For the following trajectory, find the speed associated with the trajectory and then find the length of the trajectory on the given interval. r(t) = (&e¹ sint, &e¹ cost, -8e¹), for 0≤t≤ In 6 The speed associated with the trajectory is. (Type an exact answer, using radicals as needed.) The length of the trajectory on the given interval is (Type an exact answer, using radicals as needed.) units.

Q: Suppose that a particle moves along a straight line with velocity v(t) = 13 – 4t, where 0 ≤ t ≤ 2.5…

A:

Q: Question 18 ▼ = Starting with an initial population of P(0) = 19, the population of a pride of…

A:

Q: What is the derivative of f(x) = −‡x³ a at the point x = 3? Type an exact answer.

A: f(x)=−43x23 at the point x=3Using the power Ruleddxxn=nxn−1

Q: The time it takes an object to hit the ground, if air resistance is ignored, is a function only of…

A:

Q: Given f(x)dx= 3 and 3 } pixkidk g(x)dx= -1, find 3 158x [5f(x)-2g(x)]dx. ...

A: Integral f(x) is equal to 3 limit from 3 to 12.Integral g(x) is equal to -1 limit from 3 to 12.

Q: Use symmetry and the fundamental theorem of calculus to evaluate the following integrals. Question 8…

A:

Q: 2) Find the first derivative given that f(x)= 5x √2x+3

A: we need to find out the first derivative of the given function."As per the rules, we are supposed to…

Q: lim f(x)=-5, lim g(x)=3, and lim h(x) = 3. Given x→a x→a xa the limit does not exist, explain why.…

A:

Q: The function f(x) = x¹ = 7x³ +9x² +27x - 54 can be factored in the form f(x) = (x-r₁)(x - ₂)². Using…

A: From graph zeros are ● The graph crosses the x-axis at .  with multiplicity 1● The graph passes…

Q: 7) Apply the Mean Value Theorem tof on the indicated interval. Find all values f'(c)=- f(b)-f(a) b-a…

A: (7) Mean Value Theoremf′(c)=f(b)−f(a)b−af(x)=3x−52x+1,2≤x≤4

Q: Question For which value(s) of x does f(x) = 3x - 10 have a tangent line of slope -4? If there is…

A:

Q: Determine whether the series is convergent or divergent. If it is convergent, find its sum 125 b)…

A: The given series

Q: Find a parametric equation for the line through the point (1,3,-3) and perpendicular to the plane 3x…

A:

Q: Complete the table to determine the balance A for P dollars invested at rater for t years,…

A: The objective of the question is to calculate the future value of an investment of $2500 at an…

Q: Question Given the price-demand and price-supply equations below, determine the equilibrium price…

A: The objective of the question is to find the equilibrium price and the producers' surplus using the…

Q: 3. Is there a relation between the domain of a function and its interval of convergence?

A: From the given statement

Q: Find the Taylor polynomial of degree 3, centered at a = 1 for the function f(x) = √x + 5.

A:

Q: A poster has an area of ​​150 square centimeters with margins of 3 cm on the top and bottom and 2 cm…

A:

Q: Suppose the equation 1 40 y = 22 models the height of an arrow where is the horizontal distance in…

A:

Q: (No Technology) Region R is bounded by y=√x, y = 1 and the y-axis. Region S is bounded by y=√√x, x =…

A: We have to use the concept of integration

Q: The graphs of y=-e following. y=esin 4x and y-e are shown. Use them to graph the For one period of y…

A: Draw the graph of the given function

Q: Find af ?х af ду af дz af af 7 Әх ду ах af = = ду af = af дz f(x, y, z) = 3xy + 3xz - 3yz Find their…

A:

Q: Given the following limit g(2+ h) - g(2) lim h→0 h which of the following must be true? Select two…

A:

Q: Find the work done by a force of 18 lbs acting in the direction N35°E (this means start by pointing…

A: The objective of this question is to calculate the work done by a force acting at an angle to the…

Q: A sample of radioactive material with decay constant 0.08 is decaying at a rate R(t) = -2e-0.08t…

A: A sample of radioactive material with a decay constant is decaying at a rate of  grams per year.The…

Q: A person invests 4500 dollars in a bank. The bank pays 5.25% interest compounded monthly. To the…

A:

Q: (0) Σ n=1 (-1)" τα ηλ -(3x - 1)"

A: We are given the series  and we are to find the radius of convergence R and interval of convergence…

Q: The producers' surplus when A units are produced at price B is the area of the shaded region in the…

A: The objective of this question is to calculate the producers' surplus at a given sales level for a…

Q: Which of the following expressions represents the volume of the solid generated when the region…

A: Region is bounded by y=x2−5x+9 and y=4+6x−x2Rotating the region about line y=−5Using the washer…

Q: Compute the curl of the vector field F = -2z7+5yj - 8x k. curl =

A: To find the curl of the vector field .

Q: Hi b and c are incorect

A: From the given table

Q: The temperature of a town t months after January can be estimated by the function…

A: The temperature of a town is defined by .The aim is to find the average temperature from month  to…

Q: Trust Fund A deposit of $15,000 is made in a trust fund that pays 8% interest, compounded…

A: The objective of the question is to find the future value of a deposit made in a trust fund that…

Q: What is the lim f(x) for the following graph? X-3 ㅇㅇ 01 6 3 5 4 3 2 1 0 -1 O-2 -2 리 스 -5 -4 -3 -2 -1…

A: A graph of the function is given.The aim is to find the limit .

Q: Evaluate the spherical coordinate integral 2π π/3 3 S S S 4p² sin dp do de. & 0 seco

A: I=∫02π∫0π/3∫sec⁡ϕ34ρ2sin⁡ϕdρdϕdθUsing the Power Rule∫xndx=xn+1n+1+C

Q: Values of f(x) at selected values of x are shown in the table. x 0.75 0.9 0.99 1.01 1.1 1.25 f(x)…

A: A table of values is given about the function .The aim is to find the limit .

Q: Use integration by substitution to evaluate (In(x)) ² f(m(x 2x -dx

A: I=∫(ln⁡(x))22xdx

Q: Determine the area of the given region under the curve. 1 y X

A:

Q: Suppose the height of this motorbike's jump is given by h = -16t² +32.1t+5.7 where h is the height…

A:

Q: Find the area of the part of the plane with vector equation r(u, v) = (6 + v, u - 5v, 9-4u + v) that…

A:

Q: Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the…

A:

Q: Find the value or values of c that satisfy the equation the following function and interval. f(x) =…

A:

Q: Calculate af ax af Əy af ax af Əy (1, -1) (1, -1) af af af af , and ax' ay' ax (1,-1)" ay (1,-1)…

A:

Q: A calculator is required for the following questions. Questions 12-14 refer to the following…

A: Given that the velocity of a particle moving along a line given by

Q: solution is -3/2

A:

Q: 3 40 32 24 16 8 4 5 Evaluate the definite integral * 3 6 (4x + 10)dx =

A:

Q: 6. Use a triple integral to find the volume of the solid bounded by the parabolic cylinder y = x²…

A:

Q: 2x² + 5x = x + 4y

A: 2x2+5x=x+4y

Q: Determine if the following function has an inverse function. Answer r(x) = (x+4)³ Or has an inverse…

A: We know that, a function y = r(x) has an inverse function if it is one-to-one i.e. if for each…

Q: A particular commodity has a price-supply equation given by p= 368(1.039), where x is the numbers of…

A: