Find r'(t), r"(t), r'(t) - r"(t), and r'(t) x r"(t). r(t) = 2t2i – 3tj + t3k (a) r'(t) (b) r"(t) (c) r'(t) r"(t) (d) r'(t) x r"(t) Need Help? Read It

Q: Use the fundamental theorem of calculus to evaluate the following definite integral. | (3x2 + 9) dx…

A: Given query is to find the value of the integral.

Q: Find the derivative of F (x) = S (t3 – t)° dt. O 5( – t)* (3t2 – 1) - O (2 - 2) O 5(x³ – 2)* O 3t2 –…

A:

Q: Find the area of the plane region bounded by y = x°, x = -2 andx= 2:

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

Q: Evaluate the following limit. lim /x + 13 x-6 Select the correct choice below and, if necessary,…

A:

Q: 6. sin x (1 + sin x cos x) dx y csc² ( tan (y²)) dy 7. cos²(y²) sec (11w) tan (11w) V (2 – sec…

A:

Q: 7. Sketch the region of integration, and evaluate the integral. 22л г JI * zdz d0 dr 0 л 0

A:

Q: 7

A: We have to find out

Q: The number N of beavers in a given area after x years can be approximated by the following. N = 5.5…

A: Given  population of beavers in a given area after x area N=5.5×100.23x    ,  0≤x≤10

Q: A population of 200 kangaroo is released into the forest. During the first three years, the…

A: We need to predict population.

Q: csc?y dy is equal to A -у соty — coty dy B) None у сoty — coty dy D у сoty + coty dy

A:

Q: ||r'(t) × r"(t)|| ||r"(t)||* Use the formula k(t) to find k(t). r(t) = 4 cos(7t)i+4 sin(7t)j + 3tk…

A:

Q: Determine whether the improper integral converges and, if so, evaluate it. (Use symbolic notation…

A:

Q: S- dx x?V4-x?

A:

Q: A rectangular tank with a square base, an open top, and a volume of 5324 ft is to be constructed of…

A:

Q: One of the correct steps to evaluate x2Inx dx to yield the correct integral x³Inx A x² dx 3 O ---fa…

A:

Q: ..... .... .............. ............... The values y (in billions of dollars) of U.S. currency in…

A: topic- inequality

Q: The figure to the right shows four regions bounded by the graph of y = x sin x: R1, R2, R3, and R4,…

A: To find the value of the  given integral .

Q: 81 fx, y) dy dx 10 10 O-10 10 1아 1아 -10 10 -10 -10 81 -x F(x, y) dy dx = f(x, y) dx dy

A: we have to change the limit of integration.

Q: At the beginning, an experiment records 1 gram of bacterial culture, and the culture's weight is…

A: we have to find weight at t=10 hr.

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

A:

Q: x++ dx 1.

A:

Q: Use the Integral Test to determine whether the infinite series E is convergent. (Use symbolic…

A: We have to find if the series converges.

Q: If f(2) = 10, f' is continuous, and f'(x) dx = 20, what is the value of f(3)? f(3) =

A:

Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), Y = e' sin(t), z =…

A: Given;  x=etcost, y=etsint, z=11et.

Q: 4- The graph of f is given in the figure to the right. Let A(x) = | f(t) dt and evaluate A(4), A(6),…

A: Integration gives area under curve  area above x axis is positive  area under x axis is negative.

Q: Find the PV of an income stream that pays out continuously at a rate of R(t) = 3000e0.1" dollars per…

A: Given problem:- Find the PV of an income stream that pays out continuously at a rate of R(t) =…

Q: Use the ratio test to determine whether the series is Converyent divorgent or 2" n! (-1)" 5.8.…

A: an=(-1)n 2n n! 5·8·11·.....· (3n+2) When applying ratio test for alternatingseries, the absolute…

Q: A company determines that its demand function is given by p(g) = - 0.8q + 576 and that its cost…

A:

Q: Evaluate the line integral |-ydx + xdy along the curve C : y² = 24x from (24, 24) to (0, 0).

A:

Q: Identify u and dv for finding the integral using integration by parts. Do not integrate. In(5x) dx u…

A:

Q: Write an equation for the level surface of f(x, y, z) = r² + 10y? + 20z2 corresponding to the level…

A:

Q: Given a = 3 units, = 1 unit and the angle between a and b is 30°, determine o) the exact value of (…

A: Solution:

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 10 cos(t)i + 11 sin(t)j +…

A:

Q: Write an equation for the ellipse that has vertices (+7,0) and co-vertices (0, +6). Provide your…

A: Vertices : (7,0) and (-7,0)Co-Vertices: (0,6) and (0,-6)Vertices are of the form : (h±a , k)h+a=7 ,…

Q: y = sec?(x), 0s

A: Here is the solution

Q: a) Find the average acceleration in the first 3 seconds. b) The particle changes direction twice.…

A: Here I am providing my handwritten solution.

Q: - 3 Let f(x) = 8xVæ + x2. f'(x) =

A: Use the derivative for finding the answer.

Q: Consider the following. RX) = x In x², (-1, 0) (a) Find an equation of the tangent line to the graph…

A:

Q: Express the derivative in "subscript" notation. NOTE: Your answer should take the form fo.

A:

Q: Find V · (V × F) if F(x, y, z) = 3 sin xi + 9 cos(5x – 6y)j+ 10zk.

A:

Q: 9+ 5+ g(x) 8 4 7- 6- h(x) 3 5 4 3 1 5 4 5 2 3 x-values 4 2 3 x-values If f(x) = g(x) · h(x), then…

A: Solve the following

Q: A company determines that its demand function is given by p(g) = - 0.4q + 2211 and that its cost…

A: Given

Q: Find for the parametric curve c(t) (t-1 – 5t, 41) at the point t = -2. dx (Use symbolic notation and…

A: Given problem:- Find dy/dt for the parametric curve c(t) = (t-1 - 5t, 4t3) at the point t = −2.

Q: x*dx Using trigonometric substitution , (1+x²) = A) None sec³9d0 B tan20 tan*Ode sec®

A:

Q: So 32 (z + 4)° da = 5120 %3D Select one: O True O False S sin4a da = 4 7/3 7/12 %3D Select one: O…

A:

Q: Given the function f(x) = 2x – 2, evaluate and simplify the expressions below. See special…

A:

Q: - 0.26t ng If C(t) = 53.3t e measures the concentration, in of a drug in a person's systemt hours…

A: Given query is to find the time when concentration will be maximum.

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

A:

Q: Find the standard form of the equation of the ellipse with the given characteristics.

A:

Q: sin' (12x) dx =

A: TO find : ∫sin3(12x)dx=?