1 from x = 0 to x = 2, using 4 left-endpoint…

A:

Q: n° 3. Determine whether the sequence a, - converges or diverges. If it n – 2n° converges, find the…

A:

Q: Evaluate JJ Xy dA, where R is the region in LA ... y = x? R 2 A) 13/7 B) 16/3 c) 18 D) 20

A: A detailed solution is given below

Q: True/False Indicate whether the statement is true or false. 9. A normal vector to a line is parallel…

A: We have to state whether the given statements are true or false: Statements are as follows: 9. A…

Q: 4. A commercial cattle company currently allows 20 steer per acre of grazing land. On average a…

A:

Q: Find the divergence of the vector field F. F(x, y, 2) = In(9x+ 8y² )i + 72xyj + In(8y² + 5z? )k #6…

A: Solution is done in step 2 and 3

Q: A torus formed by revolving the region bounded by the circle x2 + y2 = 49 about the line x = 8 (see…

A:

Q: +1++4+ +7++10 written in sigma notation is equal to The sum 3k-5 A k=1 3k - 4 B k=1 3k-2 k=1 3k-1…

A: Let's find.

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

A:

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1.

A: The given integral is ∫c(x+3y2)dy   and the curve C is x=2t,  y= 6t   where 0≤t≤1 Now, y=6t⇒dy =…

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. V64-22 xy dy dx dz

A: Given: I=∫08∫064-z2∫0xxydydxdz   The Power rule: ∫xndx=xn+1n+1+C