blem #3: The inverse Laplace transform f(t) = -¹ {F(s)} of the function e-25(6s - 8) F(s) = S² +49 is of the form g(t) U[h(t)]. (a) Enter the function g(t) into the answer box below. (h) Enter the function h(t) into the answer box below.

Q: Determine the resulting definite integral after making the following substitution: • ¹/3 So 1 4+9x²…

A: I =∫01/314+9x2 dx

Q: Suzanne must choose between two job offers. The first job offers $56,000 for the first year. Each…

A: Given that Suzanne must choose between two job offers. The first job offers $56,000 for the first…

Q: Find the area under the given curve. y = √√x +6; from x=0 to x = 16

A: Consider the curve

Q: Let u = (1, -7). Find the component form and magnitude (length) of the vector 3u. The component form…

A:

Q: K Find the indefinite integral √(-2 -2 sec x tan x +5 sec x +5 sec² x) dx = -2 sec x tan x +5 x) dx.

A:

Q: -2 n=1 (2n+5)(2n+3) a) Find the first four sequence of the partial Sum that is S₁, S₂, S3, and 54 b)…

A:

Q: you have been asked to design a one-liter oil can shaped like a right circular cylinder. what…

A:

Q: 个 Use the definition of the definite integral to evaluate [(x²-2) dx. [(x²-2) dx = (Type an integer…

A:

Q: K Sketch a continuous function f on some interval that has the properties described. The function f…

A:

Q: Let y = g (a) be the solution to the differential equation dy y with the initial condition g (1.5) =…

A: To approximate g( 0) using Euler's method with three steps:1. Determine the step size: Since there…

Q: d) In (x²)dx

A: we need to find out the integration."As per the rules, we are supposed to answer the first question…

Q: Determine the average value of f(x) = sec²x over the interval 0, 0,4 2

A:

Q: Determine the value of x(t) at t = 0 given its Laplace transform. Choose your answers form the…

A:

Q: Evaluate the improper integral O a.-2 O b. 1 042 C 3 X

A:

Q: Graph the following function. Then use geometry (not Riemann sums) to find the area and the net area…

A:

Q: 10) Find the indicated limit 2x x+1 lim( x-x

A: (10) limx→∞(2xx2+1)

Q: Find the exact length of the polar curve described by: r = 10e-0 on the interval 9 2 ㅠ T≤ 0 ≤ 9TT.

A: The arc is any part of the Circu mference of the circle. The length of arc can be found by using the…

Q: Find the domain of the following function. f(x) = log 3 (x-4)

A:

Q: Use the figures to calculate the left and right Riemann sums for f on the given interval and the…

A:

Q: Sex. (x+y)ds where C is the straight-line segment x = 3t, y = (3-3t), z = 0 from C (0,3,0) to…

A:

Q: Question For which value(s) of x does f (x) = 16x³ - 4x² + 6x - 13 have a tangent line of slope 5?…

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: 2η 3. Σ. 1 n=1 nn

A:

Q: A particle starts out from the origin. Its velocity, in miles per hour, after t hours is given by…

A: We have to use the concept of integration

Q: Question Given f (x) below, find f'(x). Do not include "f'(x) =" in your answer. Provide your answer…

A:

Q: Using n=2 equal-width subintervals, approximate the area of the region bounded by the graph of, f(x)…

A: By using left endpoint and using  equal-width subintervals, to approximate the area of the region…

Q: Draw the region whose area is given by the definite integral. (6-2 (6 - 2x)dx

A:

Q: 3. g(x) x² +5

A:

Q: Suppose f(x) = 3x -2. Find f (x+²) 3 (x+2) 3 (Simplify your answer.)

A:

Q: Question The graph of f(x) is shown below. Find the graph of f'(x). VA -6-5-4-3-2-1, 1 2 3 4 5 6 MN

A: A graph of the function  is given.The aim is to sketch the graph of the derivative function .

Q: Evaluate the double integral •x=√4-y L (x + y)dxdy by y=0Jx=1 (a) sketching the region of…

A: We have to evaluate the double integral  Then we have to answer the following...

Q: The quantity demanded x (in units of a hundred) of the Mikado miniature cameras per week is related…

A:

Q: Determine the integral by making the appropriate substitution. 1 2 x In 3x dx ⠀⠀

A:

Q: Using the € - d definition of limit, prove that 2x lim x 2 x + 6 1 NI

A:

Q: Suppose a dog jumps in the air and that its height (in feet) above the ground is given by h 16t² +…

A:

Q: A patient has an illness that typically lasts about 24 hours. The temperature, T, in degrees…

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

A:

Q: ag ²g If g(x, y) = ln[x² + (y + 1)²] show that a2 +² = 0 (except at (0,−1)). ar²

A:

Q: Find the combined area of the two regions bounded by the curves f(x)=e*-1 and g(x)=x²e¹-x² shown in…

A: Region is bounded by the curves f(x)=ex−1 and g(x)=x2e1−x3Solving for inter section…

Q: 2x² + 5x = x + 4y

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

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: JO 1/8 ន √1 16x2 dx

A: By change of variables to evaluate the following definite integrals.

Q: Find the amount of an annuity if $220/month is paid into it for a period of 20 years, earning…

A: Find the amount of an annuity if $ 220 per month is paid into it for a period of 20 years, earning…

Q: √3x + 16-5 x-3 18. lim- x 3

A: we need to find out the limit.

Q: Prove that the equation is an identity. (sin 0 - cos 0)² + 2 cos 0 sin 0 = 1 Working from the…

A:

Q: A particle moves according to the function s(t) = t³ - 3t² - 24t+5. When is the particle slowing…

A:

Q: Sketch the curve with the polar equation r = 2 + 2 cos(0). What is the name for the shape of the…

A: Given that the polar equation

Q: 8. Rewrite CLI x+2 dydadz in the order dzdxdy.

A: We need to change the order of integral.

Q: A student council consists of 15 students. (a) How many ways can a committee of eight be selected…

A: Given that total number of students = 15a) number of ways to select a committee of eight= b) Let A…