7) Using the Fourier transform to find the impulse response of the system described by: ý(t) + 2y(t) = x(t) + x(t). Find the output y(t) if x(t)=e-tu(t).

Q: Calculating limits Determine the following limits. 1 1 and lim lim rS-0 2 + e rS* 2 + e

A: a) limr→-∞12+er=limr→-∞1limr→-∞2+er=1limr→-∞2+er                           =limr→-∞2+er-1           ...

Q: State the name of the property. √3(√5 + √3) = √15 + 3

A: 3(5+3)=15+3Distributive propertya(b+c)=a*b+a*c

Q: 3. 2-1 da

A: Use the product rule to determine the derivative for the given expression.ddxx3x2−1=x2−1×ddxx3+x3×dd...

Q: Evaluate the integral.

A: Evaluate the integral.

Q: The graph below is the functicn f(x). Find the values of the limits below. If a limit does not exist...

A: To find the one-sided limit limx→-1-fx, determine the left sided limit value of f(x) as x approaches...

Q: Write the first five terms of the recursively defined sequence                                    a1...

A: Given  a1 = 3, ak+1 = 2(ak − 1)

Q: What is the least common multiple of 2 317 and 243252? a) 2332 b) 2434 c) 2434527 d) 2332527

A: Given: 23347  and  243252

Q: Write the first three terms in the binomial expansion (y3 - 1)20 expressing the result in simplified...

A: The first three terms of the binomial expansion of y3-120 can be written as, y3-120=C020y320+C120y31...

Q: Sky Diving The velocity of a sky diver t seconds after jumping is given by v(t) = 80(1 – e-0). After...

A: v(t)=801-e-0.2t

Q: L'Hôpital's Rule does not help with the following limits. Find them some other way. Vx + 5 2x a. lim...

A:

Q: Determine whether the statement is true or false. If it is false, explain why or give an example tha...

A: we have to determine whether the statement is true or false. If it is false, explain why or give an ...

Q: Find the solution to the following equation 2((xu - u²)cos(x-u)y(u)du = sin x-xcos x

A: Use the fundamental theorem for calculus I to simplify the LHS of the equation. LHS=2∫0xxu−u2cosx−uy...

Q: The polar coordinates of a point are (−2, −2.45). Plot the point and find the corresponding rectangu...

A: r, θ=-2, -2.45 The graph is,

Q: Curvature Find the unit tangent vector T and the curvature k for the following parameterized curve. ...

A: Curvature: r(t)=<cos t2,sin t2> r'(t)=<-2t sin t2, 2t cos t2> Now , |r'(t)|=4t2sin2t2+4t...

Q: Solve, a. A student earns $15 per hour for tutoring and $10 per hour as a teacher’s aide. Let x = th...

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If y...

Q: Calculate the derivative of the following functions

A: Given, y=e2x2x-75 Now by using the product rule, fg'=f'g+g'f Here, f=e2x & g=2x-75⇒ddxe2x2x-75+d...

Q: Use a calculator to solve the equation sin x = 0.7392 correct to four decimal places, on the interva...

A: GivenSinx=0.7392 interval [0,2π)

Q: simplify x² + 7x + 12 x + 5x + 6 31. х? + 3x + 2 х? + 6х + 9 + 2ху + y? 2x* - ху — у? - ху — 2у? 32....

A: NOTE We’ll answer the first question since the exact one wasn’t specified. Please submit a new quest...

Q: Use properties of integrals and the Fundamental Theorem of Calculus to find the integral. You MUST w...

A:

Q: 5) y= 4x + x- 5x Find dx d'y dy 6) y=-2r – 4x* + 2r Find dx |

A:

Q: Give the slope and y-intercept of the line whose equation is given. Then graph the linear function :...

A: Given f(x)=34x-3we have to find the slope and y-intercept of the given line.

Q: 3.6y″ − y′ − y = 0

A: 6y''-y'-y=0 Let, y=erx⇒y'=r·erx⇒y''=r2·erx Therefore given differential equation becomes, ⇒6r2·erx-r...

Q: Estimate the following limit using graphs or tables.

A: Limit:       x→1lim92x-x4-x231-x34  

Q: Use the disk method to find the volume of the solid generated by revolving the given curve about the...

A: The curves given are : y=21+x , x=0 , y=0, x=3 about y-axis. Using disk method , to find the volume ...

Q: solve the given differential equation 5. dy/ dx =( x − (e ^(− x)) /(y + e^ y)

A: Solution:-  The given differential equation is  dydx=(x-e-x)(y+ey)

Q: Let f(x) = 17 – x? The slope of the tangent line to the graph of f(x) at the point ( – 4, 1) is The ...

A:

Q: Classifying Numbers. Choose the first set in the list natural numbers, whole numbers, integers, rati...

A: Whole Numbers - Whole numbers are those that starts from 0.ex = 0, 1, 2, 3, .......................∞...

Q: Factor completely, or state that the polynomial is prime: x3 - 4x

A: x3-4x

Q: Evaluate the limit of the sequence or state that it does not exist. an = ((2n + 2)!)/((2n)! n2)

A: Consider the given nth term of the sequence, an=2n+2!2n! ·n2 Since, 2n+2!=2n+2· 2n+1· 2n! Then, an=2...

Q: Evaluate and simplify the following expression. d rcos(x) dx. ex /t3 +1dt

A: Given expression is ddx∫excosxt3+1dt

Q: Consider the function ƒ and its graph.a. Estimate the zeros of the area function shown , for 0 ≤ x ≤...

A: to find the zeros of the graph we have to see the coordinates at which the graph cuts the x-axis.  h...

Q: Use a calculator to find the value sin π/4 to four decimal places:

A: we have to find the value of sin π4 by using a calculator

Q: Find the indefinite integral. Use a computer algebra system to confirm your result ∫csc4 3x dx

A: ∫ csc43x dx