Find V × (V × F) if F(x, y, z) = 4xyj+2xyz k. V × (V × F) :

Q: Find div F and curl F if F(x, y, z) = 6e#Y i – 7 cos yj+ 9 sin² z k. div F= curl F=

A:

Q: ах 2xy 2.xy +3y x +2xy dy dx

A:

Q: 4. Use L'Hopital's rule to evaluate lim(1 – 2 sinh(r))ach(=).

A: 4) To evaluate: limx→0(1-2sinh(x))csch(x)  which is in 1∞ form.

Q: 1. E(n + -3 2 n=1

A:

Q: 1 — х b. lim х36 (х — 6)2

A: b) limx-6(1-x) /(x-6) 2 a) limx-5 (x-1 sqrt(3x+1))/(x-5).

Q: Find the average value of the function f(x,y)=eˆ(y/x) over the region bounded by y=x, the x-axis and…

A:

Q: SHOW THAT THE DIFFERENTIAL EQUATION IS LINEAR EQUATION OF ORDER ONE 3. Vdx + (2x +1 – Vx)dV = 0

A:

Q: 3. Draw an example where ja + D|

A:

Q: Determine whether the improper integral converges or diverges. Evaluate the integral if it…

A: To evaluate the value of  ∫-∞∞7x2+4x+8dx=7∫-∞∞7x2+4x+4+4dx=7∫-∞∞7(x+2)2+22dx

Q: Describe the graph of the equation. r= 5 cos t i - 18 sin 1 j +k O An ellipse in the planex = 1,…

A:

Q: If f(x) = cos(2x) then find II f (t|4)

A: Given query is to find the Indicated derivative.

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

A: Solution: ∯∂∂x6xy -∂∂y3xydxdy   (By green's theorem)

Q: dx 1-e-* Evaluate A. 2ln|e* – 1|+ c B. Inle* – 1|+x +c C. 2 In|e* – 1| +x+c D. Inle* – 1|+ c

A:

Q: Evaluate the iterated integral: x + 4y dx dy Answer :

A: We can solve as follows

Q: Calculate r'(t) and T(t), where r(t) = (2t – 5, 4 – 4t, 1 + 4t). %3D r'(t) = { %3D T(t) = {

A:

Q: In the year 2000, the population of a small city was 47,000. The population grows at a rate of r(t)…

A: For the following problem,

Q: Consider the following statements. 1-If B is a symmetric matrix of 9x9 so the elements b32 and bz3…

A:

Q: Approximate the point of intersection of the graphs of fand g. Then solve the equation f(x)=g(x)…

A:

Q: Solve the exponential equation algebraically. Approximate the result to three decimal places. e2x –…

A: Solve the exponential equation algebraically.

Q: Find div F and curl F if F(x,y, z) = x*i – 7j + yzk. - div F= curl F=

A:

Q: Given that f'(x) is continuous everywhere and changes from negative to positive at x=a, which of the…

A:

Q: Find the limits of integration ly, uy, Ix, ux, Iz, uz (some of which will involve variables a, y, z)…

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

Q: Change the order of integration. f(x, y) dy dx Jo

A: 0≤x≤10≤y≤xRegion bounded by:x=0, x=1y=0, y=x

Q: 1. Sketch a single graph of a function f(x) which satisfies all of the following the limits and…

A: The function satisfies,f-3=1, limx→-4f(x)=-1, limx→2-f(x)=-∞, limx→2+f(x)=∞, f'(4)=0f(2)=2,…

Q: find (2n +1)! = 120

A: Here we have to find the value of n.  2n+1!=120

Q: test conerg ence and clivergence h!

A:

Q: Evaluate (2x – y) dx + (x + 3y) dy. C: x-axis from x = 0 to x = 4

A:

Q: Find the derivative of this function

A:

Q: For the function f(x)=2x^{2}+4x-1f(x)=2x2+4x−1, find the slope of the secant line between x=-1x=−1…

A:

Q: For each sign chart for f. Carefully sketch the graph of both functions f and f. Upload your work as…

A: When derivative of f is positive then f is Increasing and when f' is negative f is Decreasing

Q: y x = y - 2 y = 1 x = e -3 -1 1 2 4 | y = -1 3. 3.

A:

Q: -945° is equal to i radians. (Type your answer in this format: a*pi/b where a and b are integers.)

A:

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: I have stated the used formula in the solution

Q: Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x? b.…

A: area under the curve

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

A:

Q: Find curl (6z i + 7x j + 8y k). curl(6z i + 7x j + 8y k) = ( i )i + ( i )j + ( i )k

A:

Q: dy 2 + y = 0, y(0) = -3 dt

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

Q: L, f(x)dx + [° f(x)dx = 5. Si f(x)dx – Sº f(x)dx = 4.

A:

Q: Determine the value of t that maximizes the area above the x-axis and below the graph of the…

A:

Q: Integral calculus, partial fraction decomposition

A:

Q: n What is the closed-form expression for the series 2 (k-2)², k=1 37 A + 6 n³ -n²+ 13 B 6 6

A:

Q: Evaluate the following sum: 3x + cos 2016 + cos (Write your answer in the simplest form, use…

A: The given sum,1+cosπ3+cos2π3+cos3π3+cos4π3+......+cos2016π3

Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

A: To find the volume of the given solid using triple integral.

Q: Evaluate lim (x)/

A: We can find the  limit as below.

Q: Find the solution of y' = 2(2x-y) which passes through the point (0, -1) the answer should be y=2x-1

A:

Q: For nEN, simplify: 1 +1+2+ +4+ +8+ 금+ 1 .+2"-1+ 2n-1 (A 2" - 21-n+1 2" +2-n 2n - 2-n 3 D 22n - 23-2n

A:

Q: Use the linearization L(3,-2) (x, y) of f(x, y) = -x²y-xy² near the point (3, -2) to approximate the…

A:

Q: Solve the system of differential equations. [ 3 x' 0 - 4. x1(0) = – 12, x2(0) = – 10 - æ1(t) = %3D…

A:

Q: Between 1 seconds and 9 seconds the ball's average velocity is If necessary, round the answer to two…

A:

Q: 2x (x – 3)² A = 6, B = 2 A = 2, B = 6 A = 2, B = - 6

A: The given integral is 2x/(x-3) 2.