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

Q: cos (0 + 11) y = Use symbolic notation and fractions where needed.) dy -4 cos (0+11) sin(0+11)| do

A:

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 4 cos(t)i…

A: To find unit tangent vector at given parameter.

Q: Find V· (V × F), if F(x, y, z) = e*²i+3xe'j – 7e*k. V . (V × F) = x z evz 三

A:

Q: Find the distance of the centerof gravity of the area on the first quadrant region bounded by the…

A:

Q: 2. Write the given (total) area as an integral! a. The area above the x - axis and below y = 4 -x2 T…

A: Area between the curve  y=f(x) and x-axis is defined as ∫abf(x)dx where a, b are point of the…

Q: Example 6 Video Example 0 A particle moves along a line so that its velocity at time t is v(t) = t2…

A: Given;  v(t)=t2-t-12.

Q: Question 16 Use double integration to find the volume of the solid bounded by the paraboloid z = 9x…

A:

Q: Inx Evaluate the limit using L'Hospital's rule: Lima0 cosh

A:

Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

A:

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: (a) Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 19, (1,…

A:

Q: Question 15 1-sine Evaluate the iterated integrals J. J. p2 cose dr de̟ A 1 В) 2

A: ddθ(sinθ)=cosθ ∫rndr=rn+1n+1, for any real number n.

Q: ,2 COS cos n Σ n3 n=1

A: Given problem:-

Q: 8. 1) Use the Integral Test to determine whether the series is convergent or dive n' +1 n=1 Please…

A:

Q: 12. Find an equation for the tangent plane to the surface given by 2xy? = 2z2 – ryz at the point (2,…

A: We know that the equation of the tangent plane is: nxx-x0+nyy-y0+nzz-z0=0 Where n→-nxi+nyj+nzk is…

Q: Find the area of the surface that is generated by revolving the portion of the curve y = x between x…

A: Given; y=x^2 between x=1 to x=2

Q: 1. Determine whether the series is convergent or divergent. If it's n=l e"+1 convergent, find its…

A:

Q: 7. -4 3. ) -3 7. 1) 10. 2)

A:

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (e2i + Sin(/e) j+e-k 7t

A: Limt-0 (e2ti+sin(7t)j/(7t) +e-5tk).

Q: Find the following for the given equation. r(t) = ( + 6t)i + (t² – 6t)j %3D (a) r'(t) = (b) r"(t) =…

A:

Q: r2 cose dr de valuate the iterated integrals A) 1

A: ∫0π∫01-sinθr2cosθdrdθ

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

A:

Q: Find the area of the region enclosed by x2 and y = 5x by integrating with respect to y. the curves Y…

A:

Q: Find lim f(x) for the given piecewise function. x-4 2х + 5 if x 4 If the limit does not exist,…

A:

Q: Skatch the curve in polar coordinates. r=I+ 3sino 2 -6 -4 -4

A: Given curve r= 1+ 3sin( theta)

Q: +4

A: To check the convergence of the given improper integral:∫-∞2dxx2+4

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: Use a double integral to find the volume under the plane z = 32x + y and over the rectangle R = {(x,…

A:

Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A:

Q: (xy)=efr sin), Plo,0l Q(5,1)

A:

Q: 3. -2 -1 5. Find the velocity, acceleration, and speed of a particle traveling along the curve…

A:

Q: Question 6 Use double integration to find the volume of the solid. ... 3 3x + 2y + 4z = 12 A) 6 B) 9…

A:

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

A:

Q: Use a triple integral to find the volume of the solid. The solid bounded by the surface y = x and…

A:

Q: Question 11 Find the approximate area under the curve of f (x) =cos from x = 0 to x = Tt, using 4…

A: We have to find it from Trapezoidal rule.

Q: Where is each function continuous? (a) f(x) = Vi %3D

A: According to the company rule we can answer only first question and rest can be reposted.

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

A:

Q: Find V · (V × F) if F(x, y, z) = 10 sin xi + 5 cos(8x – 9y)j+ 4zk. V· (V × F)

A:

Q: Find r'(t) r(t) = 6yEi + t²/ij + In[? }« %3D r'(t) = %3D

A:

Q: Find the unit tangent vector to the curve at the specified value of the parameten r(t) = 4 cos(t)i +…

A:

Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A:

Q: (a) Select the correct choice below and fill in the answer box within the choice. O A. lim f(x) =…

A:

Q: Question 9 1 2 1 Evaluate the iterated integral. J, J. J. (x²+ y2 + z?) dx dy dz -1°0 0, А) 5 В) з 8…

A: The solution is given in the next step.

Q: Evaluate the definite integral. i+e"j+tk)dt (e^ – 1) i – (e- - 1) j+ k O e - i+ (e" - 1) j + k 1 O…

A: A detailed solution is given below

Q: O A) B) 8 C) n O D) T

A: Given; y=√2 x

Q: 7-18 Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 7.…

A:

Q: find SCE) at timet V=-5t+5, S0) = 14

A:

Q: y+1 - Z 4. Find the distance between the lines = z and x = 3 %3D -2

A: topic- distance between lines

Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). 13 r(t) = t'i+ t3j K(t) =

A:

Q: ||r'(t) x r"(t)|| Use the formula k(t) to find k(t). 13 r(t) = t’i+t5j K(t) =

A: We have to find k(t)