(b) Evaluate the velocity vector and acceleration vector of the object at the given point. %3D %3D 不一4

Q: For the curve given by r(t) = (5 sin(t), –2t, – 5 cos(t)), Find the unit tangent T(t) = (| Find the…

A:

Q: Find the derivatives of the following functions: Inx i) y = sin3x? ii) y = e2*cosx iii) y = 3r+5

A: i)y= sin 3x2y' =ddx sin 3x2y' =cos 3x2  ddx(3x2)y'=cos 3x2 (3)(2x2-1)y'=(6x) cos 3x2

Q: Calculate y" (x) and y" (x). бх — 6 y(x) (Use symbolic notation and fractions where needed.) y"(x) =…

A:

Q: Find V· (F × G), if F(x, y, z) = 8xi+j+8yk and G(x, y, z) = xi+ yj – zk. V · (F × G)

A:

Q: Evaluate the integral / (2x + 6y)dx + (15x – y)dy a C arc y = x² from (0,0) to (1, 1). NOTE: Enter…

A:

Q: Find div F and curl F if F(x, y, z) = 13y*z'i – 11a'2®j – 5xy*k. div F= curl F=

A: We can solve as follows

Q: Point Func tion h(x.y)-7ycos (x-y) Co,Ti/3) Dn(o,1/3) = %3D

A:

Q: f(x, y) = x3 - y³, P(4, 3), v = (i+ j) %3D 2

A:

Q: 1 19 9. -10 -k Consider the matrix it corresponds to an augmented matrixial representation of a…

A: To find for given conditions of alpha and k and the system have how many solutions.

Q: 5 + 5(-5) + 5(-5)' +.. 4 Σ. 4 i= 1 8.

A:

Q: P(x) Let P(x) and Q (x) be polynomials with the degree of Q (x) greater than the degree of P (x) and…

A:

Q: es ring (free) e 365 pursEval 2- -6 -5 -4 -3 -2 -1 Write an equation for the function graphed above.…

A:

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: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 3…

A:

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

A: maxima minima

Q: Find the area bounded by the graphs of 1, y= and X=1 (Ao the right)

A: Find your answer below

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

A: Use geometric series concept

Q: lim 48V x 487Y

A:

Q: Compute each sum below. If applicable, write your answer as a fraction. 4 + ...+ 4(3)- 0 + 4(3) +…

A: Use geometric series sum concept

Q: Consider the matrix -8 A = 13 21 1 4 -2 15, Where a;, represents the entries for A, for i= 1,2,3 and…

A: Given,        -8    0    5 A= 13    21  1         4    -2   15 a ij represents the entries for A,…

Q: 27. | (u + 2)(u - 3) du 2+x 29.

A:

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

A:

Q: Use the first principles delta method to find the derivative of y = x2 – x. %3D

A: Here we have to find the derivative of y by using the first principles delta method.

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: Calculate the (f(g(x)))' and (g(f(x)))' derivatives if f(x) = x8 1 g(x) 5x + 1 (Express numbers in…

A:

Q: 2. Find the area of the parallelogram whose vertices are given by: P: (1,2, –1), P2 = (4, 2, -3), P3…

A:

Q: Find [r(t) u(t)] and [r(t) × u(t)] in two different ways. dt dt r(t) = cos ti + sin tj + tk, u(t) j+…

A:

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

A:

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: H.W (5) Solve the following differential equations of (x'+y')dx+(2xy cos y)dy phee

A:

Q: Find the Laplace Transform of the following functions: a. L(sinxcosxe*} b. L{

A:

Q: 5. Use the Second Fundamental Theorem of Calculus to find F'(x). х 1 F(x) = S* dt.

A:

Q: AX = B is a matrixial representation of a lineal system of equations. Over the augmented matrix (…

A: Here we have to choose the correct option.

Q: Use the Comparison or the Limit Comparison test to show convergence or divergence of each series.

A: Explained below

Q: For each of the following series determine if the series converges or diverges. 00 In(n) Σ n n=2 n3…

A: The given series,1. ∑n=2∞ln(n)n2. ∑n=0∞n3n4+1

Q: Find div F and curl F if F(x, y, z) = 3e*"i – cos yj+ 7sin? z k. %3D div F= curl F=

A:

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

A:

Q: im Y cosx t Zx メナロ0 7x¢ し

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

Q: п! n4 n=1

A: The given series is: ∑n=1∞n!n4 Let, an=n!n4; n≥1

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: Find the volume of the region enclosed by z = 1 – y? and z = y² – 1 for 0 < x < 21. V =

A:

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.

Q: i(x) = 2-0.8(x-43.79)

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

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

A:

Q: Find r'(t) %3D r'(t) = %3D

A: Given;  r(t)=6 sqrt(t)i +t2 sqrt(t)j +ln(t2)k.

Q: im Y cosx tZx 7x¢ with squeze thearem

A:

Q: For each of the following series determine if the series converges or diverges. In(n) Σ n=2

A: Since you have asked multiple questions in a single request we would be answering only the first…

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: Derive the Maclaurin series expansion for f(x) = COS x

A:

Q: dy If y = 3e5 . Find dz

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