Find r(t) u(t). r(t) = (3-7)i + +³1+ j+ 4k u(t) = t²i - 8j + t³k r(t) u(t)= Is the result a vector-valued function? Explain. Yes, the dot product is a vector-valued function. No, the dot product is a scalar-valued function. Need Help? Watch It

Q: Write the first five terms of the arithmetic sequence defined recu = 2.5, a 0+1=3 +0.75 (0 82 N 33…

A:

Q: A first order differential equation involving current i in a series R-L circuit is given by: di/dt…

A: Laplace transform

Q: Find the limit using l'Hospital's rule when appropriate. Find the limit as x approaches 0 of…

A: L'Hospital Rule :-  If a function f(x)=p(x)q(x)  then limx→af(x)=limx→ap(x)q(x) is of the form 00…

Q: Highway engineers design a parabolic curve for an entrance ramp from a straight street to an…

A:

Q: 2x Summarize the pertinent information obtained by applying the graphing strategy and sketch the…

A: Here we have to find the domain of a function.

Q: Consider the function f(x) = 3x³-36x on the interval [-3, 1] Find the absolute extrema for the…

A: We will find the solution

Q: Evaluate the line integral curve C: x = = 4 cost, y (5x + 7y)dx + (3x − 6y)dy along the = 8 sint (0…

A:

Q: Use the definition of the Laplace transform to find L{f(t)}. (Enter your answer in terms of s.) f(t)…

A:

Q: Find the exact value of the trigonometric expression given that sin u = - cos(u + v) Need Help? Read…

A:

Q: On a hot summer afternoon, a city's electricity consumption is -3t² + 12t + 10 units per hour, where…

A:

Q: Σ 500(1.07)" ΕΞΟ

A:

Q: Determine whether f is continuous, piecewise continuous, or neither on the interval 0 ≤ t ≤ 3. 31²,…

A:

Q: Consider making monthly deposits of P = $250 in a savings account at an annual interest rate r =…

A:

Q: Factor the expression and use the fundamental identities to simplify. There is more than one correct…

A:

Q: Find dy/dx: 1 II 22²+(²+1)¹

A: Important Formulae:1)ddx(xn)=n xn-12)ddx(1x)=-1x2

Q: The second derivative has been found and already factored to be f"(x) = (3x) (x + 6). Use interval…

A:

Q: Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the…

A:

Q: Evaluate the integral arc y = x² from (0,0) to (1,1). NOTE: Enter the exact answer. (2x + 18y)dx +…

A: Given integral is ∫C(2x+18y)dx +(3x-y)dy We have to evaluate given integral along a parabolic arc…

Q: Find div F and curl F if F(x, y, z) = 16yªz³i – 17x7zºj − 3xy¹k. div F= curl F=

A:

Q: A thermometer is removed from a room where the temperature is 70° F and is taken outside, where the…

A:

Q: the open interval on which the function is increasing or decreasing. (Enter your answers using…

A: Topic:- function and application of derivatives

Q: A large tank is filled to capacity with 700 gallons of pure water. Brine containing 3 pounds of salt…

A:

Q: Complete the table for each radioactive isotope. See Example 1. (Enter all amounts in grams. Round…

A: Please refer to the image below

Q: Describe the domain of the function f(x, y) = ln(4 x - Y).

A: as per guideline i am answering one question .please give a like !

Q: 8. Show the following limit does not exist: ay +1 lim (au)-(1,-1) 22²-2²

A:

Q: Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the…

A: answer is in next step. please give a like!!

Q: A dead body was found within a closed room of a house where the temperature was a constant 65° F. At…

A: Using Newton's law of cooling: T(t)=Ta+(T0-Ta)e-kt...(1) where Ta= room tempeature=65°F, T0=the…

Q: = 4 sec 0. Find the Cartesian equation for the polar curve r =

A:

Q: 6. A population grows exponentially according to the differential equation P =kP , where P is the…

A:

Q: a) xin x-x Q3. If f(x)=x+2e b) 2 b) 4xln x-4x then find ¹)'(2)= c)-2 b) 2 d) 1

A:

Q: Solve the initial value problem y" + 8y' + 16y = 0, y(-1) = 3, y'(-1) = 6. y(t) = = e -4t -4t + xe X

A:

Q: For the function, do the following. f(x)=√x from a = 2 to b = 5. (a) Approximate the area under the…

A:

Q: (3) Since ● d dx In(x)) (4) Recall the integration formula for n-1 (why?) fr" dx = (5) Find the…

A:

Q: The number N(t) of supermarkets throughout the country that are using a computerized checkout system…

A: Given differential equation:- dNdt=N1-0.0008N , N(0)=1

Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

A: We know that for a position vector  rt = xt, yt, zt, velocity  vt = r't = x't, y't, z't speed  st =…

Q: Determine the interval(s) on which the vector-valued function is continuous. (Enter your answer…

A: Given vector valued function:- rt=13t+1i+1tj Determine the interval(s) on which the given…

Q: lim, 0 6 tan² (5x) 15x²

A:

Q: Laplace Transform. Solve the following differential equation completely. y" + y = 1+ 2t³ et…

A:

Q: B- Find the local extreme points of the function f(x, y) = 4xy - x - y^.

A:

Q: Find the area of the region common to the circles r=-6 sin 9 and r= 3.

A: answer is in next step. please give a like !!

Q: Find div F and curl F if F(x, y, z) = x³i - 7j+yzk. div F= curl F=

A:

Q: Verify the identity. (Simplify at each step.) Let 8 = sin X-2 tan(sin−¹(*²)) = √9+ (x - 2)² X-2 -¹…

A:

Q: 4. Verify that the y defined below satisfies the following boundary value problem. -x Sy" = 8(x -…

A: The Dirac delta function is defined such that ddxHx=δx, where Hx=1x>00x≤0is unit step function.…

Q: A manufacturer can produce 5130 cell phones when a dollars is spent on labor and y dollars is spent…

A: Topic- Implicit differentiation

Q: Use the given conditions to find the values of all six trigonometric functions. (If an answer is…

A:

Q: Find the inverse Laplace transform L¯¹{F(s)} of the given functio 5s² - 10s + 50 s(s² +25) Your…

A:

Q: Obtain the particular solution. 1. 2y dx = 3x dy ; when x = 2 , y = -1 .

A:

Q: 03. a) b) 2 Q4. lim (e* + 2x)² = c)-2 b) 2 c) e³ d) 1 In 3

A: Accoding to given ,only (4) is solved .Given :limx→0ex+2x1x

Q: tan (sin-1)=

A:

Q: Question A particle moves along a line with a velocity v(t) = t2-9, measured in meters per second.…

A: Here, the velocity of the particle is: v(t)=t2-9 Now, v(t)=0⇒t2-9=0⇒t2=9⇒t=-3,3